- NAME
- VERSION
- convolve.c
- FUNCTIONS
- fpixConvolve
- fpixConvolveSep
- gaussDistribSampling
- l_setConvolveSampling
- pixAddGaussianNoise
- pixBlockconv
- pixBlockconvAccum
- pixBlockconvGray
- pixBlockconvGrayTile
- pixBlockconvGrayUnnormalized
- pixBlockconvTiled
- pixBlockrank
- pixBlocksum
- pixCensusTransform
- pixConvolve
- pixConvolveRGB
- pixConvolveRGBSep
- pixConvolveSep
- pixConvolveWithBias
- pixMeanSquareAccum
- pixWindowedMean
- pixWindowedMeanSquare
- pixWindowedStats
- pixWindowedVariance

- AUTHOR
- COPYRIGHT AND LICENSE

# NAME

Image::Leptonica::Func::convolve

# VERSION

version 0.04

`convolve.c`

```
convolve.c
Top level grayscale or color block convolution
PIX *pixBlockconv()
Grayscale block convolution
PIX *pixBlockconvGray()
Accumulator for 1, 8 and 32 bpp convolution
PIX *pixBlockconvAccum()
Un-normalized grayscale block convolution
PIX *pixBlockconvGrayUnnormalized()
Tiled grayscale or color block convolution
PIX *pixBlockconvTiled()
PIX *pixBlockconvGrayTile()
Convolution for mean, mean square, variance and rms deviation
in specified window
l_int32 pixWindowedStats()
PIX *pixWindowedMean()
PIX *pixWindowedMeanSquare()
l_int32 pixWindowedVariance()
DPIX *pixMeanSquareAccum()
Binary block sum and rank filter
PIX *pixBlockrank()
PIX *pixBlocksum()
Census transform
PIX *pixCensusTransform()
Generic convolution (with Pix)
PIX *pixConvolve()
PIX *pixConvolveSep()
PIX *pixConvolveRGB()
PIX *pixConvolveRGBSep()
Generic convolution (with float arrays)
FPIX *fpixConvolve()
FPIX *fpixConvolveSep()
Convolution with bias (for non-negative output)
PIX *pixConvolveWithBias()
Set parameter for convolution subsampling
void l_setConvolveSampling()
Additive gaussian noise
PIX *pixAddGaussNoise()
l_float32 gaussDistribSampling()
```

# FUNCTIONS

## fpixConvolve

FPIX * fpixConvolve ( FPIX *fpixs, L_KERNEL *kel, l_int32 normflag )

```
fpixConvolve()
Input: fpixs (32 bit float array)
kernel
normflag (1 to normalize kernel to unit sum; 0 otherwise)
Return: fpixd (32 bit float array)
Notes:
(1) This gives a float convolution with an arbitrary kernel.
(2) If normflag == 1, the result is normalized by scaling all
kernel values for a unit sum. If the sum of kernel values
is very close to zero, the kernel can not be normalized and
the convolution will not be performed. A warning is issued.
(3) With the FPix, there are no issues about negative
array or kernel values. The convolution is performed
with single precision arithmetic.
(4) To get a subsampled output, call l_setConvolveSampling().
The time to make a subsampled output is reduced by the
product of the sampling factors.
(5) This uses a mirrored border to avoid special casing on
the boundaries.
```

## fpixConvolveSep

FPIX * fpixConvolveSep ( FPIX *fpixs, L_KERNEL *kelx, L_KERNEL *kely, l_int32 normflag )

```
fpixConvolveSep()
Input: fpixs (32 bit float array)
kelx (x-dependent kernel)
kely (y-dependent kernel)
normflag (1 to normalize kernel to unit sum; 0 otherwise)
Return: fpixd (32 bit float array)
Notes:
(1) This does a convolution with a separable kernel that is
is a sequence of convolutions in x and y. The two
one-dimensional kernel components must be input separately;
the full kernel is the product of these components.
The support for the full kernel is thus a rectangular region.
(2) The normflag parameter is used as in fpixConvolve().
(3) Warning: if you use l_setConvolveSampling() to get a
subsampled output, and the sampling factor is larger than
the kernel half-width, it is faster to use the non-separable
version pixConvolve(). This is because the first convolution
here must be done on every raster line, regardless of the
vertical sampling factor. If the sampling factor is smaller
than kernel half-width, it's faster to use the separable
convolution.
(4) This uses mirrored borders to avoid special casing on
the boundaries.
```

## gaussDistribSampling

l_float32 gaussDistribSampling ( )

```
gaussDistribSampling()
Return: gaussian distributed variable with zero mean and unit stdev
Notes:
(1) For an explanation of the Box-Muller method for generating
a normally distributed random variable with zero mean and
unit standard deviation, see Numerical Recipes in C,
2nd edition, p. 288ff.
(2) This can be called sequentially to get samples that can be
used for adding noise to each pixel of an image, for example.
```

## l_setConvolveSampling

void l_setConvolveSampling ( l_int32 xfact, l_int32 yfact )

```
l_setConvolveSampling()
Input: xfact, yfact (integer >= 1)
Return: void
Notes:
(1) This sets the x and y output subsampling factors for generic pix
and fpix convolution. The default values are 1 (no subsampling).
```

## pixAddGaussianNoise

PIX * pixAddGaussianNoise ( PIX *pixs, l_float32 stdev )

```
pixAddGaussianNoise()
Input: pixs (8 bpp gray or 32 bpp rgb; no colormap)
stdev (of noise)
Return: pixd (8 or 32 bpp), or null on error
Notes:
(1) This adds noise to each pixel, taken from a normal
distribution with zero mean and specified standard deviation.
```

## pixBlockconv

PIX * pixBlockconv ( PIX *pix, l_int32 wc, l_int32 hc )

```
pixBlockconv()
Input: pix (8 or 32 bpp; or 2, 4 or 8 bpp with colormap)
wc, hc (half width/height of convolution kernel)
Return: pixd, or null on error
Notes:
(1) The full width and height of the convolution kernel
are (2 * wc + 1) and (2 * hc + 1)
(2) Returns a copy if both wc and hc are 0
(3) Require that w >= 2 * wc + 1 and h >= 2 * hc + 1,
where (w,h) are the dimensions of pixs.
```

## pixBlockconvAccum

PIX * pixBlockconvAccum ( PIX *pixs )

```
pixBlockconvAccum()
Input: pixs (1, 8 or 32 bpp)
Return: accum pix (32 bpp), or null on error.
Notes:
(1) The general recursion relation is
a(i,j) = v(i,j) + a(i-1, j) + a(i, j-1) - a(i-1, j-1)
For the first line, this reduces to the special case
a(i,j) = v(i,j) + a(i, j-1)
For the first column, the special case is
a(i,j) = v(i,j) + a(i-1, j)
```

## pixBlockconvGray

PIX * pixBlockconvGray ( PIX *pixs, PIX *pixacc, l_int32 wc, l_int32 hc )

```
pixBlockconvGray()
Input: pix (8 bpp)
accum pix (32 bpp; can be null)
wc, hc (half width/height of convolution kernel)
Return: pix (8 bpp), or null on error
Notes:
(1) If accum pix is null, make one and destroy it before
returning; otherwise, just use the input accum pix.
(2) The full width and height of the convolution kernel
are (2 * wc + 1) and (2 * hc + 1).
(3) Returns a copy if both wc and hc are 0.
(4) Require that w >= 2 * wc + 1 and h >= 2 * hc + 1,
where (w,h) are the dimensions of pixs.
```

## pixBlockconvGrayTile

PIX * pixBlockconvGrayTile ( PIX *pixs, PIX *pixacc, l_int32 wc, l_int32 hc )

```
pixBlockconvGrayTile()
Input: pixs (8 bpp gray)
pixacc (32 bpp accum pix)
wc, hc (half width/height of convolution kernel)
Return: pixd, or null on error
Notes:
(1) The full width and height of the convolution kernel
are (2 * wc + 1) and (2 * hc + 1)
(2) Assumes that the input pixs is padded with (wc + 1) pixels on
left and right, and with (hc + 1) pixels on top and bottom.
The returned pix has these stripped off; they are only used
for computation.
(3) Returns a copy if both wc and hc are 0
(4) Require that w > 2 * wc + 1 and h > 2 * hc + 1,
where (w,h) are the dimensions of pixs.
```

## pixBlockconvGrayUnnormalized

PIX * pixBlockconvGrayUnnormalized ( PIX *pixs, l_int32 wc, l_int32 hc )

```
pixBlockconvGrayUnnormalized()
Input: pixs (8 bpp)
wc, hc (half width/height of convolution kernel)
Return: pix (32 bpp; containing the convolution without normalizing
for the window size), or null on error
Notes:
(1) The full width and height of the convolution kernel
are (2 * wc + 1) and (2 * hc + 1).
(2) Require that w >= 2 * wc + 1 and h >= 2 * hc + 1,
where (w,h) are the dimensions of pixs.
(3) Returns a copy if both wc and hc are 0.
(3) Adds mirrored border to avoid treating the boundary pixels
specially. Note that we add wc + 1 pixels to the left
and wc to the right. The added width is 2 * wc + 1 pixels,
and the particular choice simplifies the indexing in the loop.
Likewise, add hc + 1 pixels to the top and hc to the bottom.
(4) To get the normalized result, divide by the area of the
convolution kernel: (2 * wc + 1) * (2 * hc + 1)
Specifically, do this:
pixc = pixBlockconvGrayUnnormalized(pixs, wc, hc);
fract = 1. / ((2 * wc + 1) * (2 * hc + 1));
pixMultConstantGray(pixc, fract);
pixd = pixGetRGBComponent(pixc, L_ALPHA_CHANNEL);
(5) Unlike pixBlockconvGray(), this always computes the accumulation
pix because its size is tied to wc and hc.
(6) Compare this implementation with pixBlockconvGray(), where
most of the code in blockconvLow() is special casing for
efficiently handling the boundary. Here, the use of
mirrored borders and destination indexing makes the
implementation very simple.
```

## pixBlockconvTiled

PIX * pixBlockconvTiled ( PIX *pix, l_int32 wc, l_int32 hc, l_int32 nx, l_int32 ny )

```
pixBlockconvTiled()
Input: pix (8 or 32 bpp; or 2, 4 or 8 bpp with colormap)
wc, hc (half width/height of convolution kernel)
nx, ny (subdivision into tiles)
Return: pixd, or null on error
Notes:
(1) The full width and height of the convolution kernel
are (2 * wc + 1) and (2 * hc + 1)
(2) Returns a copy if both wc and hc are 0
(3) Require that w >= 2 * wc + 1 and h >= 2 * hc + 1,
where (w,h) are the dimensions of pixs.
(4) For nx == ny == 1, this defaults to pixBlockconv(), which
is typically about twice as fast, and gives nearly
identical results as pixBlockconvGrayTile().
(5) If the tiles are too small, nx and/or ny are reduced
a minimum amount so that the tiles are expanded to the
smallest workable size in the problematic direction(s).
(6) Why a tiled version? Three reasons:
(a) Because the accumulator is a uint32, overflow can occur
for an image with more than 16M pixels.
(b) The accumulator array for 16M pixels is 64 MB; using
tiles reduces the size of this array.
(c) Each tile can be processed independently, in parallel,
on a multicore processor.
```

## pixBlockrank

PIX * pixBlockrank ( PIX *pixs, PIX *pixacc, l_int32 wc, l_int32 hc, l_float32 rank )

```
pixBlockrank()
Input: pixs (1 bpp)
accum pix (<optional> 32 bpp)
wc, hc (half width/height of block sum/rank kernel)
rank (between 0.0 and 1.0; 0.5 is median filter)
Return: pixd (1 bpp)
Notes:
(1) The full width and height of the convolution kernel
are (2 * wc + 1) and (2 * hc + 1)
(2) This returns a pixd where each pixel is a 1 if the
neighborhood (2 * wc + 1) x (2 * hc + 1)) pixels
contains the rank fraction of 1 pixels. Otherwise,
the returned pixel is 0. Note that the special case
of rank = 0.0 is always satisfied, so the returned
pixd has all pixels with value 1.
(3) If accum pix is null, make one, use it, and destroy it
before returning; otherwise, just use the input accum pix
(4) If both wc and hc are 0, returns a copy unless rank == 0.0,
in which case this returns an all-ones image.
(5) Require that w >= 2 * wc + 1 and h >= 2 * hc + 1,
where (w,h) are the dimensions of pixs.
```

## pixBlocksum

PIX * pixBlocksum ( PIX *pixs, PIX *pixacc, l_int32 wc, l_int32 hc )

```
pixBlocksum()
Input: pixs (1 bpp)
accum pix (<optional> 32 bpp)
wc, hc (half width/height of block sum/rank kernel)
Return: pixd (8 bpp)
Notes:
(1) If accum pix is null, make one and destroy it before
returning; otherwise, just use the input accum pix
(2) The full width and height of the convolution kernel
are (2 * wc + 1) and (2 * hc + 1)
(3) Use of wc = hc = 1, followed by pixInvert() on the
8 bpp result, gives a nice anti-aliased, and somewhat
darkened, result on text.
(4) Require that w >= 2 * wc + 1 and h >= 2 * hc + 1,
where (w,h) are the dimensions of pixs.
(5) Returns in each dest pixel the sum of all src pixels
that are within a block of size of the kernel, centered
on the dest pixel. This sum is the number of src ON
pixels in the block at each location, normalized to 255
for a block containing all ON pixels. For pixels near
the boundary, where the block is not entirely contained
within the image, we then multiply by a second normalization
factor that is greater than one, so that all results
are normalized by the number of participating pixels
within the block.
```

## pixCensusTransform

PIX * pixCensusTransform ( PIX *pixs, l_int32 halfsize, PIX *pixacc )

```
pixCensusTransform()
Input: pixs (8 bpp)
halfsize (of square over which neighbors are averaged)
accum pix (<optional> 32 bpp)
Return: pixd (1 bpp)
Notes:
(1) The Census transform was invented by Ramin Zabih and John Woodfill
("Non-parametric local transforms for computing visual
correspondence", Third European Conference on Computer Vision,
Stockholm, Sweden, May 1994); see publications at
http://www.cs.cornell.edu/~rdz/index.htm
This compares each pixel against the average of its neighbors,
in a square of odd dimension centered on the pixel.
If the pixel is greater than the average of its neighbors,
the output pixel value is 1; otherwise it is 0.
(2) This can be used as an encoding for an image that is
fairly robust against slow illumination changes, with
applications in image comparison and mosaicing.
(3) The size of the convolution kernel is (2 * halfsize + 1)
on a side. The halfsize parameter must be >= 1.
(4) If accum pix is null, make one, use it, and destroy it
before returning; otherwise, just use the input accum pix
```

## pixConvolve

PIX * pixConvolve ( PIX *pixs, L_KERNEL *kel, l_int32 outdepth, l_int32 normflag )

```
pixConvolve()
Input: pixs (8, 16, 32 bpp; no colormap)
kernel
outdepth (of pixd: 8, 16 or 32)
normflag (1 to normalize kernel to unit sum; 0 otherwise)
Return: pixd (8, 16 or 32 bpp)
Notes:
(1) This gives a convolution with an arbitrary kernel.
(2) The input pixs must have only one sample/pixel.
To do a convolution on an RGB image, use pixConvolveRGB().
(3) The parameter @outdepth determines the depth of the result.
If the kernel is normalized to unit sum, the output values
can never exceed 255, so an output depth of 8 bpp is sufficient.
If the kernel is not normalized, it may be necessary to use
16 or 32 bpp output to avoid overflow.
(4) If normflag == 1, the result is normalized by scaling all
kernel values for a unit sum. If the sum of kernel values
is very close to zero, the kernel can not be normalized and
the convolution will not be performed. A warning is issued.
(5) The kernel values can be positive or negative, but the
result for the convolution can only be stored as a positive
number. Consequently, if it goes negative, the choices are
to clip to 0 or take the absolute value. We're choosing
to take the absolute value. (Another possibility would be
to output a second unsigned image for the negative values.)
If you want to get a clipped result, or to keep the negative
values in the result, use fpixConvolve(), with the
converters in fpix2.c between pix and fpix.
(6) This uses a mirrored border to avoid special casing on
the boundaries.
(7) To get a subsampled output, call l_setConvolveSampling().
The time to make a subsampled output is reduced by the
product of the sampling factors.
(8) The function is slow, running at about 12 machine cycles for
each pixel-op in the convolution. For example, with a 3 GHz
cpu, a 1 Mpixel grayscale image, and a kernel with
(sx * sy) = 25 elements, the convolution takes about 100 msec.
```

## pixConvolveRGB

PIX * pixConvolveRGB ( PIX *pixs, L_KERNEL *kel )

```
pixConvolveRGB()
Input: pixs (32 bpp rgb)
kernel
Return: pixd (32 bpp rgb)
Notes:
(1) This gives a convolution on an RGB image using an
arbitrary kernel (which we normalize to keep each
component within the range [0 ... 255].
(2) The input pixs must be RGB.
(3) The kernel values can be positive or negative, but the
result for the convolution can only be stored as a positive
number. Consequently, if it goes negative, we clip the
result to 0.
(4) To get a subsampled output, call l_setConvolveSampling().
The time to make a subsampled output is reduced by the
product of the sampling factors.
(5) This uses a mirrored border to avoid special casing on
the boundaries.
```

## pixConvolveRGBSep

PIX * pixConvolveRGBSep ( PIX *pixs, L_KERNEL *kelx, L_KERNEL *kely )

```
pixConvolveRGBSep()
Input: pixs (32 bpp rgb)
kelx (x-dependent kernel)
kely (y-dependent kernel)
Return: pixd (32 bpp rgb)
Notes:
(1) This does a convolution on an RGB image using a separable
kernel that is a sequence of convolutions in x and y. The two
one-dimensional kernel components must be input separately;
the full kernel is the product of these components.
The support for the full kernel is thus a rectangular region.
(2) The kernel values can be positive or negative, but the
result for the convolution can only be stored as a positive
number. Consequently, if it goes negative, we clip the
result to 0.
(3) To get a subsampled output, call l_setConvolveSampling().
The time to make a subsampled output is reduced by the
product of the sampling factors.
(4) This uses a mirrored border to avoid special casing on
the boundaries.
```

## pixConvolveSep

PIX * pixConvolveSep ( PIX *pixs, L_KERNEL *kelx, L_KERNEL *kely, l_int32 outdepth, l_int32 normflag )

```
pixConvolveSep()
Input: pixs (8, 16, 32 bpp; no colormap)
kelx (x-dependent kernel)
kely (y-dependent kernel)
outdepth (of pixd: 8, 16 or 32)
normflag (1 to normalize kernel to unit sum; 0 otherwise)
Return: pixd (8, 16 or 32 bpp)
Notes:
(1) This does a convolution with a separable kernel that is
is a sequence of convolutions in x and y. The two
one-dimensional kernel components must be input separately;
the full kernel is the product of these components.
The support for the full kernel is thus a rectangular region.
(2) The input pixs must have only one sample/pixel.
To do a convolution on an RGB image, use pixConvolveSepRGB().
(3) The parameter @outdepth determines the depth of the result.
If the kernel is normalized to unit sum, the output values
can never exceed 255, so an output depth of 8 bpp is sufficient.
If the kernel is not normalized, it may be necessary to use
16 or 32 bpp output to avoid overflow.
(2) The @normflag parameter is used as in pixConvolve().
(4) The kernel values can be positive or negative, but the
result for the convolution can only be stored as a positive
number. Consequently, if it goes negative, the choices are
to clip to 0 or take the absolute value. We're choosing
the former for now. Another possibility would be to output
a second unsigned image for the negative values.
(5) Warning: if you use l_setConvolveSampling() to get a
subsampled output, and the sampling factor is larger than
the kernel half-width, it is faster to use the non-separable
version pixConvolve(). This is because the first convolution
here must be done on every raster line, regardless of the
vertical sampling factor. If the sampling factor is smaller
than kernel half-width, it's faster to use the separable
convolution.
(6) This uses mirrored borders to avoid special casing on
the boundaries.
```

## pixConvolveWithBias

PIX * pixConvolveWithBias ( PIX *pixs, L_KERNEL *kel1, L_KERNEL *kel2, l_int32 force8, l_int32 *pbias )

```
pixConvolveWithBias()
Input: pixs (8 bpp; no colormap)
kel1
kel2 (can be null; use if separable)
force8 (if 1, force output to 8 bpp; otherwise, determine
output depth by the dynamic range of pixel values)
&bias (<return> applied bias)
Return: pixd (8 or 16 bpp)
Notes:
(1) This does a convolution with either a single kernel or
a pair of separable kernels, and automatically applies whatever
bias (shift) is required so that the resulting pixel values
are non-negative.
(2) The kernel is always normalized. If there are no negative
values in the kernel, a standard normalized convolution is
performed, with 8 bpp output. If the sum of kernel values is
very close to zero, the kernel can not be normalized and
the convolution will not be performed. An error message results.
(3) If there are negative values in the kernel, the pix is
converted to an fpix, the convolution is done on the fpix, and
a bias (shift) may need to be applied.
(4) If force8 == TRUE and the range of values after the convolution
is > 255, the output values will be scaled to fit in [0 ... 255].
If force8 == FALSE, the output will be either 8 or 16 bpp,
to accommodate the dynamic range of output values without scaling.
```

## pixMeanSquareAccum

DPIX * pixMeanSquareAccum ( PIX *pixs )

```
pixMeanSquareAccum()
Input: pixs (8 bpp grayscale)
Return: dpix (64 bit array), or null on error
Notes:
(1) Similar to pixBlockconvAccum(), this computes the
sum of the squares of the pixel values in such a way
that the value at (i,j) is the sum of all squares in
the rectangle from the origin to (i,j).
(2) The general recursion relation (v are squared pixel values) is
a(i,j) = v(i,j) + a(i-1, j) + a(i, j-1) - a(i-1, j-1)
For the first line, this reduces to the special case
a(i,j) = v(i,j) + a(i, j-1)
For the first column, the special case is
a(i,j) = v(i,j) + a(i-1, j)
```

## pixWindowedMean

PIX * pixWindowedMean ( PIX *pixs, l_int32 wc, l_int32 hc, l_int32 hasborder, l_int32 normflag )

```
pixWindowedMean()
Input: pixs (8 or 32 bpp grayscale)
wc, hc (half width/height of convolution kernel)
hasborder (use 1 if it already has (wc + 1) border pixels
on left and right, and (hc + 1) on top and bottom;
use 0 to add kernel-dependent border)
normflag (1 for normalization to get average in window;
0 for the sum in the window (un-normalized))
Return: pixd (8 or 32 bpp, average over kernel window)
Notes:
(1) The input and output depths are the same.
(2) A set of border pixels of width (wc + 1) on left and right,
and of height (hc + 1) on top and bottom, must be on the
pix before the accumulator is found. The output pixd
(after convolution) has this border removed.
If @hasborder = 0, the required border is added.
(3) Typically, @normflag == 1. However, if you want the sum
within the window, rather than a normalized convolution,
use @normflag == 0.
(4) This builds a block accumulator pix, uses it here, and
destroys it.
(5) The added border, along with the use of an accumulator array,
allows computation without special treatment of pixels near
the image boundary, and runs in a time that is independent
of the size of the convolution kernel.
```

## pixWindowedMeanSquare

PIX * pixWindowedMeanSquare ( PIX *pixs, l_int32 wc, l_int32 hc, l_int32 hasborder )

```
pixWindowedMeanSquare()
Input: pixs (8 bpp grayscale)
wc, hc (half width/height of convolution kernel)
hasborder (use 1 if it already has (wc + 1) border pixels
on left and right, and (hc + 1) on top and bottom;
use 0 to add kernel-dependent border)
Return: pixd (32 bpp, average over rectangular window of
width = 2 * wc + 1 and height = 2 * hc + 1)
Notes:
(1) A set of border pixels of width (wc + 1) on left and right,
and of height (hc + 1) on top and bottom, must be on the
pix before the accumulator is found. The output pixd
(after convolution) has this border removed.
If @hasborder = 0, the required border is added.
(2) The advantage is that we are unaffected by the boundary, and
it is not necessary to treat pixels within @wc and @hc of the
border differently. This is because processing for pixd
only takes place for pixels in pixs for which the
kernel is entirely contained in pixs.
(3) Why do we have an added border of width (@wc + 1) and
height (@hc + 1), when we only need @wc and @hc pixels
to satisfy this condition? Answer: the accumulators
are asymmetric, requiring an extra row and column of
pixels at top and left to work accurately.
(4) The added border, along with the use of an accumulator array,
allows computation without special treatment of pixels near
the image boundary, and runs in a time that is independent
of the size of the convolution kernel.
```

## pixWindowedStats

l_int32 pixWindowedStats ( PIX *pixs, l_int32 wc, l_int32 hc, l_int32 hasborder, PIX **ppixm, PIX **ppixms, FPIX **pfpixv, FPIX **pfpixrv )

```
pixWindowedStats()
Input: pixs (8 bpp grayscale)
wc, hc (half width/height of convolution kernel)
hasborder (use 1 if it already has (wc + 1) border pixels
on left and right, and (hc + 1) on top and bottom;
use 0 to add kernel-dependent border)
&pixm (<optional return> 8 bpp mean value in window)
&pixms (<optional return> 32 bpp mean square value in window)
&fpixv (<optional return> float variance in window)
&fpixrv (<optional return> float rms deviation from the mean)
Return: 0 if OK, 1 on error
Notes:
(1) This is a high-level convenience function for calculating
any or all of these derived images.
(2) If @hasborder = 0, a border is added and the result is
computed over all pixels in pixs. Otherwise, no border is
added and the border pixels are removed from the output images.
(3) These statistical measures over the pixels in the
rectangular window are:
- average value: <p> (pixm)
- average squared value: <p*p> (pixms)
- variance: <(p - <p>)*(p - <p>)> = <p*p> - <p>*<p> (pixv)
- square-root of variance: (pixrv)
where the brackets < .. > indicate that the average value is
to be taken over the window.
(4) Note that the variance is just the mean square difference from
the mean value; and the square root of the variance is the
root mean square difference from the mean, sometimes also
called the 'standard deviation'.
(5) The added border, along with the use of an accumulator array,
allows computation without special treatment of pixels near
the image boundary, and runs in a time that is independent
of the size of the convolution kernel.
```

## pixWindowedVariance

l_int32 pixWindowedVariance ( PIX *pixm, PIX *pixms, FPIX **pfpixv, FPIX **pfpixrv )

```
pixWindowedVariance()
Input: pixm (mean over window; 8 or 32 bpp grayscale)
pixms (mean square over window; 32 bpp)
&fpixv (<optional return> float variance -- the ms deviation
from the mean)
&fpixrv (<optional return> float rms deviation from the mean)
Return: 0 if OK, 1 on error
Notes:
(1) The mean and mean square values are precomputed, using
pixWindowedMean() and pixWindowedMeanSquare().
(2) Either or both of the variance and square-root of variance
are returned as an fpix, where the variance is the
average over the window of the mean square difference of
the pixel value from the mean:
<(p - <p>)*(p - <p>)> = <p*p> - <p>*<p>
(3) To visualize the results:
- for both, use fpixDisplayMaxDynamicRange().
- for rms deviation, simply convert the output fpix to pix,
```

# 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.