# NAME

Image::Leptonica::Func::graymorphlow

version 0.04

# `graymorphlow.c`

``````  graymorphlow.c

Low-level grayscale morphological operations

void     dilateGrayLow()
void     erodeGrayLow()

We use the van Herk/Gil-Werman (vHGW) algorithm, [van Herk,
Patt. Recog. Let. 13, pp. 517-521, 1992; Gil and Werman,
IEEE Trans PAMI 15(5), pp. 504-507, 1993.]
This was the first grayscale morphology
algorithm to compute dilation and erosion with
complexity independent of the size of the structuring
element.  It is simple and elegant, and surprising that
it was discovered as recently as 1992.  It works for
SEs composed of horizontal and/or vertical lines.  The
general case requires finding the Min or Max over an
arbitrary set of pixels, and this requires a number of
pixel comparisons equal to the SE "size" at each pixel
in the image.  The vHGW algorithm requires not
more than 3 comparisons at each point.  The algorithm has been
recently refined by Gil and Kimmel ("Efficient Dilation
Erosion, Opening and Closing Algorithms", in "Mathematical
Morphology and its Applications to Image and Signal Processing",
the proceedings of the International Symposium on Mathematical
Morphology, Palo Alto, CA, June 2000, Kluwer Academic
Publishers, pp. 301-310).  They bring this number down below
1.5 comparisons per output pixel but at a cost of significantly
increased complexity, so I don't bother with that here.

In brief, the method is as follows.  We evaluate the dilation
in groups of "size" pixels, equal to the size of the SE.
For horizontal, we start at x = "size"/2 and go
(w - 2 * ("size"/2))/"size" steps.  This means that
we don't evaluate the first 0.5 * "size" pixels and, worst
case, the last 1.5 * "size" pixels.  Thus we embed the
image in a larger image with these augmented dimensions, where
the new border pixels are appropriately initialized (0 for
dilation; 255 for erosion), and remove the boundary at the end.
(For vertical, use h instead of w.)   Then for each group
of "size" pixels, we form an array of length 2 * "size" + 1,
consisting of backward and forward partial maxima (for
dilation) or minima (for erosion).  This represents a
jumping window computed from the source image, over which
the SE will slide.  The center of the array gets the source
pixel at the center of the SE.  Call this the center pixel
of the window.  Array values to left of center get
the maxima(minima) of the pixels from the center
one and going to the left an equal distance.  Array
values to the right of center get the maxima(minima) to
the pixels from the center one and going to the right
an equal distance.  These are computed sequentially starting
from the center one.  The SE (of length "size") can slide over this
window (of length 2 * "size + 1) at "size" different places.
At each place, the maxima(minima) of the values in the window
that correspond to the end points of the SE give the extremal
values over that interval, and these are stored at the dest
pixel corresponding to the SE center.  A picture is worth
at least this many words, so if this isn't clear, see the
leptonica documentation on grayscale morphology.``````

# FUNCTIONS

## dilateGrayLow

void dilateGrayLow ( l_uint32 *datad, l_int32 w, l_int32 h, l_int32 wpld, l_uint32 *datas, l_int32 wpls, l_int32 size, l_int32 direction, l_uint8 *buffer, l_uint8 *maxarray )

``````  dilateGrayLow()

Input:  datad, w, h, wpld (8 bpp image)
datas, wpls  (8 bpp image, of same dimensions)
size  (full length of SEL; restricted to odd numbers)
direction  (L_HORIZ or L_VERT)
buffer  (holds full line or column of src image pixels)
maxarray  (array of dimension 2*size+1)
Return: void

Notes:
(1) To eliminate border effects on the actual image, these images
are prepared with an additional border of dimensions:
leftpix = 0.5 * size
rightpix = 1.5 * size
toppix = 0.5 * size
bottompix = 1.5 * size
and we initialize the src border pixels to 0.
This allows full processing over the actual image; at
the end the border is removed.
(2) Uses algorithm of van Herk, Gil and Werman``````

## erodeGrayLow

void erodeGrayLow ( l_uint32 *datad, l_int32 w, l_int32 h, l_int32 wpld, l_uint32 *datas, l_int32 wpls, l_int32 size, l_int32 direction, l_uint8 *buffer, l_uint8 *minarray )

``````  erodeGrayLow()

Input:  datad, w, h, wpld (8 bpp image)
datas, wpls  (8 bpp image, of same dimensions)
size  (full length of SEL; restricted to odd numbers)
direction  (L_HORIZ or L_VERT)
buffer  (holds full line or column of src image pixels)
minarray  (array of dimension 2*size+1)
Return: void

Notes:
(1) See notes in dilateGrayLow()``````

# 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.