- NAME
- VERSION
- morph.c
- FUNCTIONS
- getMorphBorderPixelColor
- pixClose
- pixCloseBrick
- pixCloseCompBrick
- pixCloseGeneralized
- pixCloseSafe
- pixCloseSafeBrick
- pixCloseSafeCompBrick
- pixDilate
- pixDilateBrick
- pixDilateCompBrick
- pixErode
- pixErodeBrick
- pixErodeCompBrick
- pixHMT
- pixOpen
- pixOpenBrick
- pixOpenCompBrick
- pixOpenGeneralized
- resetMorphBoundaryCondition
- selectComposableSels
- selectComposableSizes

- AUTHOR
- COPYRIGHT AND LICENSE

# NAME

Image::Leptonica::Func::morph

# VERSION

version 0.04

`morph.c`

```
morph.c
Generic binary morphological ops implemented with rasterop
PIX *pixDilate()
PIX *pixErode()
PIX *pixHMT()
PIX *pixOpen()
PIX *pixClose()
PIX *pixCloseSafe()
PIX *pixOpenGeneralized()
PIX *pixCloseGeneralized()
Binary morphological (raster) ops with brick Sels
PIX *pixDilateBrick()
PIX *pixErodeBrick()
PIX *pixOpenBrick()
PIX *pixCloseBrick()
PIX *pixCloseSafeBrick()
Binary composed morphological (raster) ops with brick Sels
l_int32 selectComposableSels()
l_int32 selectComposableSizes()
PIX *pixDilateCompBrick()
PIX *pixErodeCompBrick()
PIX *pixOpenCompBrick()
PIX *pixCloseCompBrick()
PIX *pixCloseSafeCompBrick()
Functions associated with boundary conditions
void resetMorphBoundaryCondition()
l_int32 getMorphBorderPixelColor()
Static helpers for arg processing
static PIX *processMorphArgs1()
static PIX *processMorphArgs2()
You are provided with many simple ways to do binary morphology.
In particular, if you are using brick Sels, there are six
convenient methods, all specially tailored for separable operations
on brick Sels. A "brick" Sel is a Sel that is a rectangle
of solid SEL_HITs with the origin at or near the center.
Note that a brick Sel can have one dimension of size 1.
This is very common. All the brick Sel operations are
separable, meaning the operation is done first in the horizontal
direction and then in the vertical direction. If one of the
dimensions is 1, this is a special case where the operation is
only performed in the other direction.
These six brick Sel methods are enumerated as follows:
(1) Brick Sels: pix*Brick(), where * = {Dilate, Erode, Open, Close}.
These are separable rasterop implementations. The Sels are
automatically generated, used, and destroyed at the end.
You can get the result as a new Pix, in-place back into the src Pix,
or written to another existing Pix.
(2) Brick Sels: pix*CompBrick(), where * = {Dilate, Erode, Open, Close}.
These are separable, 2-way composite, rasterop implementations.
The Sels are automatically generated, used, and destroyed at the end.
You can get the result as a new Pix, in-place back into the src Pix,
or written to another existing Pix. For large Sels, these are
considerably faster than the corresponding pix*Brick() functions.
N.B.: The size of the Sels that are actually used are typically
close to, but not exactly equal to, the size input to the function.
(3) Brick Sels: pix*BrickDwa(), where * = {Dilate, Erode, Open, Close}.
These are separable dwa (destination word accumulation)
implementations. They use auto-gen'd dwa code. You can get
the result as a new Pix, in-place back into the src Pix,
or written to another existing Pix. This is typically
about 3x faster than the analogous rasterop pix*Brick()
function, but it has the limitation that the Sel size must
be less than 63. This is pre-set to work on a number
of pre-generated Sels. If you want to use other Sels, the
code can be auto-gen'd for them; see the instructions in morphdwa.c.
(4) Same as (1), but you run it through pixMorphSequence(), with
the sequence string either compiled in or generated using sprintf.
All intermediate images and Sels are created, used and destroyed.
You always get the result as a new Pix. For example, you can
specify a separable 11 x 17 brick opening as "o11.17",
or you can specify the horizontal and vertical operations
explicitly as "o11.1 + o1.11". See morphseq.c for details.
(5) Same as (2), but you run it through pixMorphCompSequence(), with
the sequence string either compiled in or generated using sprintf.
All intermediate images and Sels are created, used and destroyed.
You always get the result as a new Pix. See morphseq.c for details.
(6) Same as (3), but you run it through pixMorphSequenceDwa(), with
the sequence string either compiled in or generated using sprintf.
All intermediate images and Sels are created, used and destroyed.
You always get the result as a new Pix. See morphseq.c for details.
If you are using Sels that are not bricks, you have two choices:
(a) simplest: use the basic rasterop implementations (pixDilate(), ...)
(b) fastest: generate the destination word accumumlation (dwa)
code for your Sels and compile it with the library.
For an example, see flipdetect.c, which gives implementations
using hit-miss Sels with both the rasterop and dwa versions.
For the latter, the dwa code resides in fliphmtgen.c, and it
was generated by prog/flipselgen.c. Both the rasterop and dwa
implementations are tested by prog/fliptest.c.
A global constant MORPH_BC is used to set the boundary conditions
for rasterop-based binary morphology. MORPH_BC, in morph.c,
is set by default to ASYMMETRIC_MORPH_BC for a non-symmetric
convention for boundary pixels in dilation and erosion:
All pixels outside the image are assumed to be OFF
for both dilation and erosion.
To use a symmetric definition, see comments in pixErode()
and reset MORPH_BC to SYMMETRIC_MORPH_BC, using
resetMorphBoundaryCondition().
Boundary artifacts are possible in closing when the non-symmetric
boundary conditions are used, because foreground pixels very close
to the edge can be removed. This can be avoided by using either
the symmetric boundary conditions or the function pixCloseSafe(),
which adds a border before the operation and removes it afterwards.
The hit-miss transform (HMT) is the bit-and of 2 erosions:
(erosion of the src by the hits) & (erosion of the bit-inverted
src by the misses)
The 'generalized opening' is an HMT followed by a dilation that uses
only the hits of the hit-miss Sel.
The 'generalized closing' is a dilation (again, with the hits
of a hit-miss Sel), followed by the HMT.
Both of these 'generalized' functions are idempotent.
These functions are extensively tested in prog/binmorph1_reg.c,
prog/binmorph2_reg.c, and prog/binmorph3_reg.c.
```

# FUNCTIONS

## getMorphBorderPixelColor

l_uint32 getMorphBorderPixelColor ( l_int32 type, l_int32 depth )

```
getMorphBorderPixelColor()
Input: type (L_MORPH_DILATE, L_MORPH_ERODE)
depth (of pix)
Return: color of border pixels for this operation
```

## pixClose

PIX * pixClose ( PIX *pixd, PIX *pixs, SEL *sel )

```
pixClose()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
sel
Return: pixd
Notes:
(1) Generic morphological closing, using hits in the Sel.
(2) This implementation is a strict dual of the opening if
symmetric boundary conditions are used (see notes at top
of this file).
(3) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(4) For clarity, if the case is known, use these patterns:
(a) pixd = pixClose(NULL, pixs, ...);
(b) pixClose(pixs, pixs, ...);
(c) pixClose(pixd, pixs, ...);
(5) The size of the result is determined by pixs.
```

## pixCloseBrick

PIX * pixCloseBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixCloseBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd, or null on error
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do separably if both hsize and vsize are > 1.
(4) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(5) For clarity, if the case is known, use these patterns:
(a) pixd = pixCloseBrick(NULL, pixs, ...);
(b) pixCloseBrick(pixs, pixs, ...);
(c) pixCloseBrick(pixd, pixs, ...);
(6) The size of the result is determined by pixs.
```

## pixCloseCompBrick

PIX * pixCloseCompBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixCloseCompBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd, or null on error
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do compositely for each dimension > 1.
(4) Do separably if both hsize and vsize are > 1.
(5) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(6) For clarity, if the case is known, use these patterns:
(a) pixd = pixCloseCompBrick(NULL, pixs, ...);
(b) pixCloseCompBrick(pixs, pixs, ...);
(c) pixCloseCompBrick(pixd, pixs, ...);
(7) The dimensions of the resulting image are determined by pixs.
(8) CAUTION: both hsize and vsize are being decomposed.
The decomposer chooses a product of sizes (call them
'terms') for each that is close to the input size,
but not necessarily equal to it. It attempts to optimize:
(a) for consistency with the input values: the product
of terms is close to the input size
(b) for efficiency of the operation: the sum of the
terms is small; ideally about twice the square
root of the input size.
So, for example, if the input hsize = 37, which is
a prime number, the decomposer will break this into two
terms, 6 and 6, so that the net result is a dilation
with hsize = 36.
```

## pixCloseGeneralized

PIX * pixCloseGeneralized ( PIX *pixd, PIX *pixs, SEL *sel )

```
pixCloseGeneralized()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
sel
Return: pixd
Notes:
(1) Generalized morphological closing, using both hits and
misses in the Sel.
(2) This does a dilation using the hits, followed by a
hit-miss transform.
(3) This operation is a dual of the generalized opening.
(4) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(5) For clarity, if the case is known, use these patterns:
(a) pixd = pixCloseGeneralized(NULL, pixs, ...);
(b) pixCloseGeneralized(pixs, pixs, ...);
(c) pixCloseGeneralized(pixd, pixs, ...);
(6) The size of the result is determined by pixs.
```

## pixCloseSafe

PIX * pixCloseSafe ( PIX *pixd, PIX *pixs, SEL *sel )

```
pixCloseSafe()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
sel
Return: pixd
Notes:
(1) Generic morphological closing, using hits in the Sel.
(2) If non-symmetric boundary conditions are used, this
function adds a border of OFF pixels that is of
sufficient size to avoid losing pixels from the dilation,
and it removes the border after the operation is finished.
It thus enforces a correct extensive result for closing.
(3) If symmetric b.c. are used, it is not necessary to add
and remove this border.
(4) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(5) For clarity, if the case is known, use these patterns:
(a) pixd = pixCloseSafe(NULL, pixs, ...);
(b) pixCloseSafe(pixs, pixs, ...);
(c) pixCloseSafe(pixd, pixs, ...);
(6) The size of the result is determined by pixs.
```

## pixCloseSafeBrick

PIX * pixCloseSafeBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixCloseSafeBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd, or null on error
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do separably if both hsize and vsize are > 1.
(4) Safe closing adds a border of 0 pixels, of sufficient size so
that all pixels in input image are processed within
32-bit words in the expanded image. As a result, there is
no special processing for pixels near the boundary, and there
are no boundary effects. The border is removed at the end.
(5) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(6) For clarity, if the case is known, use these patterns:
(a) pixd = pixCloseBrick(NULL, pixs, ...);
(b) pixCloseBrick(pixs, pixs, ...);
(c) pixCloseBrick(pixd, pixs, ...);
(7) The size of the result is determined by pixs.
```

## pixCloseSafeCompBrick

PIX * pixCloseSafeCompBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixCloseSafeCompBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd, or null on error
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do compositely for each dimension > 1.
(4) Do separably if both hsize and vsize are > 1.
(5) Safe closing adds a border of 0 pixels, of sufficient size so
that all pixels in input image are processed within
32-bit words in the expanded image. As a result, there is
no special processing for pixels near the boundary, and there
are no boundary effects. The border is removed at the end.
(6) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(7) For clarity, if the case is known, use these patterns:
(a) pixd = pixCloseSafeCompBrick(NULL, pixs, ...);
(b) pixCloseSafeCompBrick(pixs, pixs, ...);
(c) pixCloseSafeCompBrick(pixd, pixs, ...);
(8) The dimensions of the resulting image are determined by pixs.
(9) CAUTION: both hsize and vsize are being decomposed.
The decomposer chooses a product of sizes (call them
'terms') for each that is close to the input size,
but not necessarily equal to it. It attempts to optimize:
(a) for consistency with the input values: the product
of terms is close to the input size
(b) for efficiency of the operation: the sum of the
terms is small; ideally about twice the square
root of the input size.
So, for example, if the input hsize = 37, which is
a prime number, the decomposer will break this into two
terms, 6 and 6, so that the net result is a dilation
with hsize = 36.
```

## pixDilate

PIX * pixDilate ( PIX *pixd, PIX *pixs, SEL *sel )

```
pixDilate()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
sel
Return: pixd
Notes:
(1) This dilates src using hits in Sel.
(2) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(3) For clarity, if the case is known, use these patterns:
(a) pixd = pixDilate(NULL, pixs, ...);
(b) pixDilate(pixs, pixs, ...);
(c) pixDilate(pixd, pixs, ...);
(4) The size of the result is determined by pixs.
```

## pixDilateBrick

PIX * pixDilateBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixDilateBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do separably if both hsize and vsize are > 1.
(4) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(5) For clarity, if the case is known, use these patterns:
(a) pixd = pixDilateBrick(NULL, pixs, ...);
(b) pixDilateBrick(pixs, pixs, ...);
(c) pixDilateBrick(pixd, pixs, ...);
(6) The size of the result is determined by pixs.
```

## pixDilateCompBrick

PIX * pixDilateCompBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixDilateCompBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd, or null on error
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do compositely for each dimension > 1.
(4) Do separably if both hsize and vsize are > 1.
(5) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(6) For clarity, if the case is known, use these patterns:
(a) pixd = pixDilateCompBrick(NULL, pixs, ...);
(b) pixDilateCompBrick(pixs, pixs, ...);
(c) pixDilateCompBrick(pixd, pixs, ...);
(7) The dimensions of the resulting image are determined by pixs.
(8) CAUTION: both hsize and vsize are being decomposed.
The decomposer chooses a product of sizes (call them
'terms') for each that is close to the input size,
but not necessarily equal to it. It attempts to optimize:
(a) for consistency with the input values: the product
of terms is close to the input size
(b) for efficiency of the operation: the sum of the
terms is small; ideally about twice the square
root of the input size.
So, for example, if the input hsize = 37, which is
a prime number, the decomposer will break this into two
terms, 6 and 6, so that the net result is a dilation
with hsize = 36.
```

## pixErode

PIX * pixErode ( PIX *pixd, PIX *pixs, SEL *sel )

```
pixErode()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
sel
Return: pixd
Notes:
(1) This erodes src using hits in Sel.
(2) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(3) For clarity, if the case is known, use these patterns:
(a) pixd = pixErode(NULL, pixs, ...);
(b) pixErode(pixs, pixs, ...);
(c) pixErode(pixd, pixs, ...);
(4) The size of the result is determined by pixs.
```

## pixErodeBrick

PIX * pixErodeBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixErodeBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do separably if both hsize and vsize are > 1.
(4) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(5) For clarity, if the case is known, use these patterns:
(a) pixd = pixErodeBrick(NULL, pixs, ...);
(b) pixErodeBrick(pixs, pixs, ...);
(c) pixErodeBrick(pixd, pixs, ...);
(6) The size of the result is determined by pixs.
```

## pixErodeCompBrick

PIX * pixErodeCompBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixErodeCompBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd, or null on error
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do compositely for each dimension > 1.
(4) Do separably if both hsize and vsize are > 1.
(5) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(6) For clarity, if the case is known, use these patterns:
(a) pixd = pixErodeCompBrick(NULL, pixs, ...);
(b) pixErodeCompBrick(pixs, pixs, ...);
(c) pixErodeCompBrick(pixd, pixs, ...);
(7) The dimensions of the resulting image are determined by pixs.
(8) CAUTION: both hsize and vsize are being decomposed.
The decomposer chooses a product of sizes (call them
'terms') for each that is close to the input size,
but not necessarily equal to it. It attempts to optimize:
(a) for consistency with the input values: the product
of terms is close to the input size
(b) for efficiency of the operation: the sum of the
terms is small; ideally about twice the square
root of the input size.
So, for example, if the input hsize = 37, which is
a prime number, the decomposer will break this into two
terms, 6 and 6, so that the net result is a dilation
with hsize = 36.
```

## pixHMT

PIX * pixHMT ( PIX *pixd, PIX *pixs, SEL *sel )

```
pixHMT()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
sel
Return: pixd
Notes:
(1) The hit-miss transform erodes the src, using both hits
and misses in the Sel. It ANDs the shifted src for hits
and ANDs the inverted shifted src for misses.
(2) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(3) For clarity, if the case is known, use these patterns:
(a) pixd = pixHMT(NULL, pixs, ...);
(b) pixHMT(pixs, pixs, ...);
(c) pixHMT(pixd, pixs, ...);
(4) The size of the result is determined by pixs.
```

## pixOpen

PIX * pixOpen ( PIX *pixd, PIX *pixs, SEL *sel )

```
pixOpen()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
sel
Return: pixd
Notes:
(1) Generic morphological opening, using hits in the Sel.
(2) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(3) For clarity, if the case is known, use these patterns:
(a) pixd = pixOpen(NULL, pixs, ...);
(b) pixOpen(pixs, pixs, ...);
(c) pixOpen(pixd, pixs, ...);
(4) The size of the result is determined by pixs.
```

## pixOpenBrick

PIX * pixOpenBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixOpenBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd, or null on error
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do separably if both hsize and vsize are > 1.
(4) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(5) For clarity, if the case is known, use these patterns:
(a) pixd = pixOpenBrick(NULL, pixs, ...);
(b) pixOpenBrick(pixs, pixs, ...);
(c) pixOpenBrick(pixd, pixs, ...);
(6) The size of the result is determined by pixs.
```

## pixOpenCompBrick

PIX * pixOpenCompBrick ( PIX *pixd, PIX *pixs, l_int32 hsize, l_int32 vsize )

```
pixOpenCompBrick()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
hsize (width of brick Sel)
vsize (height of brick Sel)
Return: pixd, or null on error
Notes:
(1) Sel is a brick with all elements being hits
(2) The origin is at (x, y) = (hsize/2, vsize/2)
(3) Do compositely for each dimension > 1.
(4) Do separably if both hsize and vsize are > 1.
(5) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(6) For clarity, if the case is known, use these patterns:
(a) pixd = pixOpenCompBrick(NULL, pixs, ...);
(b) pixOpenCompBrick(pixs, pixs, ...);
(c) pixOpenCompBrick(pixd, pixs, ...);
(7) The dimensions of the resulting image are determined by pixs.
(8) CAUTION: both hsize and vsize are being decomposed.
The decomposer chooses a product of sizes (call them
'terms') for each that is close to the input size,
but not necessarily equal to it. It attempts to optimize:
(a) for consistency with the input values: the product
of terms is close to the input size
(b) for efficiency of the operation: the sum of the
terms is small; ideally about twice the square
root of the input size.
So, for example, if the input hsize = 37, which is
a prime number, the decomposer will break this into two
terms, 6 and 6, so that the net result is a dilation
with hsize = 36.
```

## pixOpenGeneralized

PIX * pixOpenGeneralized ( PIX *pixd, PIX *pixs, SEL *sel )

```
pixOpenGeneralized()
Input: pixd (<optional>; this can be null, equal to pixs,
or different from pixs)
pixs (1 bpp)
sel
Return: pixd
Notes:
(1) Generalized morphological opening, using both hits and
misses in the Sel.
(2) This does a hit-miss transform, followed by a dilation
using the hits.
(3) There are three cases:
(a) pixd == null (result into new pixd)
(b) pixd == pixs (in-place; writes result back to pixs)
(c) pixd != pixs (puts result into existing pixd)
(4) For clarity, if the case is known, use these patterns:
(a) pixd = pixOpenGeneralized(NULL, pixs, ...);
(b) pixOpenGeneralized(pixs, pixs, ...);
(c) pixOpenGeneralized(pixd, pixs, ...);
(5) The size of the result is determined by pixs.
```

## resetMorphBoundaryCondition

void resetMorphBoundaryCondition ( l_int32 bc )

```
resetMorphBoundaryCondition()
Input: bc (SYMMETRIC_MORPH_BC, ASYMMETRIC_MORPH_BC)
Return: void
```

## selectComposableSels

l_int32 selectComposableSels ( l_int32 size, l_int32 direction, SEL **psel1, SEL **psel2 )

selectComposableSels()

```
Input: size (of composed sel)
direction (L_HORIZ, L_VERT)
&sel1 (<optional return> contiguous sel; can be null)
&sel2 (<optional return> comb sel; can be null)
Return: 0 if OK, 1 on error
Notes:
(1) When using composable Sels, where the original Sel is
decomposed into two, the best you can do in terms
of reducing the computation is by a factor:
2 * sqrt(size) / size
In practice, you get quite close to this. E.g.,
Sel size | Optimum reduction factor
-------- ------------------------
36 | 1/3
64 | 1/4
144 | 1/6
256 | 1/8
```

## selectComposableSizes

l_int32 selectComposableSizes ( l_int32 size, l_int32 *pfactor1, l_int32 *pfactor2 )

```
selectComposableSizes()
Input: size (of sel to be decomposed)
&factor1 (<return> larger factor)
&factor2 (<return> smaller factor)
Return: 0 if OK, 1 on error
Notes:
(1) This works for Sel sizes up to 62500, which seems sufficient.
(2) The composable sel size is typically within +- 1 of
the requested size. Up to size = 300, the maximum difference
is +- 2.
(3) We choose an overall cost function where the penalty for
the size difference between input and actual is 4 times
the penalty for additional rasterops.
(4) Returned values: factor1 >= factor2
If size > 1, then factor1 > 1.
```

# 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.