# NAME

Image::Leptonica::Func::binarize

# VERSION

version 0.04

`binarize.c`

```
binarize.c
===================================================================
Image binarization algorithms are found in:
grayquant.c: standard, simple, general grayscale quantization
adaptmap.c: local adaptive; mostly gray-to-gray in preparation
for binarization
binarize.c: special binarization methods, locally adaptive.
===================================================================
Adaptive Otsu-based thresholding
l_int32 pixOtsuAdaptiveThreshold() 8 bpp
Otsu thresholding on adaptive background normalization
PIX *pixOtsuThreshOnBackgroundNorm() 8 bpp
Masking and Otsu estimate on adaptive background normalization
PIX *pixMaskedThreshOnBackgroundNorm() 8 bpp
Sauvola local thresholding
l_int32 pixSauvolaBinarizeTiled()
l_int32 pixSauvolaBinarize()
PIX *pixSauvolaGetThreshold()
PIX *pixApplyLocalThreshold();
Notes:
(1) pixOtsuAdaptiveThreshold() computes a global threshold over each
tile and performs the threshold operation, resulting in a
binary image for each tile. These are stitched into the
final result.
(2) pixOtsuThreshOnBackgroundNorm() and
pixMaskedThreshOnBackgroundNorm() are binarization functions
that use background normalization with other techniques.
(3) Sauvola binarization computes a local threshold based on
the local average and square average. It takes two constants:
the window size for the measurment at each pixel and a
parameter that determines the amount of normalized local
standard deviation to subtract from the local average value.
```

# FUNCTIONS

## pixApplyLocalThreshold

PIX * pixApplyLocalThreshold ( PIX *pixs, PIX *pixth, l_int32 redfactor )

```
pixApplyLocalThreshold()
Input: pixs (8 bpp grayscale; not colormapped)
pixth (8 bpp array of local thresholds)
redfactor ( ... )
Return: pixd (1 bpp, thresholded image), or null on error
```

## pixMaskedThreshOnBackgroundNorm

PIX * pixMaskedThreshOnBackgroundNorm ( PIX *pixs, PIX *pixim, l_int32 sx, l_int32 sy, l_int32 thresh, l_int32 mincount, l_int32 smoothx, l_int32 smoothy, l_float32 scorefract, l_int32 *pthresh )

```
pixMaskedThreshOnBackgroundNorm()
Input: pixs (8 bpp grayscale; not colormapped)
pixim (<optional> 1 bpp 'image' mask; can be null)
sx, sy (tile size in pixels)
thresh (threshold for determining foreground)
mincount (min threshold on counts in a tile)
smoothx (half-width of block convolution kernel width)
smoothy (half-width of block convolution kernel height)
scorefract (fraction of the max Otsu score; typ. ~ 0.1)
&thresh (<optional return> threshold value that was
used on the normalized image)
Return: pixd (1 bpp thresholded image), or null on error
Notes:
(1) This begins with a standard background normalization.
Additionally, there is a flexible background norm, that
will adapt to a rapidly varying background, and this
puts white pixels in the background near regions with
significant foreground. The white pixels are turned into
a 1 bpp selection mask by binarization followed by dilation.
Otsu thresholding is performed on the input image to get an
estimate of the threshold in the non-mask regions.
The background normalized image is thresholded with two
different values, and the result is combined using
the selection mask.
(2) Note that the numbers 255 (for bgval target) and 190 (for
thresholding on pixn) are tied together, and explicitly
defined in this function.
(3) See pixBackgroundNorm() for meaning and typical values
of input parameters. For a start, you can try:
sx, sy = 10, 15
thresh = 100
mincount = 50
smoothx, smoothy = 2
```

## pixOtsuAdaptiveThreshold

l_int32 pixOtsuAdaptiveThreshold ( PIX *pixs, l_int32 sx, l_int32 sy, l_int32 smoothx, l_int32 smoothy, l_float32 scorefract, PIX **ppixth, PIX **ppixd )

```
pixOtsuAdaptiveThreshold()
Input: pixs (8 bpp)
sx, sy (desired tile dimensions; actual size may vary)
smoothx, smoothy (half-width of convolution kernel applied to
threshold array: use 0 for no smoothing)
scorefract (fraction of the max Otsu score; typ. 0.1;
use 0.0 for standard Otsu)
&pixth (<optional return> array of threshold values
found for each tile)
&pixd (<optional return> thresholded input pixs, based on
the threshold array)
Return: 0 if OK, 1 on error
Notes:
(1) The Otsu method finds a single global threshold for an image.
This function allows a locally adapted threshold to be
found for each tile into which the image is broken up.
(2) The array of threshold values, one for each tile, constitutes
a highly downscaled image. This array is optionally
smoothed using a convolution. The full width and height of the
convolution kernel are (2 * @smoothx + 1) and (2 * @smoothy + 1).
(3) The minimum tile dimension allowed is 16. If such small
tiles are used, it is recommended to use smoothing, because
without smoothing, each small tile determines the splitting
threshold independently. A tile that is entirely in the
image bg will then hallucinate fg, resulting in a very noisy
binarization. The smoothing should be large enough that no
tile is only influenced by one type (fg or bg) of pixels,
because it will force a split of its pixels.
(4) To get a single global threshold for the entire image, use
input values of @sx and @sy that are larger than the image.
For this situation, the smoothing parameters are ignored.
(5) The threshold values partition the image pixels into two classes:
one whose values are less than the threshold and another
whose values are greater than or equal to the threshold.
This is the same use of 'threshold' as in pixThresholdToBinary().
(6) The scorefract is the fraction of the maximum Otsu score, which
is used to determine the range over which the histogram minimum
is searched. See numaSplitDistribution() for details on the
underlying method of choosing a threshold.
(7) This uses enables a modified version of the Otsu criterion for
splitting the distribution of pixels in each tile into a
fg and bg part. The modification consists of searching for
a minimum in the histogram over a range of pixel values where
the Otsu score is within a defined fraction, @scorefract,
of the max score. To get the original Otsu algorithm, set
@scorefract == 0.
```

## pixOtsuThreshOnBackgroundNorm

PIX * pixOtsuThreshOnBackgroundNorm ( PIX *pixs, PIX *pixim, l_int32 sx, l_int32 sy, l_int32 thresh, l_int32 mincount, l_int32 bgval, l_int32 smoothx, l_int32 smoothy, l_float32 scorefract, l_int32 *pthresh )

```
pixOtsuThreshOnBackgroundNorm()
Input: pixs (8 bpp grayscale; not colormapped)
pixim (<optional> 1 bpp 'image' mask; can be null)
sx, sy (tile size in pixels)
thresh (threshold for determining foreground)
mincount (min threshold on counts in a tile)
bgval (target bg val; typ. > 128)
smoothx (half-width of block convolution kernel width)
smoothy (half-width of block convolution kernel height)
scorefract (fraction of the max Otsu score; typ. 0.1)
&thresh (<optional return> threshold value that was
used on the normalized image)
Return: pixd (1 bpp thresholded image), or null on error
Notes:
(1) This does background normalization followed by Otsu
thresholding. Otsu binarization attempts to split the
image into two roughly equal sets of pixels, and it does
a very poor job when there are large amounts of dark
background. By doing a background normalization first,
to get the background near 255, we remove this problem.
Then we use a modified Otsu to estimate the best global
threshold on the normalized image.
(2) See pixBackgroundNorm() for meaning and typical values
of input parameters. For a start, you can try:
sx, sy = 10, 15
thresh = 100
mincount = 50
bgval = 255
smoothx, smoothy = 2
```

## pixSauvolaBinarize

l_int32 pixSauvolaBinarize ( PIX *pixs, l_int32 whsize, l_float32 factor, l_int32 addborder, PIX **ppixm, PIX **ppixsd, PIX **ppixth, PIX **ppixd )

```
pixSauvolaBinarize()
Input: pixs (8 bpp grayscale; not colormapped)
whsize (window half-width for measuring local statistics)
factor (factor for reducing threshold due to variance; >= 0)
addborder (1 to add border of width (@whsize + 1) on all sides)
&pixm (<optional return> local mean values)
&pixsd (<optional return> local standard deviation values)
&pixth (<optional return> threshold values)
&pixd (<optional return> thresholded image)
Return: 0 if OK, 1 on error
Notes:
(1) The window width and height are 2 * @whsize + 1. The minimum
value for @whsize is 2; typically it is >= 7..
(2) The local statistics, measured over the window, are the
average and standard deviation.
(3) The measurements of the mean and standard deviation are
performed inside a border of (@whsize + 1) pixels. If pixs does
not have these added border pixels, use @addborder = 1 to add
it here; otherwise use @addborder = 0.
(4) The Sauvola threshold is determined from the formula:
t = m * (1 - k * (1 - s / 128))
where:
t = local threshold
m = local mean
k = @factor (>= 0) [ typ. 0.35 ]
s = local standard deviation, which is maximized at
127.5 when half the samples are 0 and half are 255.
(5) The basic idea of Niblack and Sauvola binarization is that
the local threshold should be less than the median value,
and the larger the variance, the closer to the median
it should be chosen. Typical values for k are between
0.2 and 0.5.
```

## pixSauvolaBinarizeTiled

l_int32 pixSauvolaBinarizeTiled ( PIX *pixs, l_int32 whsize, l_float32 factor, l_int32 nx, l_int32 ny, PIX **ppixth, PIX **ppixd )

```
pixSauvolaBinarizeTiled()
Input: pixs (8 bpp grayscale, not colormapped)
whsize (window half-width for measuring local statistics)
factor (factor for reducing threshold due to variance; >= 0)
nx, ny (subdivision into tiles; >= 1)
&pixth (<optional return> Sauvola threshold values)
&pixd (<optional return> thresholded image)
Return: 0 if OK, 1 on error
Notes:
(1) The window width and height are 2 * @whsize + 1. The minimum
value for @whsize is 2; typically it is >= 7..
(2) For nx == ny == 1, this defaults to pixSauvolaBinarize().
(3) Why a tiled version?
(a) Because the mean value accumulator is a uint32, overflow
can occur for an image with more than 16M pixels.
(b) The mean value accumulator array for 16M pixels is 64 MB.
The mean square accumulator array for 16M pixels is 128 MB.
Using tiles reduces the size of these arrays.
(c) Each tile can be processed independently, in parallel,
on a multicore processor.
(4) The Sauvola threshold is determined from the formula:
t = m * (1 - k * (1 - s / 128))
See pixSauvolaBinarize() for details.
```

## pixSauvolaGetThreshold

PIX * pixSauvolaGetThreshold ( PIX *pixm, PIX *pixms, l_float32 factor, PIX **ppixsd )

```
pixSauvolaGetThreshold()
Input: pixm (8 bpp grayscale; not colormapped)
pixms (32 bpp)
factor (factor for reducing threshold due to variance; >= 0)
&pixsd (<optional return> local standard deviation)
Return: pixd (8 bpp, sauvola threshold values), or null on error
Notes:
(1) The Sauvola threshold is determined from the formula:
t = m * (1 - k * (1 - s / 128))
where:
t = local threshold
m = local mean
k = @factor (>= 0) [ typ. 0.35 ]
s = local standard deviation, which is maximized at
127.5 when half the samples are 0 and half are 255.
(2) See pixSauvolaBinarize() for other details.
(3) Important definitions and relations for computing averages:
v == pixel value
E(p) == expected value of p == average of p over some pixel set
S(v) == square of v == v * v
mv == E(v) == expected pixel value == mean value
ms == E(S(v)) == expected square of pixel values
== mean square value
var == variance == expected square of deviation from mean
== E(S(v - mv)) = E(S(v) - 2 * S(v * mv) + S(mv))
= E(S(v)) - S(mv)
= ms - mv * mv
s == standard deviation = sqrt(var)
So for evaluating the standard deviation in the Sauvola
threshold, we take
s = sqrt(ms - mv * mv)
```

# AUTHOR

Zakariyya Mughal <zmughal@cpan.org>

# COPYRIGHT AND LICENSE

This software is copyright (c) 2014 by Zakariyya Mughal.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.