# Fusing Multiple Images with Enfuse 4.0-753b534c819d

## Enfuse

This manual is for Enfuse (version 4.0-753b534c819d, 4 December 2009), a program to merge different exposures of the same scene to produce an image that looks much like a tonemapped image.

## 1 Overview

Enfuse merges overlapping images using the Mertens-Kautz-Van Reeth exposure fusion algorithm.1 This is a quick way for example to blend differently exposed images into a nice output image, without producing intermediate high-dynamic range (HDR) images that are then tonemapped to a viewable image. This simplified process often works much better than tonemapping algorithms.

Enfuse can also be used to build extended depth-of-field (DOF) images by blending a focus stack.

The idea is that pixels in the input images are weighted according to qualities such as, for example, proper exposure, good local contrast, or high saturation. These weights determine how much a given pixel will contribute to the final image.

A Burt-Adelson multiresolution spline blender2 is used to combine the images according to the weights. The multiresolution blending ensures that transitions between regions where different images contribute are difficult to spot.

Enfuse uses up to four criteria to judge the quality of a pixel, which Table:weighting-criteria briefly describes.

Exposure
The exposure criteria favors pixels with luminance close to the middle of the range. These pixels are considered better exposed than those with high or low luminance levels.
Saturation
The saturation criteria favors highly-saturated pixels. (Note that saturation is only defined for color pixels.)
Local Contrast
The contrast criteria favors pixels inside a high-contrast neighborhood. Enfuse can use standard deviation, Laplacian magnitude, or a blend of both as local contrast measure.
Local Entropy
The entropy criteria prefers pixels inside a high-entropy neighborhood. In addition, Enfuse allows the user to mitigate the problem of noisy images when using entropy weighting by setting a black threshold.

Table 1.1: Enfuse's four weighting criteria.

For the concept of pixel weighting, and details on the different weighting functions, see Weighting Functions.

Adjust how much importance is given to each criterion by setting the weight parameters on the command line. For example, if you set ‘--exposure-weight=1.0’ and ‘--saturation-weight=0.5’, Enfuse will favor well-exposed pixels over highly-saturated pixels when blending the source images. The effect of these parameters on the final result will not always be clear in advance. The quality of the result is subject to your artistic interpretation. Playing with the weights may or may not give a more pleasing result. The authors encourage you to experiment, perhaps using down-sized3 or cropped images for speed.

Enfuse expects but does not require each input image to have an alpha channel. By setting the alpha values of pixels to zero, users can manually remove those pixels from consideration when blending. If an input image lacks an alpha channel, Enfuse will issue a warning and continue assuming all pixels should contribute to the final output. Any alpha value other than zero is interpreted as “this pixel should contribute to the final image”.

Enfuse reads all layers of multi-layer images, like, for example, multi-directory TIFF images4. The input images are processed in the order they appear on the command line. Multi-layer images are processed from the first layer to the last before Enfuse considers the next image on the command line.

Find out more about Enfuse on its SourceForge web page.

## 2 Workflow

Enblend and Enfuse are parts of a chain of tools to assemble images.

• Enblend combines a series of pictures taken at the same location but in different directions.
• Enfuse merges photos of the same subject at the same location and same direction, but taken with varying exposure parameters.

Figure:photographic-workflow shows where Enblend and Enfuse sit in this tool chain.

Figure 2.1: Photographic workflow with Enblend and Enfuse.

Take Images
Take multiple images to form a panorama, an exposure series, a focus stack, etc.
          There is one exception with Enfuse when a single raw image is
converted multiple times to get several – typically differently
“exposed” – images.


Exemplary Benefits

• Many pictures taken from the same vantage point but showing different viewing directions. – Panorama
• Pictures of the same subject exposed with different shutter speeds. – Exposure series
• Images of the same subject focussed at differing distances. – Focus stack

Remaining Problem: The “overlayed” images may not fit together, that is the overlay regions may not match exactly.

Convert Images
Convert the raw data exploiting the full dynamic range of the camera and capitalize on a high-quality conversion.
Align Images
Align the images so as to make them match as well as possible.
          Again there is one exception and this is when images naturally align.
For example, a series of images taken from a rock solid tripod with a
cable release without touching the camera, or images taken with a
shift lens, can align without further user intervention.


This step submits the images to affine transformations. If necessary, it rectifies the lens' distortions (e.g. barrel or pincushion), too. Sometimes even luminance or color differences between pairs of overlaying images are corrected (“photometric alignment”).

Benefit: The overlay areas of images match as closely as possible given the quality if the input images and the lens model used in the transformation.

Remaining Problem: The images may still not align perfectly, for example, because of parallax errors, or blur produced by camera shake.

Combine Images
Enblend and Enfuse combine the aligned images into one.

Benefit: The overlay areas become imperceptible for all but the most mal-aligned images.

Remaining Problem: Enblend and Enfuse write images with an alpha channel. (For more information on alpha channels see Understanding Masks.) Furthermore, the final image rarely is rectangular.

Postprocess
Postprocess the combined image with your favorite tool. Often the user will want to crop the image and simultaneously throw away the alpha channel.

View

Print

Enjoy

## 3 Invocation

enfuse [OPTIONS] [--output=IMAGE] INPUT...

Fuse the sequence of images INPUT... into a single IMAGE.

Input images are either specified literally or via so-called response files (see below). The latter are an alternative to specifying image filenames on the command line.

### 3.1 Response Files

A response file contains names of images or other response filenames. Introduce response file names with an at-character (‘@’).

Enblend and Enfuse process the list INPUT strictly from left to right, expanding response files in depth-first order. (Multi-layer files are processed from first layer to the last.) The following examples only show Enblend, but Enfuse works exactly the same.

Solely image filenames.
Example:
          enblend image-1.tif image-2.tif image-3.tif


The ultimate order in which the images are processed is: image-1.tif, image-2.tif, image-3.tif.

Single response file.
Example:
          enblend @list


where file list contains

          img1.exr
img2.exr
img3.exr
img4.exr


Ultimate order: img1.exr, img2.exr, img3.exr, img4.exr.

Mixed literal names and response files.
Example:
          enblend @master.list image-09.png image-10.png


where file master.list comprises of

          image-01.png
@first.list
image-04.png
@second.list
image-08.png


first.list is

          image-02.png
image-03.png


and second.list contains

          image-05.png
image-06.png
image-07.png


Ultimate order: image-01.png, image-02.png, image-03.png, image-04.png, image-05.png, image-06.png, image-07.png, image-08.png, image-09.png, image-10.png,

#### 3.1.1 Response File Format

Response files contain one filename per line. Blank lines or lines beginning with a sharp sign (‘#’) are ignored; the latter can serve as comments. Filenames that begin with an at-character (‘@’) denote other response files. Table:response-file-format states a formal grammar of response files in EBNF.

 response-file ::= line* line ::= (comment | file-spec) [‘\r’] ‘\n’ comment ::= space* ‘#’ text file-spec ::= space* ‘@’ filename space* space ::= ‘ ’ | ‘\t’

where text is an arbitrary string and filename is any filename.

Table 3.1: EBNF definition of the grammar of response files.

In a response file relative filenames are used relative the response file itself, not relative to the current-working directory of the application.

The above grammar might unpleasantly surprise the user in the some ways.

Whitespace trimmed at both line ends
For convenience, whitespace at the beginning and at the end of each line is ignored. However, this implies that response files cannot represent filenames that start or end with whitespace, as there is no quoting syntax. Filenames with embedded whitespace cause no problems, though.
Comments in response files always occupy a complete line. There are no “line-ending comments”. Thus, in
          # exposure series
img-0.33ev.tif # "middle" EV
img-1.33ev.tif
img+0.67ev.tif


only the first line contains a comment, whereas the second line includes none. Rather, it refers to a file called ‘img-0.33ev.tif # "middle" EV.

An at-sign invariably introduces a response file, even if the filename's extension hints towards an image.

If Enblend or Enfuse do not recognize a response file, they will skip the file and issue a warning. To force a file being recognized as a response file add one of the following syntactic comments to the first line of the file.

     response-file: true
enblend-response-file: true
enfuse-response-file: true


Finally, here is an example of a valid response file.

     # 4\pi panorama!

# These pictures were taken with the panorama head.
@round-shots.list

# Freehand sky shot.
zenith.tif

# "Legs, will you go away?" images.


Comments that follow the format described in Table:response-file-syntactic-comment are treated as instructions how to interpret the rest of the response file. A syntactic comment is effective immediately and its effect persists to the end of the response file, unless another syntactic comment undoes it.

 syntactic-comment ::= space* ‘#’ space* key space* ‘:’ space* value key ::= (‘A’ .. ‘Z’ | ‘a’ .. ‘z’ | ‘-’)+

where value is an arbitrary string.

Table 3.2: EBNF definition of the grammar of syntactic comments in response files.

Unknown syntactic comments are silently ignored.

#### 3.1.3 Globbing Algorithms

The three equivalent syntactic keys

• glob,
• globbing, or
• filename-globbing

control the algorithm that Enblend or Enfuse use to glob filenames in response files.

All versions of Enblend and Enfuse support at least two algorithms: literal, which is the default, and wildcard. See Table:globbing-algorithms for a list of all possible globbing algorithms. To find out about the algorithms in your version of Enblend or Enfuse team up the options --version and --verbose.

literal
Do not glob. Interpret all filenames in response files as literals. This is the default.

Please keep in mind that whitespace at both ends of a line in a response file always gets discarded.

wildcard
Glob using the wildcard characters ‘?’, ‘*’, ‘[’, and ‘]’.

The W*N32 implementation only globs the filename part of a path, whereas all other implementations perform wildcard expansion in all path components. Also see glob(7).

none
Alias for literal.
shell
The shell globbing algorithm works as literal does. In addition, it interprets the wildcard characters ‘{’, ‘}’, and ‘~’. This makes the expansion process behave more like common UN*X shells.
sh
Alias for shell.

Table 3.3: Globbing algorithms for the use in response files

Example:

     # Horizontal panorama
# 15 images

# filename-globbing: wildcard

image_000[0-9].tif
image_001[0-4].tif


### 3.2 Common Options

Common options control some overall features of Enfuse.

--compression=COMPRESSION
Write a compressed output file.

Depending on the output file format, Enfuse accepts different values for COMPRESSION.

JPEG
COMPRESSION is a JPEG quality level ranging from 0–100.
TIFF
COMPRESSION is one of the keywords:
NONE
Do not compress. This is the default.
DEFLATE
Use the Deflate compression scheme also called ZIP-in-TIFF. Deflate is a lossless data compression algorithm that uses a combination of the LZ77 algorithm and Huffman coding.
LZW
Use Lempel-Ziv-Welch (LZW) adaptive compression scheme. LZW compression is lossless.
PACKBITS
Use PackBits compression scheme. PackBits is a particular variant of run-length compression; it is lossless.

Any other format
Other formats do not accept a COMPRESSION setting.

However, VIGRA automatically compresses png-files with the Deflate method.

-h
--help
Print information on the available options then exit.
-l LEVELS
--levels=LEVELS
Use at most this many LEVELS for pyramid 5 blending if LEVELS is positive, or reduce the maximum number of levels used by −LEVELS if LEVELS is negative.

The number of levels used in a pyramid controls the balance between local and global image features (contrast, saturation, ...) in the blended region. Fewer levels emphasize local features and suppress global ones. The more levels a pyramid has, the more global features will be taken into account.

As a guideline, remember that each new level works on a linear scale twice as large as the previous one. So, the zeroth layer, the original image, obviously defines the image at single-pixel scale, the first level works at two-pixel scale, and generally, the n-th level contains image data at 2^n-pixel scale. This is the reason why an image of width×height pixels cannot be deconstructed into a pyramid of more than $⌊{log}_{2}\left(min\left(\mathit{width},\mathit{height}\right)\right)⌋$

levels.

If too few levels are used, “halos” around regions of strong local feature variation can show up. On the other hand, if too many levels are used, the image might contain too much global features. Usually, the latter is not a problem, but is highly desired. This is the reason, why the default is to use as many levels as is possible given the size of the overlap regions. Enfuse may still use a smaller number of levels if the geometry of the overlap region demands.

Positive values of LEVELS limit the maximum number of pyramid levels. Depending on the size and geometry of the overlap regions this may or may not influence any pyramid. Negative values of LEVELS reduce the number of pyramid levels below the maximum no matter what the actual maximum is and thus always influence all pyramids.

The valid range of the absolute value of LEVELS is 1 to 29.

-o
--output=FILE
Place output in FILE.

If --output is not specified, the default is to put the resulting image in a.tif.

-v
--verbose[=LEVEL]
Without an argument, increase the verbosity of progress reporting. Giving more --verbose options will make Enfuse more verbose. Directly set a verbosity level with a non-negative integral LEVEL.

Each level includes all messages of the lower levels.

Level
Messages
0
only warnings and errors
1
2
3
reading of response files, color conversions
4
image sizes, bounding boxes and intersection sizes
5
detailed information on the optimizer runs (Enblend only)
6
estimations of required memory in selected processing steps

The default verbosity level of Enfuse is 1.

-V
--version
Output information on the Enfuse version.

Team this option with --verbose to show configuration details, like the extra features that have been compiled in.

-w
--wrap=MODE
Blend around the boundaries of the panorama.

With this option, Enfuse treats the panorama of width w and height h as an infinite data structure, where each pixel P(x, y) of the input images represents the set of pixels S_P(x, y)6.

MODE takes the following values:

none
open
This is a “no-op”; it has the same effect as not giving --wrap at all. The set of input images is considered open at its boundaries.
horizontal
Wrap around horizontally: ${S}_{P}\left(x,y\right)=\left\{P\left(x+mw,y\right):m\text{ in }Z\right\}\text{.}$

This is useful for 360° horizontal panoramas as it eliminates the left and right borders.

vertical
Wrap around vertically: ${S}_{P}\left(x,y\right)=\left\{P\left(x,y+nh\right):n\text{ in }Z\right\}\text{.}$

This is useful for 360° vertical panoramas, as it eliminates the top and bottom borders.

both
horizontal+vertical
vertical+horizontal
Wrap around both horizontally and vertically: ${S}_{P}\left(x,y\right)=\left\{P\left(x+mw,y+nh\right):m,n\text{ in }Z\right\}\text{.}$

In this mode, both left and right borders, as well as top and bottom borders, are eliminated.

Specifying --wrap without MODE selects horizontal wrapping.

### 3.3 Extended Options

Extended options control the image cache, the color model, and the cropping of the output image.

-b BLOCKSIZE
Set the BLOCKSIZE in kilobytes (KB) of Enfuse's image cache.

This is the amount of data that Enfuse will move to and from the disk at one time. The default is 2048KB, which should be ok for most systems. See Tuning Memory Usage for details.

Note that Enfuse must have been compiled with the image-cache feature for this option to be effective. Find out about extra features with enfuse --version --verbose.

-c
Use the CIECAM02 color appearance model for blending colors.

The input files should have embedded ICC profiles when this option is specified. If no ICC profile is present, Enfuse will assume that the image uses the sRGB color space. The difference between this option and Enfuse's default color blending algorithm is slight, and will only be noticeable when areas of different primary colors are blended together.

-d
--depth=DEPTH
Force the number of bits per channel and the numeric format of the output image.

Enfuse always uses a smart way to change the channel depth, to assure highest image quality (at the expense of memory), whether requantization is implicit because of the output format or explicit with option --depth.

• If the output-channel width is larger than the input-channel width of the input images, the input images' channels are widened to the output channel width immediately after loading, that is, as soon as possible. Enfuse then performs all blending operations at the output-channel width, thereby preserving minute color details which can appear in the blending areas.
• If the output-channel width is smaller than the input-channel width of the input images, the output image's channels are narrowed only right before it is written to disk, that is, as late as possible. Thus the data benefits from the wider input channels for the longest time.

All DEPTH specifications are valid in lowercase as well as uppercase letters. For integer format use

8, uint8
Unsigned 8bit; range: 0..255
int16
Signed 16bit; range: −32768..32767
16, uint16
Unsigned 16bit; range: 0..65535
int32
Signed 32bit; range: −2147483648..2147483647
32, uint32
Unsigned 32bit; range: 0..4294967295

For floating-point format use

r32, real32, float
IEEE754 single precision floating-point, 32bit wide, 24bit significant
• Minimal normalized value: $1.2×{10}^{-38}$
• Epsilon: $1.2×{10}^{-7}$
• Maximal finite value: $3.4×{10}^{38}$

r64, real64, double
IEEE754 double precision floating-point, 64bit wide, 53bit significant
• Minimal normalized value: $2.2×{10}^{-308}$
• Epsilon: $2.2×{10}^{-16}$
• Maximal finite value: $1.8×{10}^{308}$

If the requested DEPTH is not supported by the output file format, Enfuse warns and chooses the DEPTH that matches best.

The OpenEXR data format is treated as IEEE754 float internally. Externally, on disk, OpenEXR data is represented by “half” precision floating-point numbers.

OpenEXR half precision floating-point, 16bit wide, 10bit significant

• Minimum normalized value: $9.3×{10}^{-10}$
• Epsilon: $2.0×{10}^{-3}$
• Maximum finite value: $4.3×{10}^{9}$

-f WIDTHxHEIGHT
-f WIDTHxHEIGHT+xX-OFFSET+yY-OFFSET
Set the size of the output image manually to WIDTH×HEIGHT. Optionally specify the X-OFFSET and Y-OFFSET, too.

This option is useful when the input images are cropped TIFF files, such as those produced by nona. The stitcher nona is part of Hugin. See Helpful Programs.

-g
Save alpha channel as “associated”. See the TIFF documentation for an explanation.

Gimp (before version 2.0) and CinePaint (see Helpful Programs) exhibit unusual behavior when loading images with unassociated alpha channels. Use option -g to work around this problem. With this flag Enfuse will create the output image with the associated alpha tag set, even though the image is really unassociated alpha.

-m CACHESIZE
Set the CACHESIZE in megabytes (MB) of Enfuse's image cache.

This is the amount of memory Enfuse will use for storing image data before swapping to disk. The default is 1024MB, which is good for systems with 3–4gigabytes (GB) of RAM. See Tuning Memory Usage for details.

Note that Enfuse must have been compiled with the image-cache feature for this option to be effective. Find out about extra features with enfuse --version --verbose.

### 3.4 Fusion Options

Fusion options define the proportion to which each input image's pixel contributes to the output image.

--contrast-weight=WEIGHT
(This option supersedes the deprecated option --wContrast.)

Sets the relative WEIGHT of high local-contrast pixels. Default: 0.0. Valid range: $0\le \mathit{WEIGHT}\le 1\text{.}$

--entropy-weight=WEIGHT
(This option supersedes the deprecated option --wEntropy.)

Sets the relative WEIGHT of high local entropy pixels. Default: 0.0. Valid range: $0\le \mathit{WEIGHT}\le 1\text{.}$

--exposure-weight=WEIGHT
(This option supersedes the deprecated option --wExposureMu.)

Sets the relative WEIGHT of the well-exposedness criterion. Increasing this weight relative to the others will make well-exposed pixels contribute more to the final output. Default: 1.0. Valid range: $0\le \mathit{WEIGHT}\le 1\text{.}$

--exposure-mu=MEAN
(This option supersedes the deprecated option --wExposureMu.)

Set the MEAN (this is, the center) of the Gaussian exposure weight curve. Default: 0.5. Valid range: $0\le \mathit{MEAN}\le 1\text{.}$

Use this option to fine-tune exposure weighting (see Exposure Weighting).

--exposure-sigma=STD-DEV
(This option supersedes the deprecated option --wExposureSigma.)

Standard deviation STD-DEV of the Gaussian exposure weight curve. Default: 0.2. Low numbers give less weight to pixels that are far from --wMu and vice versa. Valid range: $0\le \mathit{STD-DEV}\text{.}$

Use this option to fine-tune exposure weighting (see Exposure Weighting).

--saturation-weight=WEIGHT
(This option supersedes the deprecated option --wSaturation.)

Sets the relative WEIGHT of high-saturation pixels. Increasing this weight makes pixels with high saturation contribute more to the final output. Default: 0.2. Valid range: $0\le \mathit{WEIGHT}\le 1\text{.}$

Saturation weighting is only defined for color images. See Saturation Weighting.

### 3.5 Expert Options

Expert options influence the workings of Enfuse that require the user to read the manual before applying them successfully.

--contrast-window-size=SIZE
(This option supersedes the deprecated option --ContrastWindowSize.)

Set the window SIZE for local contrast analysis. The window will be a square of SIZE×SIZE pixels.

For contrast analysis SIZE values larger than 5 might result in a blurry composite image. Values of 3 and 5 have given good results on focus stacks.

Valid range: $\mathit{SIZE}\ge 3\text{.}$

If given an even SIZE, Enfuse will automatically use the next odd number.

--contrast-edge-scale=EDGE-SCALE
--contrast-edge-scale=EDGE-SCALE:LCE-SCALE:LCE-FACTOR
(This option supersedes the deprecated option --EdgeScale.)

A non-zero value for EDGE-SCALE switches on the Laplacian-of-Gaussian (LoG) edge detection algorithm. EDGE-SCALE is the radius of the Gaussian used in the search for edges. Default: 0.0pixels.

A positive LCE-SCALE turns on local contrast enhancement (LCE) before the LoG edge detection. LCE-SCALE is the radius of the Gaussian used in the enhancement step, LCE-FACTOR is the weight factor (“strength”). $\begin{array}{ccc}\mathit{enhanced}& =& \left(1+\mathit{LCE-FACTOR}\right)×\mathit{original}\\ & & -\mathit{LCE-FACTOR}×GaussianSmooth\left(\mathit{original},\mathit{LCE-SCALE}\right)\end{array}$

LCE-SCALE defaults to 0.0 pixels and LCE-FACTOR defaults to 0.0. Append ‘%’ to LCE-SCALE to specify the radius as a percentage of EDGE-SCALE. Append ‘%’ to LCE-FACTOR to specify the weight as a percentage.

--entropy-cutoff=LOWER-CUTOFF
--entropy-cutoff=LOWER-CUTOFF:UPPER-CUTOFF
(This option supersedes the deprecated option --EntropyCutoff.)

The first form defines the lower cutoff value below which pixels are treated as pure black when calculating the local entropy. The second form also defines the upper cutoff value above which pixels are treated as pure white.

For color images LOWER-CUTOFF and UPPER-CUTOFF are applied separately and independently to each channel.

Defaults: 0% for LOWER-CUTOFF and 100% for UPPER-CUTOFF, that is, all pixels' values are taken into account. Append a ‘%’ to specify the cutoff relative to maximum pixel value in the source image (for example 255 or 65535). Figure:entropy-cutoff shows an example.

Figure 3.1: Linear lightness Y in comparison with an entropy-cutoff function for LOWER-CUTOFF = 5% and UPPER-CUTOFF = 90% which are rather extreme values.

Note that a high LOWER-CUTOFF value lightens the resulting image, as dark (and presumably noisy) pixels are averaged with equal weights. With ‘--entropy-cutoff=0’, the default, on the other hand, “noise” might be interpreted as high entropy and the noisy pixels get a high weight, which in turn renders the resulting image darker. Analogously, a low UPPER-CUTOFF darkens the output image.

--entropy-window-size=SIZE
(This option supersedes the deprecated option --EntropyWindowSize.)

Window SIZE for local entropy analysis. The window will be a square of SIZE×SIZE pixels.

In the entropy calculation SIZE values of 3 to 7 yield an acceptable compromise of the locality of the information and the significance of the local entropy value itself.

Valid range: $\mathit{SIZE}\ge 3\text{.}$

If given an even SIZE Enfuse will automatically use the next odd number.

--gray-projector=PROJECTOR
(This option supersedes the deprecated option --GrayProjector.)

Use gray projector PROJECTOR for conversion of RGB images to grayscale masks: $\left(R,G,B\right)\to Y\text{.}$

In version 4.0-753b534c819d of Enfuse, the option is effective for exposure weighting and local contrast weighting. Default: ‘average’.

Valid values for PROJECTOR are:

average
Average red, green, and blue channel with equal weights. This is the default, and it often is a good projector for gamma = 1 data. $Y=\frac{R+G+B}{3}$
channel-mixer:RED-WEIGHT:GREEN-WEIGHT:BLUE-WEIGHT
Weight the channels as given. $Y=\mathit{RED-WEIGHT}×R+\mathit{GREEN-WEIGHT}×G+\mathit{BLUE-WEIGHT}×B$

The weights are automatically normalized to one, so

                   --gray-projector=channel-mixer:0.25:0.5:0.25
--gray-projector=channel-mixer:1:2:1
--gray-projector=channel-mixer:25:50:25


all define the same mixer configuration.

The three weights RED-WEIGHT, GREEN-WEIGHT, and BLUE-WEIGHT define the relative weight of the respective color channel. The sum of all weights is normalized to one.

l-star
Use the L-channel of the L*a*b*-conversion of the image as its grayscale representation. This is a useful projector for gamma = 1 data. It reveals minute contrast variations even in the shadows and the highlights. This projector is computationally expensive.

See Wikipedia for a detailed description of the Lab color space.

lightness
Compute the lightness of each RGB pixel as in an Hue-Saturation-Lightness (HSL) conversion of the image. $Y=\frac{max\left(R,G,B\right)+min\left(R,G,B\right)}{2}$
luminance
Use the weighted average of the RGB pixel's channels as defined by CIE (“Commission Internationale de l'Éclairage”) and the JPEG standard. $Y=0.30R+0.59G+0.11B$
value
Take the Value-channel of the Hue-Saturation-Value (HSV) conversion of the image. $Y=max\left(R,G,B\right)$

--hard-mask
(This option supersedes the deprecated option --HardMask.)

Force hard blend masks on the finest scale. This is the opposite flag of --soft-mask.

This blending mode avoids averaging of fine details (only) at the expense of increasing the noise. However it considerably improves the sharpness of focus stacks. Blending with hard masks has only proven useful with focus stacks.

--contrast-min-curvature=CURVATURE
(This option supersedes the deprecated option --MinCurvature.)

Define the minimum CURVATURE for the LoG edge detection. Default: 0. Append a ‘%’ to specify the minimum curvature relative to maximum pixel value in the source image (for example 255 or 65535).

A positive value makes Enfuse use the local contrast data (controlled with --contrast-window-size) for curvatures less than CURVATURE and LoG data for values above it.

A negative value truncates all curvatures less than −CURVATURE to zero. Values above CURVATURE are left unchanged. This effectively suppresses weak edges.

--save-masks
--save-masks=SOFT-MASK-TEMPLATE
--save-masks=SOFT-MASK-TEMPLATE:HARD-MASK-TEMPLATE
(This option supersedes the deprecated option --SaveMasks.)

Save all weight files as TIFF images. First form: Save all soft weight masks in files. If option --hard-mask is effective also save the hard masks. The defaults are softmask-%n.tif and hardmask-%n.tif. In the second form, SOFT-MASK-TEMPLATE defines the names of the soft-mask files. In the third form, HARD-MASK-TEMPLATE additionally defines the names of the hard-mask files.

Both SOFT-MASK-TEMPLATE and HARD-MASK-TEMPLATE define templates that are expanded for each mask file. In a template a percent sign (‘%’) introduces a variable part. All other characters are copied literally. Lowercase letters refer to the name of the respective input file, whereas uppercase ones refer to the name of the output file (see Common Options). Table:mask-template-characters lists all variables.

A fancy mask filename template could look like this:

          %D/soft-mask-%02n-%f.viff


It puts the mask files into the same directory as the output file (‘%D’), generates a two-digit index (‘%02n’) to keep the mask files nicely sorted, and decorates the mask filename with the name of the associated input file (‘%f’) for easy recognition.

--soft-mask
(This option supersedes the deprecated option --SoftMask.)

Consider all masks when fusing. This is the default.

%%
Produces a literal ‘%’-sign.
%i
Expands to the index of the mask file starting at zero.

%i’ supports setting a pad character or a width specification:

          % PAD WIDTH i


PAD is either ‘0’ or any punctuation character; the default pad character is ‘0’. WIDTH is an integer specifying the minimum width of the number. The default is the smallest width given the number of input images, this is 1 for 2–9 images, 2 for 10–99 images, 3 for 100–999 images, and so on.

Examples: ‘%i’, ‘%02i’, or ‘%_4i’.

%n
Expands to the number of the mask file starting at one. Otherwise it behaves identically to ‘%i’, including pad character and width specification.
%p
This is the full name (path, filename, and extension) of the input file associated with the mask.

Example: If the input file is called /home/luser/snap/img.jpg, ‘%p’ expands to /home/luser/snap/img.jpg, or shorter: ‘%p’ ⇒ /home/luser/snap/img.jpg.

%P
This is the full name of the output file.
%d
Is replaced with the directory part of the associated input file. see dirname.

Example (cont.): ‘%d’ ⇒ /home/luser/snap.

%D
Is replaced with the directory part of the output file.
%b
Is replaced with the non-directory part (often called “basename”) of the associated input file. see basename.

Example (cont.): ‘%b’ ⇒ img.jpg.

%B
Is replaced with the non-directory part of the output file.
%f
Is replaced with the filename without path and extension of the associated input file.

Example (cont.): ‘%f’ ⇒ img.

%F
Is replaced with the filename without path and extension of the output file.
%e
Is replaced with the extension (including the leading dot) of the associated input file.

Example (cont.): ‘%e’ ⇒ .jpg.

%E
Is replaced with the extension of the output file.

Table 3.4: Special characters to control the generation of mask filenames.

### 3.6 Option Delimiters

Enfuse allows the arguments supplied to the program's options to be separated by different separators. The online documentation and this manual, however, exclusively use the colon ‘:’ in every syntax definition and in all examples.

Numeric Arguments

Valid delimiters are the the semicolon ‘;’, the colon ‘:’, and the slash ‘/’. All delimiters may be mixed within any option that takes numeric arguments.

Examples:

--contrast-edge-scale=0.667:6.67:3.5
Separate all arguments with colons.
--contrast-edge-scale=0.667;6.67;3.5
Use semi-colons.
--contrast-edge-scale=0.667;6.67/3.5
Mix semicolon and slash in weird ways.
--entropy-cutoff=3%/99%
All delimiters also work in conjunction with percentages.
--gray-projector=channel-mixer:3/6/1
Separate arguments with a colon and two slashes.
--gray-projector=channel-mixer/30;60:10
Go wild and Enfuse will understand.

Filename Arguments

Here, the accepted delimiters are ‘,’, ‘;’, and ‘:’. Again, all delimiters may be mixed within any option that has filename arguments.

Examples:

Separate all arguments with colons.
Use a comma.

## 4 Weighting Functions

As has been noted in the Overview (see Overview), Enfuse supports four different types of weighting. The following subsections describe the concept of weighting and all weighting functions in detail.

### 4.1 Weighting Pixels

Image fusion maps each pixel P(i, x, y) of every input image i to a single pixel Q(x, y) in the output image: $P\left(i,x,y\right)\to Q\left(x,y\right)\text{,}$

where x runs from 1 to the common width of the images, y from 1 to the common height, and i from 1 to the number of input images n.

Enfuse allows for weighting the contribution of each P(i, x, y) to the final Q(x, y): $w\left(P\left(1,x,y\right)\right)×P\left(1,x,y\right)+...+w\left(P\left(n,x,y\right)\right)×P\left(n,x,y\right)\to Q\left(i,x,y\right)\text{,}\phantom{\rule{4em}{0ex}}\text{(W)}$

where

• each w is non-negative to yield a physical intensity and
• the sum of all w is one to leave the total intensity unchanged.

The pixel weights w themselves are weighted sums with the same constraints

$\begin{array}{ccc}w\left(P\right)& =& {w}_{\text{exp}}×{f}_{\text{exp}}\left(P\right)+\\ & & {w}_{\text{sat}}×{f}_{\text{sat}}\left(P\right)+\\ & & {w}_{\text{cont}}×{f}_{\text{cont}}\left(P,{r}_{\text{cont}}\right)+\\ & & {w}_{\text{ent}}×{f}_{\text{ent}}\left(P,{r}_{\text{ent}}\right)\end{array}$

where we have abbreviated P ( i , x , y ) to P for simplicity. The user defines the constants  w exp , w sat , w cont , and w ent with the options --exposure-weight', --saturation-weight', --contrast-weight', and --entropy-weight' respectively. The functions  f exp , f sat , f cont , and f ent along with the window sizes  r cont and r ent are explained in the next sections.

#### 4.1.1 Weighted Average

By default, Enfuse uses a weighted average, where each pixel contributes as much as its weight demands. Of course the weights can be extreme, favoring only a few pixels or even only one pixel in the input stack. Extremes are not typical, however.

Equal weights are another extreme that turns (W) into an arithmetic average. This is why we sometimes speak of the “averaging property” of this weighting algorithm, like smoothing out noise.

#### 4.1.2 Disabling Averaging: Option --hard-mask

The weighted average computation as described above has proven to be widely successful with the exception of one special case: focus stacking (see Focus Stacks), where the averaging noticeably softens the final image.

Use --hard-mask to switch Enfuse into a different (“Super Trouper”) weighting mode, where the pixel with the highest weight wins, this is, gets weight one, and all other pixels get the weight of zero (“The Winner Takes It All.”). With --hard-mask Equation (W) becomes $P\left(i,x,y\right)\to Q\left(x,y\right)\text{,}\text{ where }w\left(P\left(i,x,y\right)\right)\ge w\left(P\left(j,x,y\right)\right)\text{ for all }1\le j\le n\text{.}$

Note that this “averaging” scheme lacks the nice noise-reduction property of the weighted average (W), because only a single input pixel contributes to the output.

### 4.2 Exposure Weighting

Exposure weighting prefers pixels with a luminance Y close to the center of the normalized, real-valued luminance interval [0, 1].

RGB-pixels get converted to luminance using the grayscale projector given by --gray-projector, which defaults to average. Grayscale pixels are identified with luminance.

In the normalized luminance interval 0.0 represents pure black and 1.0 represents pure white independently of the data type of the input image. This is, for a JPEG image the luminance 255 maps to 1.0 in the normalized interval and for a 32bit TIFF picture the highest luminance value 4294967295 also maps to 1.0. The middle of the luminance interval, 0.5, is where a neutral gray tone ends up with every camera that had no exposure correction dialed in, for example the image of a gray- or white-card.

The exposure weighting algorithm only looks at a single pixel at a time; the pixel's neighborhood is not taken into account.

The weighting function is the Gaussian ${w}_{\text{exp}}\left(Y\right)=\text{exp}\left(-\frac{1}{2}{\left(\frac{Y-\mathit{Mu}}{\mathit{Sigma}}\right)}^{2}\right)$

whose center Mu and width Sigma are controlled by the command line options --exposure-mu and --exposure-sigma respectively. Mu defaults to 0.5 and Sigma defaults to 0.2. Figure:gaussian shows a Gaussian.

Figure 4.1: Gaussian function with the parameters Mu = 0.5 and Sigma = 0.2.

The options --exposure-mu and --exposure-sigma are for fine-tuning the final result without changing the set of input images. Option --exposure-mu sets the point Mu of optimum exposure. Increasing Mu makes Enfuse prefer lighter pixels, rendering the final image lighter, and vice versa. Option --exposure-sigma defines the range Sigma of acceptable exposures. Small values of Sigma penalize exposures that deviate from Mu more, and vice versa.

Summary of influential options

--exposure-weight
Fusion Options
--exposure-mu
Fusion Options
--exposure-sigma
Fusion Options
--gray-projector
Expert Options

### 4.3 Saturation Weighting

Saturation weighting prefers pixels with a high saturation.

Enfuse computes the saturation of a pixel according to the following algorithm.

     max := maximum(R, G, B)
min := minimum(R, G, B)
if max = min then
saturation := 0
else
sum := max + min
difference := max - min
if sum ≤
1 then
saturation := difference / sum
else
saturation := difference / (2 - sum)
end if
end if


Obviously, saturation weighting can only be defined for RGB images, not for grayscale ones! If you need something similar, check out Local Entropy Weighting; entropy weighting works for both RGB and grayscale pictures.

The saturation weighting algorithm only looks at a single pixel at a time; the pixel's neighborhood is not taken into account.

Summary of influential options

--saturation-weight
Fusion Options

### 4.4 Local Contrast Weighting

Local contrast weighting favors pixels inside a high contrast neighborhood. The notion of “high contrast” is defined either by two different criteria or by a blend of both:

• The standard deviation (SDev) of all the pixels in the local analysis window is large. See Standard Deviation.
• The Laplacian-of-Gaussian (LoG) has a large magnitude. See Laplacian of Gaussian.
• If the LoG magnitude is below a given threshold, use SDev data, otherwise stick with LoG. See Blend SDev and LoG.

Enfuse converts every RGB image to grayscale before it determines its contrast. Option --gray-projector (see Expert Options) controls the projector function. Depending on the subject, one of several grayscale projectors may yield the best black-and-white contrast for image fusion.

In the following sections we describe each algorithm in detail.

#### 4.4.1 Standard Deviation

The pixel under consideration C sits exactly in the center of a square, the so-called local analysis window. It always has an uneven edge length. The user sets the size with option --contrast-window-size. Figure:local-analysis-window shows two windows with different sizes.

Figure 4.2: Examples of local analysis windows for the sizes 3 and 5. “C” marks the center where the pixel gets the weight. “N” are neighboring pixels, which all contribute equally to the weight.

During the analysis, Enfuse scans the local analysis window across all rows and all columns7 of each of the input images to compute the contrast weight of every pixel.

Summary of influential options

--contrast-weight
Fusion Options
Fusion Options
--contrast-window-size
Expert Options
--gray-projector
Expert Options
##### 4.4.1.1 Statistical Moments

We start with the probability function w of the random variable X: $w:x\to p\left(\left\{\omega :X\left(\omega \right)=x\right\}\right)\text{.}$

It associates a probability p with each of the n different possible outcomes  ω of the random variable X. Based on w, we define the expectation value or “First Moment” of the random variable X: $\mathsf{Ex}X:=\sum _{i=1}^{n}{x}_{i}×w\left({x}_{i}\right)\text{.}$

Using the definition of the expectation value, we define the variance, or “Second Moment” as $\mathsf{Var}X:=\mathsf{Ex}\left({\left(X-\mathsf{Ex}X\right)}^{2}\right)$

and the standard deviation as $\sigma X:=\sqrt{\mathsf{Var}X}\text{.}$

Obviously, the variance of X is the expectation value of the squared deviation from the expectation value of X itself. Note that the variance's dimension is X's dimension squared; the standard deviation rectifies the dimension to make it comparable with X itself again.

##### 4.4.1.2 Estimators

In Enfuse, we assume that X follows a uniform probability function w(x) = const. That is, all pixel values in the local analysis window are considered to be equally probable. Thus, the expectation value and the variance can be estimated from the pixel values like this $\mathsf{Ex}X:=\frac{1}{n}\sum _{i=1}^{n}{x}_{i}\text{.}$

In other words: the expectation value is the arithmetic mean of the lightness of all pixels in the local analysis window. Analogously, the variance becomes $\mathsf{Var}X:=\frac{1}{n-1}\mathsf{Ex}\left({\left(X-\mathsf{Ex}X\right)}^{2}\right)\text{.}$

#### 4.4.2 Laplacian of Gaussian

The Laplacian of Gaussian (LoG) is an operator to detect edges in an image. Sometimes the LoG-operator is also called Marr-Hildreth operator. A Laplacian-of-Gaussian operator, vigra::laplacianOfGaussian is part of the package VIGRA that Enfuse is built upon and is used for edge detection if option --contrast-edge-scale is non-zero and --contrast-min-curvature equal to or less than zero.

Let the Gaussian function be $g\left(x,y\right)=\frac{1}{2\pi {\sigma }^{2}}\text{exp}\left(-\frac{{x}^{2}+{y}^{2}}{2{\sigma }^{2}}\right)$

The parameter  σ , the argument of option --contrast-edge-scale, is the length scale on which edges are detected by g(x, y). We apply the Laplacian operator in Cartesian coordinates $\Delta \equiv \nabla ·\nabla =\frac{{\partial }^{2}}{\partial {x}^{2}}+\frac{{\partial }^{2}}{\partial {y}^{2}}$

to g(x, y), to arrive at a continuous representation of the two-dimensional filter kernel $k\left(x,y\right)=\frac{{\xi }^{2}-1}{\pi {\sigma }^{4}}exp\left(-{\xi }^{2}\right)\text{,}$

where we have used the dimensionless distance  ξ from the origin ${\xi }^{2}=\frac{{x}^{2}+{y}^{2}}{2{\sigma }^{2}}\text{.}$

Enfuse uses a discrete approximation of k in the convolution with the image. The operator is radially symmetric with respect to the origin, which is why we can easily plot it in Figure:laplacian-of-gaussian, setting $R=\sqrt{{x}^{2}+{y}^{2}}\text{.}$

Figure 4.3: Laplacian-of-Gaussian function for σ = 0.5.

Sometimes the LoG is plagued by noise in the input images. After all, it is a numerical approximation of the second derivative and deriving always “roughens” a function. The (normalized) mask files relentlessly disclose such problems. Use option --contrast-min-curvature with a negative argument CURVATURE to suppress all edges with a curvature below −CURVATURE (which is a positive value). Check the effects with the mask files and particularly the hard-mask files (hardmask-%n.tif) if using option --hard-mask.

To indicate the CURVATURE in relative terms, which is particularly comprehensible for humans, append a percent sign (‘%’). Try minimum curvatures starting from −0.5% to −3%.

Summary of influential options

--contrast-weight
Fusion Options
Fusion Options
--contrast-edge-scale
Expert Options
--contrast-min-curvature
Expert Options

#### 4.4.3 Blend Standard Deviation and Laplacian of Gaussian

Enfuse can team the standard deviation computation and Laplacian of Gaussian to deliver the best of both methods. Use a positive argument CURVATURE with option --contrast-min-curvature to combine both algorithms. In this mode of operation Enfuse computes the SDev-weight and the LoG-weight, then uses the LoG to decide whether to go with that value or prefer the SDev data. If the LoG is greater than CURVATURE Enfuse uses the weight delivered by the LoG, otherwise the SDev-weight is rescaled such that its maximum is equal to CURVATURE, and the scaled SDev is used as weight.

This technique merges the two edge detection methods where they are best. The LoG excels with clear edges and cannot be fooled by strong but smooth gradients. However, it is bad at detecting faint edges and it is susceptible to noise. The SDev on the other hand shines with even the most marginal edges, and resists noise quite well. Its weakness is that is is easily deceived by strong and smooth gradients. Tuning CURVATURE the user can pick the best threshold for a given set of images.

Summary of influential options

--contrast-weight
Fusion Options
Fusion Options
--contrast-window-size
Expert Options
--gray-projector
Expert Options
--contrast-edge-scale
Expert Options
--contrast-min-curvature
Expert Options

#### 4.4.4 Scaling and Choice of Mode

Experience has shown that neither the parameters EDGESCALE and CURVATURE nor the mode of operation (SDev-only, LoG-only, or a blend of both) scales to different image sizes. In practice, this means that if you start with a set of reduced size images, say 2808×1872 pixels, carefully optimize EDGESCALE, CURVATURE and so on, and find LoG-only the best mode, and then switch to the original resolution of 5616×3744 pixels, multiplying (or dividing) the parameters by four and sticking to LoG-only might not result in the best fused image. For best quality, perform the parameter optimization and the search for the most appropriate mode at the final resolution.

### 4.5 Local Entropy Weighting

Entropy weighting prefers pixels inside a high entropy neighborhood.

Let S be an n-ary source. Watching the output of S an observer on average gains the information ${H}_{a}\left(n\right):=\sum _{x\in S}p\left(x\right)×{\text{log}}_{a}\left(1/p\left(x\right)\right)$

per emitted message, where we assume the knowledge of the probability function p(S). The expectation value H_a(n) is called entropy of the source S. Entropy measures our uncertainty if we are to guess which message gets chosen by the source in the future. The unit of the entropy depends on the choice of the constant a > 1. Obviously ${H}_{b}\left(n\right)={H}_{a}\left(n\right)/{\text{log}}_{a}\left(b\right)$

holds for all b > 1. We use a = 2 for entropy weighting and set the entropy of the “impossible message” to zero according to $\underset{p\to 0}{\text{lim}}p×{\text{log}}_{a}\left(1/p\right)=0\text{.}$

Figure:entropy shows an entropy function.

Figure 4.4: Entropy function H for an experiment with exactly two outcomes.

For more on (information) entropy visit Wikipedia.

Enfuse computes a pixel's entropy by considering the pixel itself and its surrounding pixels quite similar to Local Contrast Weighting. The size of the window is set by --entropy-window-size. Choosing the right size is difficult, because there is a serious tradeoff between the locality of the data and the size of the sample used to compute H. A large window results in a large sample size and therefore in a reliable entropy, but considering pixels far away from the center degrades H into a non-local measure. For small windows the opposite holds true.

Another difficulty arises from the use of entropy as a weighting function in dark parts of an image, that is, in areas where the signal-to-noise ratio is low. Without any precautions, high noise is taken to be high entropy, which might not be desired. Use option --entropy-cutoff to control the black level when computing the entropy.

On the other extreme side of lightness, very light parts of an image, the sensor might already have overflown without the signal reaching 1.0 in the normalized luminance interval. For these pixels the entropy is zero and Enfuse can be told of the threshold by properly setting the second argument of --entropy-cutoff.

Summary of influential options

--entropy-weight
Fusion Options
--entropy-window-size
Expert Options
--entropy-cutoff
Expert Options

A binary mask indicates for every pixel of an image if this pixel must be considered in further processing, or ignored. For a weight mask, the value of the mask determines how much the pixel contributes, zero again meaning “no contribution”.

Masks arise in two places: as part of the input files and as separate files, showing the actual pixel weights prior to image blendung or fusion. We shall explore both occurrences in the next sections.

### 5.1 Masks in Input Files

Each of the input files for Enfuse and Enblend can contain its own mask. Both applications interpret them as binary masks no matter how many bits per image pixel they contain.

Use ImageMagick's identify or, for TIFF files, tiffinfo to inquire quickly whether a file contains a mask. Helpful Programs shows where to find these programs on the web.

     $identify -format "%f %m %wx%h %r %q-bit" remapped-0000.tif remapped-0000.tif TIFF 800x533 DirectClassRGBMatte 8-bit ^^^^^ mask  $ tiffinfo remapped-0000.tif
TIFF Directory at offset 0x1a398a (1718666)
Subfile Type: (0 = 0x0)
Image Width: 800 Image Length: 533
Resolution: 150, 150 pixels/inch
Position: 0, 0
Bits/Sample: 8
Sample Format: unsigned integer
Compression Scheme: PackBits
Photometric Interpretation: RGB color
Orientation: row 0 top, col 0 lhs
Samples/Pixel: 4                           <<<<< R, G, B, and mask
Rows/Strip: 327
Planar Configuration: single image plane


The “Matte” part of the image class and the “Extra Samples” line tell us that the file features a mask. Also, many interactive image manipulation programs show the mask as a separate channel, sometimes called “Alpha”. There, the white (high mask value) parts of the mask enable pixels and black (low mask value) parts suppress them.

The multitude of terms all describing the concept of a mask is confusing.

A mask defines a selection of pixels. A value of zero represents an unselected pixel. The maximum value (“white”) represents a selected pixel and the values between zero and the maximum are partially selected pixels. See Gimp-Savy.
Alpha Channel
The alpha channel stores the transpacency value for each pixel, typically in the range from zero to one. A value of zero means the pixel is completely transparent, thus does not contribute to the image. A value of one on the other hand means the pixel is completely opaque.
Matte
The notion “matte” as used by ImageMagick refers to an inverted alpha channel, more precisely: 1 - alpha. See ImageMagick for further explanations.

Enblend and Enfuse only consider pixels that have an associated mask value other than zero. If an input image does not have an alpha channel, Enblend warns and assumes a mask of all non-zero values, that is, it will use every pixel of the input image for fusion.

Sometimes it is helpful to manually modify a mask before fusion. For example to suppress unwanted objects (insects and cars come into mind) that moved across the scene during the exposures. If the masks of all input images are black at a certain position, the output image will have a hole in that position.

...

## 6 Tuning Memory Usage

The default configuration of Enblend and Enfuse assumes a system with 3–4GB of RAM.

If Enblend and Enfuse have been compiled with the “image-cache” feature, they do not rely on the operating system's memory management, but use their own image cache in the file system. To find out whether your version uses the image cache say

     enblend --verbose --version


or

     enfuse --verbose --version


Enblend and Enfuse put the file that holds the image cache either in the directory pointed to by the environment variable TMPDIR, or, if the variable is not set, in directory /tmp. It is prudent to ensure write permissions and enough of free space on the volume with the cache file.

The size of the image cache is user configurable with the option ‘-m CACHE-SIZE’ (see Extended Options). Furthermore, option ‘-b BUFFER-SIZE’ (see Extended Options) allows for fine-tuning the size of a single buffer inside the image cache. Note that CACHE-SIZE is given in megabytes, whereas the unit of BUFFER-SIZE is kilobytes.

Usually the user lets the operating system take care of the memory management of all processes. However, users of Enblend or Enfuse might want to control the balance between the operating systems' Virtual Memory system and the image cache for several reasons.

• Paging in or out parts of a process' image runs at kernel level and thus can make user processes appear unresponsive or “jumpy”. The caching mechanism of Enblend and Enfuse of course runs as a user process, which is why it has less detrimental effects on the system's overall responsiveness.
• The image cache has been optimized for accesses to image data. All algorithms in Enblend and Enfuse have been carefully arranged to play nice with the image cache. An operating system's cache has no knowledge of these particular memory access patterns.
• The disk access of the operating system to the swap device has been highly optimized. Enblend and Enfuse on the other hand use the standard IO-layer, which is a much slower interface.
• Limiting the amount of image cache prevents Enblend and Enfuse from eating up most or all RAM, thereby forcing all user applications into the swap.

The CACHE-SIZE should be set in such a way as to reconcile all of the above aspects even for the biggest data sets, that is, projects with many large images.

Table:cache-size-settings suggests some cache- and buffer-sizes for different amounts of available RAM.

RAM CACHE-SIZE BUFFER-SIZE Comment
MB MB KB
4096 1024 2048 default
2048 512–1024 1024
1024 256–512 256–512

Table 6.1: Suggested cache-size settings

On systems with considerably more than 4GB of RAM it is recommended to run Enblend or Enfuse versions without image cache.

## 7 Applications of Enfuse

This section describes some of the novel possibilities that Enfuse offers the photographer. In contrast to the previous chapters, it centers around the image effects.

### 7.1 What Makes Images Fusable?

Images should align well to be suitable for fusion. However, there is no hard mathematical rule what “well” means. The alignment requirements for 16MPixel images to yield a sharp 4"×6" print at 300dpi (“dpi” means dots per inch) or even for web presentation are relatively low, whereas the alignment of 8MPixel images for a 12"×18" print ought to be tight.

If the input images need to be aligned, Hugin (see Helpful Programs) is the tool of choice. It produces images exactly in the format that Enfuse expects.

Sometimes images naturally align extremely well so that no re-alignment is required. An image series with preprogrammed exposure steps taken in rapid succession where the camera is mounted on a heavy tripod and a humongous ball head, mirror lockup, and a cable release are used, comes to mind.

When in doubt about what will work, try it, and judge for yourself.

Useful ideas for a good alignment:

• Fix all camera parameters that are not explicitly varied.
Aperture
Engage full manual (<M>) or aperture-priority (<A>) mode.
Auto-focus
Disable “Auto Focus”. Be aware that the auto-focus function could be linked to shutter-release button position “half pressed” or to the shutter release in insidious ways.
Closed eyepiece
(This applies only to single lens reflex cameras.) Close the eyepiece when using a cable release to suppress variations in stray light.
Exposure time/Shutter speed
Use the shortest possible exposure time or, in other words, use the fastest shutter speed to avoid blur caused by camera shake or motion blur.
Flash power
Explicitly control the flash power of all flashes. This is sometimes called “flash exposure lock”.
Sensitivity
Disable “Auto ISO”.
White balance
Disable “Auto White Balance”. Instead, use the most suitable fixed white balance or take the white balance off a white card. When in doubt, use the setting “Daylight” or equivalent.
• Steady the camera by any means.
• Apply your best camera bracing technique combined with controlled breathing.
• Prefer a monopod, or better, a rigid tripod with a heavy head.
• Use a cable release if possible.
• (This applies to cameras with a moving mirror only.) Engage “mirror lockup”.
• Consider automatic bracketing when applicable.
• Activate camera- or lens-based image stabilization if you are sure that it improves the image quality in your particular case; otherwise disengage the feature.

For some lens-based image stabilization systems, it is known that they “lock” into different positions every time they are activated. Moreover, some stabilization systems decrease the image quality when the lens is mounted on a tripod.

• Fire in rapid succession.

### 7.2 Repetition – Noise Reduction

Main Purpose: Reduce noise

With the default settings, Enfuse computes a weighted average of the input pixels. For a series of images, repeated with identical settings, this results in a reduction of (photon shot) noise. In other words, the dynamic range increases slightly, because the higher signal-to-noise ratio makes darker shades usable. Furthermore, smooth or glossy surfaces get a “cleaner” look, and edges become visually sharper. The nitty-gritty reportage look that sometimes stems from a high sensitivity setting disappears.

Averaged images, and therefore low-noise images, are the base for a multitude of techniques like, for example, differences. The most prominent method in this class is dark-frame subtraction.

The defaults set ‘--exposure-weight=1.0’ and ‘--saturation-weight=0.2’. Eliminating the saturation component with ‘--saturation-weight=0.0’ can be worth an extra run.

### 7.3 Exposure Series – Dynamic Range Increase

Main Purpose: Increase manageable dynamic range

An exposure series is a set of images taken with identical parameters except for the exposure time. Some cameras even provide special functions to automate recording exposure series. See the instruction manual of your model for details.

Enfuse's defaults, ‘--exposure-weight=1.0’ and ‘--saturation-weight=0.2’ are well suited for fusion of color images. Remember that saturation weighting only works for RGB data. Option --saturation-weight helps to control burnt-out highlights, as these are heavily desaturated. If no image suffers from troublesome highlights, the relative saturation weight can be reduced and even be set to zero. For black and white images --entropy-weight can be an alternative to --saturation-weight because it suppresses overexposed pixels, as these contain little information. However, entropy weighting is not limited to grayscale data; it has been successfully applied to RGB images, too. Note that saturation weighting considers each color channel of an RGB image separately and chooses the channel with the minimum entropy as representative for the whole pixel.

Enfuse offers the photographer tremendous flexibility in fusing differently exposed images. Whether you combine only two pictures or a series of 21, Enfuse imposes no limits on you. Accordingly, the photographic effects achieved range from subtle to surreal, like the late 1980s “Max Headroom” TV-Series, to really unreal. Like some time ago in the chemical days of photography, when a new developer opened unseen possibilities for artists, exposure fusion extends a photographer's expressive space in the digital age. Whether the results look good or bad, whether the images are dull or exciting, is entirely up the artist.

In the next sections we give assistance to starters, and rectify several misconceptions about Enfuse.

#### 7.3.1 Tips For Beginners

Here are some tips to get you in business quickly.

Include the best single exposure.
Include the exposure you would have taken if you did not use Enfuse in your series. It gives you a solid starting point. Think of the other images as augmenting this best single exposure to bring out the light and dark features you would like to see.
Begin with as small a number of images as possible.
Pre-visualizing the results of Enfuse is difficult. The more images put into the fusion process and the wider their EV-spacing is, the more challenging visualizing the output image becomes. Therefore, start off with as few images as possible.

You can take a larger series of images and only use part of it.

As has been pointed out in the previous item, a wide EV-spacing makes pre-visualization harder. So start out with a spacing of 2/3EV to 1+1/3EV.

#### 7.3.2 Common Misconceptions

Here are some surprisingly common misconceptions about exposure series.

A single image cannot be the source of an exposure series.
Raw-files in particular lend themselves to be converted multiple times and the results being fused together. The technique is simpler, faster, and usually even looks better than digital blending (as opposed to using a graduated neutral density filter) or blending exposures in an image manipulation program. Moreover, perfect alignment comes free of charge!
An exposure series must feature symmetrically-spaced exposures.
Twice wrong! Neither do the exposures have to be “symmetric” like {0EV, −2/3EV, +2/3EV}, nor does the number of exposures have to be odd. Series like {−1−1/3EV, −1/3EV, +1/3EV} or {−1EV, 1EV} might be just right. By the way, the order in which the images were taken does not matter either.
An exposure series must cover the whole dynamic range of the scene.
If you do not want to cover the whole range, you do not have to. Some HDR programs require the user to take a light probe,8 whereas Enfuse offers the user complete freedom of exposure.
All exposure values must be different.
You can repeat any exposure as often as you like. That way you combine an exposure series with parts of Repetition, emphasizing the multiply occuring exposures and reducing noise.

### 7.4 Flash Exposure Series – Directed Lighting

Main Purpose: ???

...

### 7.5 Polarization Series – Saturation Enhancement

Main Purpose: Reflection suppression, saturation enhancement

In the current implementation of Enfuse, it is not possible in general to fuse a polarization series. Naïvely abusing --saturation-weight will not work.

### 7.6 Focus Stacks – Depth-of-Field Increase

Main Purpose: Synthetic Depth-of-Field Increase

A focus stack is a series of images where the distance of the focal plane from the sensor varies. Sloppily speaking, the images were focussed at different distances. Fusing such a stack increases the depth-of-field (DOF) beyond the physical limits of diffraction.

#### 7.6.1 Why create focus stacks?

Given

• a fixed sensor or film size,
• a lens' particular focal length, and
• a notion about “sharpness”, technically speaking the size of the circle-of-confusion (CoC)

the photographer controls the depth-of-field with the aperture. Smaller apertures – this is larger aperture numbers – increase the DOF and vice versa. However, smaller apertures increase diffraction which in turn renders the image unsharp. So, there is an optimum aperture where the photographer gets maximum DOF. Sadly, for some purposes like macro shots it is not enough. One way out is to combine the sharp parts of images focused at different distances, thereby artificially increasing the total DOF. This is exactly what Enfuse can do.

All lenses have a so called “sweet spot” aperture, where their resolution is best. Taking pictures at this aperture, the photographer squeezes the maximum quality out of the lens. But: the “sweet spot” aperture often is only one or two stops away from wide open. Wouldn't it be great to be able combine these best-possible images to form one high-quality, sufficient-DOF image? Welcome to Enfuse's local-contrast selection abilities.

#### 7.6.2 Preparing Focus Stacks

We are going to combine images with limited DOF to increase their in-focus parts. The whole process is about image sharpness. Therefore, the input images must align very well, not just well, but very well. For optimum results the maximum control point distance in Hugin (see Helpful Programs) should not exceed 0.3–0.5pixels to ensure perfect blending.

As in all image fusion operations it is preferable to use 16bit linear (gamma = 1) images throughout, but 8bit gamma encoded images will do. Naturally, high SNR input data always is welcome.

#### 7.6.3 Local Contrast Based Fusing

A bare bones call to Enfuse for focus stacking could look like this.

     enfuse \
--exposure-weight=0 \
--saturation-weight=0 \
--contrast-weight=1 \
... \
--output=output.tif \
input-<0000-9999>.tif


Here is what each option causes:

--exposure-weight=0
Switch off exposure based pixel selection. The default weight is 1.0.
--saturation-weight=0
Switch off saturation based pixel selection. The default weight is 0.2.
--contrast-weight=1
Switch on pixel selection based on local contrast.
Select the best pixel from the image stack and ignore all others. Without this option, Enfuse uses all pixels in the stack and weights them according to their respective quality, which in our case is local contrast. Without --hard-mask, the result will always look a bit soft. See Local Contrast Weighting.

If you want to see some entertaining progress messages – local-contrast weighting takes a while –, also pass the --verbose option for a verbose progress report.

#### 7.6.4 Basic Focus Stacking

For a large class of image stacks Enfuse's default algorithm, as selected in Local Contrast Based Fusing, to determine the sharpness produces nice results. The algorithm uses a moving square window, the so-called contrast window. It computes the standard deviation of the pixels inside of the window. The program then selects the window's center pixel of the image in the stack where the standard deviation is largest, that is, the local contrast reaches the maximum.

However, the algorithm fails to deliver good masks for images which exhibit high contrast edges on the scale of the contrast window size. The typical artifacts that show up are

• faint dark seams on the light side of the high contrast edges and
• extremely soft, slightly lighter seams on the dark side of the high contrast edges,

where the distance of the seams from the middle of the edge is comparable to the contrast window size.

If your results do not show any of these artifacts, stick with the basic algorithm. Advanced focus stacking, as described in the next sections, delivers superior results in case of artifacts, though requires manually tuning several parameters.

If your fused image shows any of the defects described in the previous section, you can try a more difficult-to-use algorithm that effectively works around the seam artifacts. It is described in the next section.

##### 7.6.5.1 A Detailed Look at the Problem

Let us use an example to illustrate the problem of relating the sharpness with the local contrast variations. Say we use a 5×5 contrast window. Moreover, let sharp_edge and smooth_edge be two specific configurations:

     sharp_edge =  [    0,    0,  200,    0,    0;
0,  225,    0,    0,    0;
0,  255,    0,    0,    0;
215,    0,    0,    0,    0;
200,    0,    0,    0,    0]

     smooth_edge = [    0,   62,  125,  187,  250;
1,   63,  126,  188,  251;
2,   65,  127,  190,  252;
3,   66,  128,  191,  253;
5,   67,  130,  192,  255]


where ‘;’ separates the rows and ‘,’ separates the columns. This is in fact Octave syntax.

Images Figure:sharp-edge and Figure:smooth-edge show plots of the matrices sharp_edge and smooth_edge.

Figure 7.1: 3D plot augmented by contour plot of the matrix sharp_edge.

Figure 7.2: 3D plot augmented by contour plot of the matrix smooth_edge.

Our intuition lets us “see” an extremely sharp edge in the first matrix, whereas the second one describes an extraordinarily smooth diagonal intensity ramp. Which one will be selected? Well, sharp_edge has a standard deviation of 88.07 and smooth_edge has 88.41. Thus, smooth_edge wins, contradicting our intuition, and even worse, our intention!

Sadly, configurations like smooth_edge occur more often with high-quality, good bokeh lenses. In fact, they are the very manifestation of “good bokeh”. Therefore, Laplacian edge detection plays an important role when working with high-quality lenses.

##### 7.6.5.2 Laplacian Edge Detection

Enfuse provides a Laplacian-based algorithm that can help in situations where weighting based on the standard deviation fails. It is activated with a positive value for SCALE in --contrast-edge-scale=SCALE. The Laplacian will detect two-dimensional curvature on the scale of SCALE. Here and in the following we simply speak of “curvature” where we mean “magnitude of curvature”. That is, we shall not distinguish between convex and concave edges. Enfuse always use the magnitude of curvature for weighting.

Typically, SCALE ranges between 0.1pixels and 0.5pixels, where 0.3pixels is a good starting point. To find the best value for SCALE though, usually some experimentation will be necessary. Use --save-masks to get all soft-mask (default: softmask-%n.tif) and hard-mask files (default: hardmask-%n.tif). Check how different scales affect the artifacts. Also see Understanding Masks.

##### 7.6.5.3 Local Contrast Enhancement

Sometimes Enfuse misses smoother edges with --contrast-edge-scale and a little local contrast enhancement (LCE) helps. Set --contrast-edge-scale=SCALE:LCE-SCALE:LCE-FACTOR. where LCE-SCALE and LCE-FACTOR work like the unsharp mask filters in various image manipulation programs. Start with LCE-SCALE ten times the value of SCALE and a LCE-FACTOR of 2–5.

LCE-SCALE can be specified as a percentage of SCALE. LCE-FACTOR also can be specified as a percentage. Examples:

     --contrast-edge-scale=0.3:3.0:3
--contrast-edge-scale=0.3:1000%:3.0
--contrast-edge-scale=0.3:3:300%
--contrast-edge-scale=0.3:1000%:300%


By default LCE is turned off.

##### 7.6.5.4 Suppressing Noise or Recognizing Faint Edges

The Laplacian-based algorithm is much better at resisting the seam problem than the local-contrast algorithm, but it has two shortcomings:

1. The Laplacian is very susceptible to noise and
2. it fails to recognize faint edges.

The --contrast-min-curvature option helps to mitigate both flaws.

The argument to --contrast-min-curvature=CURVATURE either is an absolute lightness value, for example 0..255 for 8bit data and 0..65535 for 16bit data, or, when given with a ‘%’-sign it is a relative lightness value ranging from 0% to 100%.

To suppress unreal edges or counter excessive noise, use the --contrast-min-curvature option with a negative curvature measure CURVATURE. This forces all curvatures less than −CURVATURE to zero.

A positive curvature measure CURVATURE makes Enfuse merge the LoG data with the local-contrast data. Every curvature larger than or equal to CURVATURE is left unchanged, and every curvature less than CURVATURE gets replaced with the rescaled local-contrast data, such that the largest local contrast is just below CURVATURE. This combines the best parts of both techniques and ensures a precise edge detection over the whole range of edge curvatures.

Summary

--contrast-edge-scale=0.3
Use LoG to detect edges on a scale of 0.3pixels. Apply the default grayscale projector: average.
--contrast-edge-scale=0.3 --gray-projector=l-star
Use LoG to detect edges on a scale of 0.3pixels. Apply the L*-grayscale projector.
--contrast-edge-scale=0.3:3:300%
Use LoG to detect edges on a scale of 0.3pixels, pre-sharpen the input images by 300% on a scale of 3pixels. Apply the default grayscale projector: average.
--contrast-edge-scale=0.3 --contrast-min-curvature=−0.5%
Use LoG to detect edges on a scale of 0.3pixels. Apply the default grayscale projector: average and throw away all edges with a curvature of less than 0.5%.
--contrast-edge-scale=0.3 --contrast-min-curvature=0.5% --contrast-window-size=7
Use LoG to detect edges on a scale of 0.3pixels. Apply the default grayscale projector: average and throw away all edges with a curvature of less than 0.5% and replace the LoG data between 0% and 0.5% with SDev data. Use a window of 7×7pixel window to compute the SDev.

##### 7.6.5.5 Focus Stacking Decision Tree

Figure Figure:focus-stacking-decision-tree helps the user to arrive at a well-fused focus stack with as few steps as possible.

Figure 7.3: Focus stacking decision tree.

Always start with the default, contrast weighting with a local contrast window. Only if seams appear as described in Advanced Focus Stacking switch to Laplacian-of-Gaussian contrast detection.

If some seams remain even in LoG-mode, decrease the sensitivity of the edge detection with a positive --contrast-min-curvature. A too high value of --contrast-min-curvature suppresses fine detail though. Part of the detail can be brought back with pre-sharpening, that is, Local Contrast Enhancement or combining LoG with local-contrast-window mode by using a negative --contrast-min-curvature.

Carefully examining the masks (option --save-masks) that Enfuse uses helps to judge the effects of the parameters.

#### 7.6.6 Tips For Focus Stacking Experts

We have collected some advice with which even focus-stacking adepts can benefit.

• Ensure that the sensor is clean.

Aligning focus stacks requires varying the viewing angle, which corresponds to a changing focal length. Hence, the same pixel on the sensor gets mapped onto different positions in the final image. Dirt spots will occur not only once but as many times as there are images in the stack – something that is no fun to correct in postprocessing.

Along the same lines, the photographer may want to consider to prepare dark frames before, and possibly also after, the shoot of the focus stack, to subtract hot pixels before fusion.

• Prefer a low-sensitivity setting (“ISO”) on the camera to get low-noise images.

Fusing with --hard-mask does not average, and thus does not suppress any noise in the input images.

• If the transition of in-focus to out-of-focus areas is too abrupt, record the images with closest and farthest focusing distances twice: first with the intended working aperture, and a second time with a small aperture (large aperture number).

The small aperture will give the fused image a more natural in-focus to out-of-focus transition and the working-aperture shots supply the detail in the in-focus regions.

Several programs and libraries have proven helpful when working with Enfuse and Enblend.

Raw Image Conversion
• DCRaw is a universal raw-converter written by David Coffin.
• UFRaw, a raw converter written by Udi Fuchs and based on DCRaw, adds a GUI (ufraw), versatile batch processing (ufraw-batch), and some additional features such as cropping, noise reduction with wavelets, and automatic lens error correction.

Image Alignment and Rendering
• ALE, David Hilvert's anti-lamenessing engine for the real die-hard command-line users aligns, filters, and renders images.
• Hugin is a GUI that aligns and stitches images.

It comes with several command line tools, like nona to stitch panorama images, align_image_stack to align overlapping images for HDR or create focus stacks, and fulla to correct lens errors.

• PanoTools the successor of Helmut Dersch's original PanoTools offers a set of command-line driven applications to create panoramas. Most notable are PTOptimizer and PTmender.

Image Manipulation
• CinePaint is a branch of an early Gimp forked off at version 1.0.4. It sports much less features than the current Gimp, but offers 8bit, 16bit and 32bit color channels, HDR (for example floating-point TIFF, and OpenEXR), and a tightly integrated color management system.
• The Gimp is a general purpose image manipulation program. At the time of this writing it is still limited to images with only 8bits per channel.
• ImageMagick and its clone GraphicsMagick are general purpose command-line driven image manipulation programs, for example, convert, display, identify, and montage.

High Dynamic Range
• OpenEXR offers libraries and some programs to work with the EXR HDR format.
• PFSTools create, modify, and tonemap high-dynamic range images.

Libraries
• LibJPEG is a library for handling the JPEG (JFIF) image format.
• LibPNG is a library that handles the Portable Network Graphics (PNG) image format.
• LibTIFF offers a library and utility programs to manipulate the ubiquitous Tagged Image File Format, TIFF.

The nifty tiffinfo command quickly inquires the properties of TIFF files.

Meta-Data Handling
• EXIFTool reads and writes EXIF meta data. In particular it copies meta data from one image to another.
• LittleCMS is the color management library used by Hugin, DCRaw, UFRaw, Enblend, and Enfuse. It supplies some binaries, too. tifficc, an ICC color profile applier, is of particular interest.

## Appendix A Bug Reports

     Most of this appendix was taken from the
Octave documentation.


Bug reports play an important role in making Enblend and Enfuse reliable and enjoyable.

When you encounter a problem, the first thing to do is to see if it is already known. On the package's SourceForge homepage click “Develop” and on the development page click “Tracker”. Search the trackers for your particular problem. If it is not known, then you should report the problem.

In order for a bug report to serve its purpose, you must include the information that makes it possible to fix the bug.

### A.1 Have You Really Found a Bug?

If you are not sure whether you have found a bug, here are some guidelines:

• If Enblend or Enfuse get a fatal signal, for any options or input images, that is a bug.
• If Enblend or Enfuse produce incorrect results, for any input whatever, that is a bug.
• If Enblend or Enfuse produce an error message for valid input, that is a bug.
• If Enblend or Enfuse do not produce an error message for invalid input, that is a bug.

### A.2 How to Report Bugs

The fundamental principle of reporting bugs usefully is this: report all the facts. If you are not sure whether to state a fact or leave it out, state it. Often people omit facts because they think they know what causes the problem and they conclude that some details do not matter. Play it safe and give a specific, complete example.

Keep in mind that the purpose of a bug report is to enable someone to fix the bug if it is not known. Always write your bug reports on the assumption that the bug is not known.

Try to make your bug report self-contained. If we have to ask you for more information, it is best if you include all the previous information in your response, as well as the information that was missing.

To enable someone to investigate the bug, you should include all these things:

• The exact version and configuration of Enblend or Enfuse. You can get this by running it with the options --version and --verbose.
• A complete set of input images that will reproduce the bug. Strive for a minimal set of small9 images.
• The type of machine you are using, and the operating system name and its version number.
• A complete list of any modifications you have made to the source. Be precise about these changes. Show a diff for them.
• Details of any other deviations from the standard procedure for installing Enblend and Enfuse.
• The exact command line you use to call Enblend or Enfuse, which then triggers the bug.

Examples:

              ~/local/bin/enblend -v \
image-1.png image-2.png


or:

              /local/bin/enfuse \
--verbose \
--exposure-weight=0 --saturation-weight=0 --entropy-weight=1 \
--gray-projector=l-star \
--entropy-cutoff=1.667% \
layer-01.ppm layer-02.ppm layer-03.ppm


If you call Enblend or Enfuse from within a GUI like, for example, Hugin or KImageFuser by Harry van der Wolf, copy&paste or write down the command line that launches Enblend or Enfuse.

• A description of what behavior you observe that you believe is incorrect. For example, “The application gets a fatal signal,” or, “The output image contains black holes.”

Of course, if the bug is that the application gets a fatal signal, then one cannot miss it. But if the bug is incorrect output, we might not notice unless it is glaringly wrong.

### A.3 Sending Patches for Enblend or Enfuse

If you would like to write bug fixes or improvements for Enblend or Enfuse, that is very helpful. When you send your changes, please follow these guidelines to avoid causing extra work for us in studying the patches. If you do not follow these guidelines, your information might still be useful, but using it will take extra work.

• Send an explanation with your changes of what problem they fix or what improvement they bring about. For a bug fix, just include a copy of the bug report, and explain why the change fixes the bug.
• Always include a proper bug report for the problem you think you have fixed. We need to convince ourselves that the change is right before installing it. Even if it is right, we might have trouble judging it if we do not have a way to reproduce the problem.
• Include all the comments that are appropriate to help people reading the source in the future understand why this change was needed.
• Do not mix together changes made for different reasons. Send them individually.

If you make two changes for separate reasons, then we might not want to install them both. We might want to install just one.

• Use the version control system to make your diffs. Prefer the unified diff format: hg diff --unified 4.
• You can increase the probability that your patch gets applied by basing it on a recent revision of the sources.

## Appendix B Authors

Andrew Mihal (acmihal@users.sourceforge.net) has written Enblend and Enfuse.

Contributors

Thanks to Simon Andriot and Pablo Joubert for suggesting the Mertens-Kautz-Van Reeth technique and the name “Enfuse”.

## Appendix C GNU Free Documentation License

Version 1.2, November 2002

     Copyright © 2000, 2001, 2002 Free Software Foundation, Inc.
51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.

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## General Index

#### Voetnoten

[1] Tom Mertens, Jan Kautz, and Frank van Reeth, “Exposure Fusion”, Proceedings of the 15th Pacific Conference on Computer Graphics and Applications, pages 382–390.

[2] Peter J. Burt and Edward H. Adelson, “A Multiresolution Spline With Application to Image Mosaics”, ACM Transactions on Graphics, Vol. 2, No. 4, October 1983, pages 217–236.

[3] Downsampling with a good interpolator reduces noise, which might not desired to judge the image quality of the original-size image. Cropping might be an alternative, though.

[4] Use utilities like, e.g., tiffcopy and tiffsplit of LibTIFF to manipulate multi-directory TIFF images. See Helpful Programs.

[5] As Dr. Daniel Jackson correctly noted, actually, it is not a pyramid: “Ziggaurat, it's a Ziggaurat.”

[6] Solid-state physicists will be reminded of the http://en.wikipedia.org/wiki/Born-von_Karman_boundary_condition, Born-von Kármán boundary condition.

[7] In the current implementation a floor(contrast-window-size / 2) wide border around the images remains unprocessed and gets a weight of zero.

[8] Paul E. Debevec defines: “A light probe image is an omnidirectional, high dynamic range image that records the incident illumination conditions at a particular point in space.”

[9] Images of a size less than 1500×1000 pixels qualify as small.