/*====================================================================*
- Copyright (C) 2001 Leptonica. All rights reserved.
- This software is distributed in the hope that it will be
- useful, but with NO WARRANTY OF ANY KIND.
- No author or distributor accepts responsibility to anyone for the
- consequences of using this software, or for whether it serves any
- particular purpose or works at all, unless he or she says so in
- writing. Everyone is granted permission to copy, modify and
- redistribute this source code, for commercial or non-commercial
- purposes, with the following restrictions: (1) the origin of this
- source code must not be misrepresented; (2) modified versions must
- be plainly marked as such; and (3) this notice may not be removed
- or altered from any source or modified source distribution.
*====================================================================*/
/*
* rank.c
*
* Rank filter (gray and rgb)
* PIX *pixRankFilter()
* PIX *pixRankFilterRGB()
* PIX *pixRankFilterGray()
*
* Median filter
* PIX *pixMedianFilter()
*
* 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
* adding zeroes. Ouch!
*
* * 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!
*/
#include <stdio.h>
#include <stdlib.h>
#include "allheaders.h"
/*----------------------------------------------------------------------*
* Rank order filter *
*----------------------------------------------------------------------*/
/*!
* 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.
*/
PIX *
pixRankFilter(PIX *pixs,
l_int32 wf,
l_int32 hf,
l_float32 rank)
{
l_int32 d;
PROCNAME("pixRankFilter");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (pixGetColormap(pixs) != NULL)
return (PIX *)ERROR_PTR("pixs has colormap", procName, NULL);
d = pixGetDepth(pixs);
if (d != 8 && d != 32)
return (PIX *)ERROR_PTR("pixs not 8 or 32 bpp", procName, NULL);
if (wf < 1 || hf < 1)
return (PIX *)ERROR_PTR("wf < 1 || hf < 1", procName, NULL);
if (rank < 0.0 || rank > 1.0)
return (PIX *)ERROR_PTR("rank must be in [0.0, 1.0]", procName, NULL);
if (wf == 1 && hf == 1) /* no-op */
return pixCopy(NULL, pixs);
if (d == 8)
return pixRankFilterGray(pixs, wf, hf, rank);
else /* d == 32 */
return pixRankFilterRGB(pixs, wf, hf, 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.
*/
PIX *
pixRankFilterRGB(PIX *pixs,
l_int32 wf,
l_int32 hf,
l_float32 rank)
{
PIX *pixr, *pixg, *pixb, *pixrf, *pixgf, *pixbf, *pixd;
PROCNAME("pixRankFilterRGB");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (pixGetDepth(pixs) != 32)
return (PIX *)ERROR_PTR("pixs not 32 bpp", procName, NULL);
if (wf < 1 || hf < 1)
return (PIX *)ERROR_PTR("wf < 1 || hf < 1", procName, NULL);
if (rank < 0.0 || rank > 1.0)
return (PIX *)ERROR_PTR("rank must be in [0.0, 1.0]", procName, NULL);
if (wf == 1 && hf == 1) /* no-op */
return pixCopy(NULL, pixs);
pixr = pixGetRGBComponent(pixs, COLOR_RED);
pixg = pixGetRGBComponent(pixs, COLOR_GREEN);
pixb = pixGetRGBComponent(pixs, COLOR_BLUE);
pixrf = pixRankFilterGray(pixr, wf, hf, rank);
pixgf = pixRankFilterGray(pixg, wf, hf, rank);
pixbf = pixRankFilterGray(pixb, wf, hf, rank);
pixd = pixCreateRGBImage(pixrf, pixgf, pixbf);
pixDestroy(&pixr);
pixDestroy(&pixg);
pixDestroy(&pixb);
pixDestroy(&pixrf);
pixDestroy(&pixgf);
pixDestroy(&pixbf);
return pixd;
}
/*!
* 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.
*/
PIX *
pixRankFilterGray(PIX *pixs,
l_int32 wf,
l_int32 hf,
l_float32 rank)
{
l_int32 w, h, d, i, j, k, m, n, rankloc, wplt, wpld, val, sum;
l_int32 *histo, *histo16;
l_uint32 *datat, *linet, *datad, *lined;
PIX *pixt, *pixd;
PROCNAME("pixRankFilterGray");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
if (pixGetColormap(pixs) != NULL)
return (PIX *)ERROR_PTR("pixs has colormap", procName, NULL);
pixGetDimensions(pixs, &w, &h, &d);
if (d != 8)
return (PIX *)ERROR_PTR("pixs not 8 bpp", procName, NULL);
if (wf < 1 || hf < 1)
return (PIX *)ERROR_PTR("wf < 1 || hf < 1", procName, NULL);
if (rank < 0.0 || rank > 1.0)
return (PIX *)ERROR_PTR("rank must be in [0.0, 1.0]", procName, NULL);
if (wf == 1 && hf == 1) /* no-op */
return pixCopy(NULL, pixs);
/* For rank = 0.0, this is a grayscale erosion, and for rank = 1.0,
* a dilation. Grayscale morphology operations are implemented
* for filters of odd dimension, so we dispatch to grayscale
* morphology if both wf and hf are odd. Otherwise, we
* slightly adjust the rank (to get the correct behavior) and
* use the slower rank filter here. */
if (wf % 2 && hf % 2) {
if (rank == 0.0)
return pixErodeGray(pixs, wf, hf);
else if (rank == 1.0)
return pixDilateGray(pixs, wf, hf);
}
if (rank == 0.0) rank = 0.0001;
if (rank == 1.0) rank = 0.9999;
/* Add wf/2 to each side, and hf/2 to top and bottom of the
* image, mirroring for accuracy and to avoid special-casing
* the boundary. */
if ((pixt = pixAddMirroredBorder(pixs, wf / 2, wf / 2, hf / 2, hf / 2))
== NULL)
return (PIX *)ERROR_PTR("pixt not made", procName, NULL);
/* Set up the two histogram arrays. */
histo = (l_int32 *)CALLOC(256, sizeof(l_int32));
histo16 = (l_int32 *)CALLOC(16, sizeof(l_int32));
rankloc = (l_int32)(rank * wf * hf);
/* Place the filter center at (0, 0). This is just a
* convenient location, because it allows us to perform
* the rank filter over x:(0 ... w - 1) and y:(0 ... h - 1). */
pixd = pixCreateTemplate(pixs);
datat = pixGetData(pixt);
wplt = pixGetWpl(pixt);
datad = pixGetData(pixd);
wpld = pixGetWpl(pixd);
/* If hf > wf, it's more efficient to use row-major scanning.
* Otherwise, traverse the image in use column-major order. */
if (hf > wf) {
for (j = 0; j < w; j++) { /* row-major */
/* Start each column with clean histogram arrays. */
for (n = 0; n < 256; n++)
histo[n] = 0;
for (n = 0; n < 16; n++)
histo16[n] = 0;
for (i = 0; i < h; i++) { /* fast scan on columns */
/* Update the histos for the new location */
lined = datad + i * wpld;
if (i == 0) { /* do full histo */
for (k = 0; k < hf; k++) {
linet = datat + (i + k) * wplt;
for (m = 0; m < wf; m++) {
val = GET_DATA_BYTE(linet, j + m);
histo[val]++;
histo16[val >> 4]++;
}
}
} else { /* incremental update */
linet = datat + (i - 1) * wplt;
for (m = 0; m < wf; m++) { /* remove top line */
val = GET_DATA_BYTE(linet, j + m);
histo[val]--;
histo16[val >> 4]--;
}
linet = datat + (i + hf - 1) * wplt;
for (m = 0; m < wf; m++) { /* add bottom line */
val = GET_DATA_BYTE(linet, j + m);
histo[val]++;
histo16[val >> 4]++;
}
}
/* Find the rank value */
sum = 0;
for (n = 0; n < 16; n++) { /* search over coarse histo */
sum += histo16[n];
if (sum > rankloc) {
sum -= histo16[n];
break;
}
}
k = 16 * n; /* starting value in fine histo */
for (m = 0; m < 16; m++) {
sum += histo[k];
if (sum > rankloc) {
SET_DATA_BYTE(lined, j, k);
break;
}
k++;
}
}
}
} else { /* wf >= hf */
for (i = 0; i < h; i++) { /* column-major */
/* Start each row with clean histogram arrays. */
for (n = 0; n < 256; n++)
histo[n] = 0;
for (n = 0; n < 16; n++)
histo16[n] = 0;
lined = datad + i * wpld;
for (j = 0; j < w; j++) { /* fast scan on rows */
/* Update the histos for the new location */
if (j == 0) { /* do full histo */
for (k = 0; k < hf; k++) {
linet = datat + (i + k) * wplt;
for (m = 0; m < wf; m++) {
val = GET_DATA_BYTE(linet, j + m);
histo[val]++;
histo16[val >> 4]++;
}
}
} else { /* incremental update at left and right sides */
for (k = 0; k < hf; k++) {
linet = datat + (i + k) * wplt;
val = GET_DATA_BYTE(linet, j - 1);
histo[val]--;
histo16[val >> 4]--;
val = GET_DATA_BYTE(linet, j + wf - 1);
histo[val]++;
histo16[val >> 4]++;
}
}
/* Find the rank value */
sum = 0;
for (n = 0; n < 16; n++) { /* search over coarse histo */
sum += histo16[n];
if (sum > rankloc) {
sum -= histo16[n];
break;
}
}
k = 16 * n; /* starting value in fine histo */
for (m = 0; m < 16; m++) {
sum += histo[k];
if (sum > rankloc) {
SET_DATA_BYTE(lined, j, k);
break;
}
k++;
}
}
}
}
pixDestroy(&pixt);
FREE(histo);
FREE(histo16);
return pixd;
}
/*----------------------------------------------------------------------*
* Median filter *
*----------------------------------------------------------------------*/
/*!
* 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
*/
PIX *
pixMedianFilter(PIX *pixs,
l_int32 wf,
l_int32 hf)
{
PROCNAME("pixMedianFilter");
if (!pixs)
return (PIX *)ERROR_PTR("pixs not defined", procName, NULL);
return pixRankFilter(pixs, wf, hf, 0.5);
}