#include <math.h>
#include "allheaders.h"
Go to the source code of this file.
|
static PIX * | pixSauvolaGetThreshold (PIX *pixm, PIX *pixms, l_float32 factor, PIX **ppixsd) |
|
static PIX * | pixApplyLocalThreshold (PIX *pixs, PIX *pixth) |
|
l_ok | pixOtsuAdaptiveThreshold (PIX *pixs, l_int32 sx, l_int32 sy, l_int32 smoothx, l_int32 smoothy, l_float32 scorefract, PIX **ppixth, PIX **ppixd) |
|
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) |
|
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) |
|
l_ok | pixSauvolaBinarizeTiled (PIX *pixs, l_int32 whsize, l_float32 factor, l_int32 nx, l_int32 ny, PIX **ppixth, PIX **ppixd) |
|
l_ok | pixSauvolaBinarize (PIX *pixs, l_int32 whsize, l_float32 factor, l_int32 addborder, PIX **ppixm, PIX **ppixsd, PIX **ppixth, PIX **ppixd) |
|
PIX * | pixSauvolaOnContrastNorm (PIX *pixs, l_int32 mindiff, PIX **ppixn, PIX **ppixth) |
|
PIX * | pixThreshOnDoubleNorm (PIX *pixs, l_int32 mindiff) |
|
l_ok | pixThresholdByConnComp (PIX *pixs, PIX *pixm, l_int32 start, l_int32 end, l_int32 incr, l_float32 thresh48, l_float32 threshdiff, l_int32 *pglobthresh, PIX **ppixd, l_int32 debugflag) |
|
l_ok | pixThresholdByHisto (PIX *pixs, l_int32 factor, l_int32 halfw, l_int32 skip, l_int32 *pthresh, PIX **ppixd, NUMA **pnahisto, PIX **ppixhisto) |
|
===================================================================
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 and
global.
===================================================================
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()
static PIX *pixSauvolaGetThreshold()
static PIX *pixApplyLocalThreshold();
Sauvola binarization on contrast normalization
PIX *pixSauvolaOnContrastNorm() 8 bpp
Contrast normalization followed by bg normalization and thresholding
PIX *pixThreshOnDoubleNorm()
Global thresholding using connected components
PIX *pixThresholdByConnComp()
Global thresholding by histogram
PIX *pixThresholdByHisto()
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 measurement at each pixel and a
parameter that determines the amount of normalized local
standard deviation to subtract from the local average value.
(4) pixThresholdByConnComp() uses the numbers of 4 and 8 connected
components at different thresholding to determine if a
global threshold can be used (for text or line-art) and the
value it should have.
Definition in file binarize.c.
◆ pixApplyLocalThreshold()
static PIX * pixApplyLocalThreshold |
( |
PIX * |
pixs, |
|
|
PIX * |
pixth |
|
) |
| |
|
static |
pixApplyLocalThreshold()
- Parameters
-
[in] | pixs | 8 bpp grayscale; not colormapped |
[in] | pixth | 8 bpp array of local thresholds |
- Returns
- pixd 1 bpp, thresholded image, or NULL on error
Definition at line 791 of file binarize.c.
◆ 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()
- Parameters
-
[in] | pixs | 8 bpp grayscale; not colormapped |
[in] | pixim | [optional] 1 bpp 'image' mask; can be null |
[in] | sx,sy | tile size in pixels |
[in] | thresh | threshold for determining foreground |
[in] | mincount | min threshold on counts in a tile |
[in] | smoothx | half-width of block convolution kernel width |
[in] | smoothy | half-width of block convolution kernel height |
[in] | scorefract | fraction of the max Otsu score; typ. ~ 0.1 |
[out] | pthresh | [optional] threshold value that was used on the normalized image |
- Returns
- 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
Definition at line 367 of file binarize.c.
◆ pixOtsuAdaptiveThreshold()
l_ok pixOtsuAdaptiveThreshold |
( |
PIX * |
pixs, |
|
|
l_int32 |
sx, |
|
|
l_int32 |
sy, |
|
|
l_int32 |
smoothx, |
|
|
l_int32 |
smoothy, |
|
|
l_float32 |
scorefract, |
|
|
PIX ** |
ppixth, |
|
|
PIX ** |
ppixd |
|
) |
| |
pixOtsuAdaptiveThreshold()
- Parameters
-
[in] | pixs | 8 bpp |
[in] | sx,sy | desired tile dimensions; actual size may vary |
[in] | smoothx,smoothy | half-width of convolution kernel applied to threshold array: use 0 for no smoothing |
[in] | scorefract | fraction of the max Otsu score; typ. 0.1; use 0.0 for standard Otsu |
[out] | ppixth | [optional] array of threshold values found for each tile |
[out] | ppixd | [optional] thresholded input pixs, based on the threshold array |
- Returns
- 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.
(8) N.B. This method is NOT recommended for images with weak text
and significant background noise, such as bleedthrough, because
of the problem noted in (3) above for tiling. Use Sauvola.
Definition at line 157 of file binarize.c.
◆ 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()
- Parameters
-
[in] | pixs | 8 bpp grayscale; not colormapped |
[in] | pixim | [optional] 1 bpp 'image' mask; can be null |
[in] | sx,sy | tile size in pixels |
[in] | thresh | threshold for determining foreground |
[in] | mincount | min threshold on counts in a tile |
[in] | bgval | target bg val; typ. > 128 |
[in] | smoothx | half-width of block convolution kernel width |
[in] | smoothy | half-width of block convolution kernel height |
[in] | scorefract | fraction of the max Otsu score; typ. 0.1 |
[out] | pthresh | [optional] threshold value that was used on the normalized image |
- Returns
- 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
Definition at line 271 of file binarize.c.
◆ pixSauvolaBinarize()
l_ok pixSauvolaBinarize |
( |
PIX * |
pixs, |
|
|
l_int32 |
whsize, |
|
|
l_float32 |
factor, |
|
|
l_int32 |
addborder, |
|
|
PIX ** |
ppixm, |
|
|
PIX ** |
ppixsd, |
|
|
PIX ** |
ppixth, |
|
|
PIX ** |
ppixd |
|
) |
| |
pixSauvolaBinarize()
- Parameters
-
[in] | pixs | 8 bpp grayscale; not colormapped |
[in] | whsize | window half-width for measuring local statistics |
[in] | factor | factor for reducing threshold due to variance; >= 0 |
[in] | addborder | 1 to add border of width (whsize + 1) on all sides |
[out] | ppixm | [optional] local mean values |
[out] | ppixsd | [optional] local standard deviation values |
[out] | ppixth | [optional] threshold values |
[out] | ppixd | [optional] thresholded image |
- Returns
- 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.
Definition at line 603 of file binarize.c.
◆ pixSauvolaBinarizeTiled()
l_ok pixSauvolaBinarizeTiled |
( |
PIX * |
pixs, |
|
|
l_int32 |
whsize, |
|
|
l_float32 |
factor, |
|
|
l_int32 |
nx, |
|
|
l_int32 |
ny, |
|
|
PIX ** |
ppixth, |
|
|
PIX ** |
ppixd |
|
) |
| |
pixSauvolaBinarizeTiled()
- Parameters
-
[in] | pixs | 8 bpp grayscale, not colormapped |
[in] | whsize | window half-width for measuring local statistics |
[in] | factor | factor for reducing threshold due to variance; >= 0 |
[in] | nx,ny | subdivision into tiles; >= 1 |
[out] | ppixth | [optional] Sauvola threshold values |
[out] | ppixd | [optional] thresholded image |
- Returns
- 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) A uint32 is used for the mean value accumulator, so
overflow can occur for an image with more than 16M pixels.
(b) A dpix is used to accumulate mean square values, and it
can only accommodate images with less than 2^28 pixels.
Using tiles reduces the size of all the 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.
Definition at line 478 of file binarize.c.
◆ pixSauvolaGetThreshold()
static PIX * pixSauvolaGetThreshold |
( |
PIX * |
pixm, |
|
|
PIX * |
pixms, |
|
|
l_float32 |
factor, |
|
|
PIX ** |
ppixsd |
|
) |
| |
|
static |
pixSauvolaGetThreshold()
- Parameters
-
[in] | pixm | 8 bpp grayscale; not colormapped |
[in] | pixms | 32 bpp |
[in] | factor | factor for reducing threshold due to variance; >= 0 |
[out] | ppixsd | [optional] local standard deviation |
- Returns
- 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)
Definition at line 711 of file binarize.c.
◆ pixSauvolaOnContrastNorm()
PIX* pixSauvolaOnContrastNorm |
( |
PIX * |
pixs, |
|
|
l_int32 |
mindiff, |
|
|
PIX ** |
ppixn, |
|
|
PIX ** |
ppixth |
|
) |
| |
pixSauvolaOnContrastNorm()
- Parameters
-
[in] | pixs | 8 or 32 bpp |
[in] | mindiff | minimum diff to accept as valid in contrast normalization. Use ~130 for noisy images. |
[out] | ppixn | [optional] intermediate output from contrast normalization |
[out] | ppixth | [optional] threshold array for binarization |
- Returns
- pixd 1 bpp thresholded image, or NULL on error
Notes:
(1) This composite operation is good for adaptively removing
dark background.
Definition at line 850 of file binarize.c.
◆ pixThresholdByConnComp()
l_ok pixThresholdByConnComp |
( |
PIX * |
pixs, |
|
|
PIX * |
pixm, |
|
|
l_int32 |
start, |
|
|
l_int32 |
end, |
|
|
l_int32 |
incr, |
|
|
l_float32 |
thresh48, |
|
|
l_float32 |
threshdiff, |
|
|
l_int32 * |
pglobthresh, |
|
|
PIX ** |
ppixd, |
|
|
l_int32 |
debugflag |
|
) |
| |
pixThresholdByConnComp()
- Parameters
-
[in] | pixs | depth > 1, colormap OK |
[in] | pixm | [optional] 1 bpp mask giving region to ignore by setting pixels to white; use NULL if no mask |
[in] | start,end,incr | binarization threshold levels to test |
[in] | thresh48 | threshold on normalized difference between the numbers of 4 and 8 connected components |
[in] | threshdiff | threshold on normalized difference between the number of 4 cc at successive iterations |
[out] | pglobthresh | [optional] best global threshold; 0 if no threshold is found |
[out] | ppixd | [optional] image thresholded to binary, or null if no threshold is found |
[in] | debugflag | 1 for plotted results |
- Returns
- 0 if OK, 1 on error or if no threshold is found
Notes:
(1) This finds a global threshold based on connected components.
Although slow, it is reasonable to use it in a situation where
(a) the background in the image is relatively uniform, and
(b) the result will be fed to an OCR program that accepts 1 bpp
images and works best with easily segmented characters.
The reason for (b) is that this selects a threshold with a
minimum number of both broken characters and merged characters.
(2) If the pix has color, it is converted to gray using the
max component.
(3) Input 0 to use default values for any of these inputs:
start, end, incr, thresh48, threshdiff.
(4) This approach can be understood as follows. When the
binarization threshold is varied, the numbers of c.c. identify
four regimes:
(a) For low thresholds, text is broken into small pieces, and
the number of c.c. is large, with the 4 c.c. significantly
exceeding the 8 c.c.
(b) As the threshold rises toward the optimum value, the text
characters coalesce and there is very little difference
between the numbers of 4 and 8 c.c, which both go
through a minimum.
(c) Above this, the image background gets noisy because some
pixels are(thresholded to foreground, and the numbers
of c.c. quickly increase, with the 4 c.c. significantly
larger than the 8 c.c.
(d) At even higher thresholds, the image background noise
coalesces as it becomes mostly foreground, and the
number of c.c. drops quickly.
(5) If there is no global threshold that distinguishes foreground
text from background (e.g., weak text over a background that
has significant variation and/or bleedthrough), this returns 1,
which the caller should check.
Definition at line 995 of file binarize.c.
◆ pixThresholdByHisto()
l_ok pixThresholdByHisto |
( |
PIX * |
pixs, |
|
|
l_int32 |
factor, |
|
|
l_int32 |
halfw, |
|
|
l_int32 |
skip, |
|
|
l_int32 * |
pthresh, |
|
|
PIX ** |
ppixd, |
|
|
NUMA ** |
pnahisto, |
|
|
PIX ** |
ppixhisto |
|
) |
| |
pixThresholdByHisto()
- Parameters
-
[in] | pixs | gray 8 bpp, no colormap |
[in] | factor | subsampling factor >= 1 |
[in] | halfw | half of window width for smoothing; use 0 for default |
[in] | skip | look-ahead distance to avoid false minima; use 0 for default |
[out] | pthresh | best global threshold; 0 if no threshold is found |
[out] | ppixd | [optional] thresholded 1 bpp pix |
[out] | pnahisto | [optional] rescaled histogram of gray values |
[out] | ppixhisto | [optional] plot of rescaled histogram |
- Returns
- 0 if OK, 1 on error or if no threshold is found
Notes:
(1) This finds a global threshold. It is best for an image that
has a fairly well-defined fg and bg.
(2) If it finds a good threshold and ppixd is defined, the binarized
image is returned in otherwise it return null.
(3) See numaFindLocForThreshold() for use of skip.
(4) Suggest using default values (20) for half and skip.
(5) Returns 0 in pthresh if it can't find a good threshold.
Definition at line 1151 of file binarize.c.
◆ pixThreshOnDoubleNorm()
PIX* pixThreshOnDoubleNorm |
( |
PIX * |
pixs, |
|
|
l_int32 |
mindiff |
|
) |
| |
pixThreshOnDoubleNorm()
- Parameters
-
[in] | pixs | 8 or 32 bpp |
[in] | mindiff | minimum diff to accept as valid in contrast normalization. Use ~130 for noisy images. |
- Returns
- pixd 1 bpp thresholded image, or NULL on error
Notes:
(1) This composite operation is good for adaptively removing
dark background.
(2) The threshold for the binarization uses an estimate based
on Otsu adaptive thresholding.
Definition at line 904 of file binarize.c.