Zakariyya Mughal

# NAME

Image::Leptonica::Func::rank

version 0.04

# `rank.c`

``````  rank.c

Rank filter (gray and rgb)
PIX      *pixRankFilter()
PIX      *pixRankFilterRGB()
PIX      *pixRankFilterGray()

Median filter
PIX      *pixMedianFilter()

Rank filter (accelerated with downscaling)
PIX      *pixRankFilterWithScaling()

What is a brick rank filter?

A brick rank order filter evaluates, for every pixel in the image,
a rectangular set of n = wf x hf pixels in its neighborhood (where the
pixel in question is at the "center" of the rectangle and is
included in the evaluation).  It determines the value of the
neighboring pixel that is the r-th smallest in the set,
where r is some integer between 1 and n.  The input rank parameter
is a fraction between 0.0 and 1.0, where 0.0 represents the
smallest value (r = 1) and 1.0 represents the largest value (r = n).
A median filter is a rank filter where rank = 0.5.

It is important to note that grayscale erosion is equivalent
to rank = 0.0, and grayscale dilation is equivalent to rank = 1.0.
These are much easier to calculate than the general rank value,
thanks to the van Herk/Gil-Werman algorithm:
http://www.leptonica.com/grayscale-morphology.html
so you should use pixErodeGray() and pixDilateGray() for
rank 0.0 and 1.0, rsp.  See notes below in the function header.

How is a rank filter implemented efficiently on an image?

Sorting will not work.

* The best sort algorithms are O(n*logn), where n is the number
of values to be sorted (the area of the filter).  For large
filters this is an impractically large number.

* Selection of the rank value is O(n).  (To understand why it's not
O(n*logn), see Numerical Recipes in C, 2nd edition, 1992,  p. 355ff).
This also still far too much computation for large filters.

* Suppose we get clever.  We really only need to do an incremental
selection or sorting, because, for example, moving the filter
down by one pixel causes one filter width of pixels to be added
and another to be removed.  Can we do this incrementally in
an efficient way?  Unfortunately, no.  The sorted values will be
in an array.  Even if the filter width is 1, we can expect to
have to move O(n) pixels, because insertion and deletion can happen
anywhere in the array.  By comparison, heapsort is excellent for
incremental sorting, where the cost for insertion or deletion
is O(logn), because the array itself doesn't need to
be sorted into strictly increasing order.  However, heapsort
only gives the max (or min) value, not the general rank value.

This leaves histograms.

* Represented as an array.  The problem with an array of 256
bins is that, in general, a significant fraction of the
entire histogram must be summed to find the rank value bin.
Suppose the filter size is 5x5.  You spend most of your time

* Represented as a linked list.  This would overcome the
summing-over-empty-bin problem, but you lose random access
for insertions and deletions.  No way.

* Two histogram solution.  Maintain two histograms with
bin sizes of 1 and 16.  Proceed from coarse to fine.
First locate the coarse bin for the given rank, of which
there are only 16.  Then, in the 256 entry (fine) histogram,
you need look at a maximum of 16 bins.  For each output
pixel, the average number of bins summed over, both in the
coarse and fine histograms, is thus 16.

If someone has a better method, please let me know!

The rank filtering operation is relatively expensive, compared to most
of the other imaging operations.  The speed is only weakly dependent
on the size of the rank filter.  On standard hardware, it runs at
about 10 Mpix/sec for a 50 x 50 filter, and 25 Mpix/sec for
a 5 x 5 filter.   For applications where the rank filter can be
performed on a downscaled image, significant speedup can be
achieved because the time goes as the square of the scaling factor.
We provide an interface that handles the details, and only
requires the amount of downscaling to be input.``````

# FUNCTIONS

## pixMedianFilter

PIX * pixMedianFilter ( PIX *pixs, l_int32 wf, l_int32 hf )

``````  pixMedianFilter()

Input:  pixs (8 or 32 bpp; no colormap)
wf, hf  (width and height of filter; each is >= 1)
Return: pixd (of median values), or null on error``````

## pixRankFilter

PIX * pixRankFilter ( PIX *pixs, l_int32 wf, l_int32 hf, l_float32 rank )

``````  pixRankFilter()

Input:  pixs (8 or 32 bpp; no colormap)
wf, hf  (width and height of filter; each is >= 1)
rank (in [0.0 ... 1.0])
Return: pixd (of rank values), or null on error

Notes:
(1) This defines, for each pixel in pixs, a neighborhood of
pixels given by a rectangle "centered" on the pixel.
This set of wf*hf pixels has a distribution of values.
For each component, if the values are sorted in increasing
order, we choose the component such that rank*(wf*hf-1)
pixels have a lower or equal value and
(1-rank)*(wf*hf-1) pixels have an equal or greater value.
(2) See notes in pixRankFilterGray() for further details.``````

## pixRankFilterGray

PIX * pixRankFilterGray ( PIX *pixs, l_int32 wf, l_int32 hf, l_float32 rank )

``````  pixRankFilterGray()

Input:  pixs (8 bpp; no colormap)
wf, hf  (width and height of filter; each is >= 1)
rank (in [0.0 ... 1.0])
Return: pixd (of rank values), or null on error

Notes:
(1) This defines, for each pixel in pixs, a neighborhood of
pixels given by a rectangle "centered" on the pixel.
This set of wf*hf pixels has a distribution of values,
and if they are sorted in increasing order, we choose
the pixel such that rank*(wf*hf-1) pixels have a lower
or equal value and (1-rank)*(wf*hf-1) pixels have an equal
or greater value.
(2) By this definition, the rank = 0.0 pixel has the lowest
value, and the rank = 1.0 pixel has the highest value.
(3) We add mirrored boundary pixels to avoid boundary effects,
and put the filter center at (0, 0).
(4) This dispatches to grayscale erosion or dilation if the
filter dimensions are odd and the rank is 0.0 or 1.0, rsp.
(5) Returns a copy if both wf and hf are 1.
(6) Uses row-major or column-major incremental updates to the
histograms depending on whether hf > wf or hv <= wf, rsp.``````

## pixRankFilterRGB

PIX * pixRankFilterRGB ( PIX *pixs, l_int32 wf, l_int32 hf, l_float32 rank )

``````  pixRankFilterRGB()

Input:  pixs (32 bpp)
wf, hf  (width and height of filter; each is >= 1)
rank (in [0.0 ... 1.0])
Return: pixd (of rank values), or null on error

Notes:
(1) This defines, for each pixel in pixs, a neighborhood of
pixels given by a rectangle "centered" on the pixel.
This set of wf*hf pixels has a distribution of values.
For each component, if the values are sorted in increasing
order, we choose the component such that rank*(wf*hf-1)
pixels have a lower or equal value and
(1-rank)*(wf*hf-1) pixels have an equal or greater value.
(2) Apply gray rank filtering to each component independently.
(3) See notes in pixRankFilterGray() for further details.``````

## pixRankFilterWithScaling

PIX * pixRankFilterWithScaling ( PIX *pixs, l_int32 wf, l_int32 hf, l_float32 rank, l_float32 scalefactor )

``````  pixRankFilterWithScaling()

Input:  pixs (8 or 32 bpp; no colormap)
wf, hf  (width and height of filter; each is >= 1)
rank (in [0.0 ... 1.0])
scalefactor (scale factor; must be >= 0.2 and <= 0.7)
Return: pixd (of rank values), or null on error

Notes:
(1) This is a convenience function that downscales, does
the rank filtering, and upscales.  Because the down-
and up-scaling functions are very fast compared to
rank filtering, the time it takes is reduced from that
for the simple rank filtering operation by approximately
the square of the scaling factor.``````

# AUTHOR

Zakariyya Mughal <zmughal@cpan.org>