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Leptonica 1.68
C Image Processing Library
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Leptonica 1.68
C Image Processing Library
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4-pt bilinear transforms on images and coordinates, with sampling and interpolation More...
#include <stdio.h>#include <stdlib.h>#include <string.h>#include <math.h>#include "allheaders.h"Go to the source code of this file.
4-pt bilinear transforms on images and coordinates, with sampling and interpolation
Bilinear (4 pt) image transformation using a sampled (to nearest integer) transform on each dest point PIX *pixBilinearSampledPta() PIX *pixBilinearSampled() Bilinear (4 pt) image transformation using interpolation (or area mapping) for anti-aliasing images that are 2, 4, or 8 bpp gray, or colormapped, or 32 bpp RGB PIX *pixBilinearPta() PIX *pixBilinear() PIX *pixBilinearPtaColor() PIX *pixBilinearColor() PIX *pixBilinearPtaGray() PIX *pixBilinearGray() Bilinear transform including alpha (blend) component and gamma xform PIX *pixBilinearPtaWithAlpha() PIX *pixBilinearPtaGammaXform() Bilinear coordinate transformation l_int32 getBilinearXformCoeffs() l_int32 bilinearXformSampledPt() l_int32 bilinearXformPt() A bilinear transform can be specified as a specific functional mapping between 4 points in the source and 4 points in the dest. It can be used as an approximation to a (nonlinear) projective transform, because for small warps it is very similar and it is more stable. (Projective transforms have a division by a quantity that can get arbitrarily small.) We give both a bilinear coordinate transformation and a bilinear image transformation. For the former, we ask for the coordinate value (x',y') in the transformed space for any point (x,y) in the original space. The coefficients of the transformation are found by solving 8 simultaneous equations for the 8 coordinates of the 4 points in src and dest. The transformation can then be used to compute the associated image transform, by computing, for each dest pixel, the relevant pixel(s) in the source. This can be done either by taking the closest src pixel to each transformed dest pixel ("sampling") or by doing an interpolation and averaging over 4 source pixels with appropriate weightings ("interpolated"). A typical application would be to remove some of the keystoning due to a projective transform in the imaging system. The bilinear transform is given by specifying two equations: x' = ax + by + cxy + d y' = ex + fy + gxy + h where the eight coefficients have been computed from four sets of these equations, each for two corresponding data pts. In practice, for each point (x,y) in the dest image, this equation is used to compute the corresponding point (x',y') in the src. That computed point in the src is then used to determine the dest value in one of two ways: - sampling: take the value of the src pixel in which this point falls - interpolation: take appropriate linear combinations of the four src pixels that this dest pixel would overlap, with the coefficients proportional to the amount of overlap For small warp, like rotation, area mapping in the interpolation is equivalent to linear interpolation. Typical relative timing of transforms (sampled = 1.0): 8 bpp: sampled 1.0 interpolated 1.6 32 bpp: sampled 1.0 interpolated 1.8 Additionally, the computation time/pixel is nearly the same for 8 bpp and 32 bpp, for both sampled and interpolated.
Definition in file bilinear.c.
Input: pixs (all depths) ptad (4 pts of final coordinate space) ptas (4 pts of initial coordinate space) incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK) Return: pixd, or null on error
Notes: (1) Brings in either black or white pixels from the boundary. (2) Retains colormap, which you can do for a sampled transform.. (3) No 3 of the 4 points may be collinear. (4) For 8 and 32 bpp pix, better quality is obtained by the somewhat slower pixBilinearPta(). See that function for relative timings between sampled and interpolated.
Definition at line 130 of file bilinear.c.
References ERROR_PTR, FREE, getBilinearXformCoeffs(), L_BRING_IN_BLACK, L_BRING_IN_WHITE, NULL, pixBilinearSampled(), PROCNAME, and ptaGetCount().
Referenced by main(), and pixBilinearPta().
Input: pixs (all depths) vc (vector of 8 coefficients for bilinear transformation) incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK) Return: pixd, or null on error
Notes: (1) Brings in either black or white pixels from the boundary. (2) Retains colormap, which you can do for a sampled transform.. (3) For 8 or 32 bpp, much better quality is obtained by the somewhat slower pixBilinear(). See that function for relative timings between sampled and interpolated.
Definition at line 178 of file bilinear.c.
References bilinearXformSampledPt(), ERROR_PTR, GET_DATA_BIT, GET_DATA_BYTE, GET_DATA_DIBIT, GET_DATA_QBIT, L_BRING_IN_BLACK, L_BRING_IN_WHITE, NULL, pixClearAll(), pixcmapAddBlackOrWhite(), pixCreateTemplate(), pixGetColormap(), pixGetData(), pixGetDimensions(), pixGetWpl(), pixSetAll(), pixSetAllArbitrary(), PROCNAME, SET_DATA_BIT_VAL, SET_DATA_BYTE, SET_DATA_DIBIT, and SET_DATA_QBIT.
Referenced by pixBilinear(), and pixBilinearSampledPta().
Input: pixs (all depths; colormap ok) ptad (4 pts of final coordinate space) ptas (4 pts of initial coordinate space) incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK) Return: pixd, or null on error
Notes: (1) Brings in either black or white pixels from the boundary (2) Removes any existing colormap, if necessary, before transforming
Definition at line 273 of file bilinear.c.
References ERROR_PTR, FALSE, L_BRING_IN_BLACK, L_BRING_IN_WHITE, NULL, pixBilinearPtaColor(), pixBilinearPtaGray(), pixBilinearSampledPta(), pixClone(), pixConvertTo8(), pixDestroy(), pixGetDepth(), pixRemoveColormap(), PROCNAME, ptaGetCount(), and REMOVE_CMAP_BASED_ON_SRC.
Referenced by main().
Input: pixs (all depths; colormap ok) vc (vector of 8 coefficients for bilinear transformation) incolor (L_BRING_IN_WHITE, L_BRING_IN_BLACK) Return: pixd, or null on error
Notes: (1) Brings in either black or white pixels from the boundary (2) Removes any existing colormap, if necessary, before transforming
Definition at line 341 of file bilinear.c.
References ERROR_PTR, FALSE, L_BRING_IN_WHITE, NULL, pixBilinearColor(), pixBilinearGray(), pixBilinearSampled(), pixClone(), pixConvertTo8(), pixDestroy(), pixGetDepth(), pixRemoveColormap(), PROCNAME, and REMOVE_CMAP_BASED_ON_SRC.
Input: pixs (32 bpp) ptad (4 pts of final coordinate space) ptas (4 pts of initial coordinate space) colorval (e.g., 0 to bring in BLACK, 0xffffff00 for WHITE) Return: pixd, or null on error
Definition at line 397 of file bilinear.c.
References ERROR_PTR, FREE, getBilinearXformCoeffs(), NULL, pixBilinearColor(), pixGetDepth(), PROCNAME, and ptaGetCount().
Referenced by pixBilinearPta(), and pixBilinearPtaWithAlpha().
Input: pixs (32 bpp) vc (vector of 8 coefficients for bilinear transformation) colorval (e.g., 0 to bring in BLACK, 0xffffff00 for WHITE) Return: pixd, or null on error
Definition at line 438 of file bilinear.c.
References bilinearXformPt(), ERROR_PTR, linearInterpolatePixelColor(), NULL, pixCreateTemplate(), pixGetData(), pixGetDimensions(), pixGetWpl(), pixSetAllArbitrary(), and PROCNAME.
Referenced by pixBilinear(), and pixBilinearPtaColor().
Input: pixs (8 bpp) ptad (4 pts of final coordinate space) ptas (4 pts of initial coordinate space) grayval (0 to bring in BLACK, 255 for WHITE) Return: pixd, or null on error
Definition at line 491 of file bilinear.c.
References ERROR_PTR, FREE, getBilinearXformCoeffs(), NULL, pixBilinearGray(), pixGetDepth(), PROCNAME, and ptaGetCount().
Referenced by pixBilinearPta(), and pixBilinearPtaWithAlpha().
Input: pixs (8 bpp) vc (vector of 8 coefficients for bilinear transformation) grayval (0 to bring in BLACK, 255 for WHITE) Return: pixd, or null on error
Definition at line 532 of file bilinear.c.
References bilinearXformPt(), ERROR_PTR, linearInterpolatePixelGray(), NULL, pixCreateTemplate(), pixGetData(), pixGetDepth(), pixGetDimensions(), pixGetWpl(), pixSetAllArbitrary(), PROCNAME, and SET_DATA_BYTE.
Referenced by pixBilinear(), and pixBilinearPtaGray().
| PIX* pixBilinearPtaWithAlpha | ( | PIX * | pixs, |
| PTA * | ptad, | ||
| PTA * | ptas, | ||
| PIX * | pixg, | ||
| l_float32 | fract, | ||
| l_int32 | border | ||
| ) |
Input: pixs (32 bpp rgb) ptad (4 pts of final coordinate space) ptas (4 pts of initial coordinate space) pixg (<optional> 8 bpp, can be null) fract (between 0.0 and 1.0, with 0.0 fully transparent and 1.0 fully opaque) border (of pixels added to capture transformed source pixels) Return: pixd, or null on error
Notes: (1) The alpha channel is transformed separately from pixs, and aligns with it, being fully transparent outside the boundary of the transformed pixs. For pixels that are fully transparent, a blending function like pixBlendWithGrayMask() will give zero weight to corresponding pixels in pixs. (2) If pixg is NULL, it is generated as an alpha layer that is partially opaque, using . Otherwise, it is cropped to pixs if required and is ignored. The alpha channel in pixs is never used. (3) Colormaps are removed. (4) When pixs is transformed, it doesn't matter what color is brought in because the alpha channel will be transparent (0) there. (5) To avoid losing source pixels in the destination, it may be necessary to add a border to the source pix before doing the bilinear transformation. This can be any non-negative number. (6) The input and are in a coordinate space before the border is added. Internally, we compensate for this before doing the bilinear transform on the image after the border is added. (7) The default setting for the border values in the alpha channel is 0 (transparent) for the outermost ring of pixels and (0.5 * fract * 255) for the second ring. When blended over a second image, this (a) shrinks the visible image to make a clean overlap edge with an image below, and (b) softens the edges by weakening the aliasing there. Use l_setAlphaMaskBorder() to change these values.
Definition at line 618 of file bilinear.c.
References AlphaMaskBorderVals, ERROR_PTR, L_ALPHA_CHANNEL, L_WARNING, NULL, pixAddBorder(), pixBilinearPtaColor(), pixBilinearPtaGray(), pixCreate(), pixDestroy(), pixGetColormap(), pixGetDepth(), pixGetDimensions(), pixResizeToMatch(), pixSetAll(), pixSetAllArbitrary(), pixSetBorderRingVal(), pixSetRGBComponent(), PROCNAME, ptaDestroy(), and ptaTransform().
Referenced by main(), and pixBilinearPtaGammaXform().
| PIX* pixBilinearPtaGammaXform | ( | PIX * | pixs, |
| l_float32 | gamma, | ||
| PTA * | ptad, | ||
| PTA * | ptas, | ||
| l_float32 | fract, | ||
| l_int32 | border | ||
| ) |
Input: pixs (32 bpp rgb) gamma (gamma correction; must be > 0.0) ptad (3 pts of final coordinate space) ptas (3 pts of initial coordinate space) fract (between 0.0 and 1.0, with 1.0 fully transparent) border (of pixels to capture transformed source pixels) Return: pixd, or null on error
Notes: (1) This wraps a gamma/inverse-gamma photometric transform around pixBilinearPtaWithAlpha(). (2) For usage, see notes in pixBilinearPtaWithAlpha() and pixGammaTRCWithAlpha(). (3) The basic idea of a gamma/inverse-gamma transform is to remove any gamma correction before the bilinear transform, and restore it afterward. The effects can be subtle, but important for some applications. For example, using gamma > 1.0 will cause the dark areas to become somewhat lighter and slightly reduce aliasing effects when blending using the alpha channel.
Definition at line 714 of file bilinear.c.
References ERROR_PTR, L_WARNING, NULL, pixBilinearPtaWithAlpha(), pixDestroy(), pixGammaTRCWithAlpha(), pixGetDepth(), and PROCNAME.
Referenced by main().
Input: ptas (source 4 points; unprimed) ptad (transformed 4 points; primed) &vc (<return> vector of coefficients of transform) Return: 0 if OK; 1 on error
We have a set of 8 equations, describing the bilinear transformation that takes 4 points (ptas) into 4 other points (ptad). These equations are:
x1' = c[0]*x1 + c[1]*y1 + c[2]*x1*y1 + c[3] y1' = c[4]*x1 + c[5]*y1 + c[6]*x1*y1 + c[7] x2' = c[0]*x2 + c[1]*y2 + c[2]*x2*y2 + c[3] y2' = c[4]*x2 + c[5]*y2 + c[6]*x2*y2 + c[7] x3' = c[0]*x3 + c[1]*y3 + c[2]*x3*y3 + c[3] y3' = c[4]*x3 + c[5]*y3 + c[6]*x3*y3 + c[7] x4' = c[0]*x4 + c[1]*y4 + c[2]*x4*y4 + c[3] y4' = c[4]*x4 + c[5]*y4 + c[6]*x4*y4 + c[7]
This can be represented as
AC = B
where B and C are column vectors
B = [ x1' y1' x2' y2' x3' y3' x4' y4' ] C = [ c[0] c[1] c[2] c[3] c[4] c[5] c[6] c[7] ]
and A is the 8x8 matrix
x1 y1 x1*y1 1 0 0 0 0 0 0 0 0 x1 y1 x1*y1 1 x2 y2 x2*y2 1 0 0 0 0 0 0 0 0 x2 y2 x2*y2 1 x3 y3 x3*y3 1 0 0 0 0 0 0 0 0 x3 y3 x3*y3 1 x4 y4 x4*y4 1 0 0 0 0 0 0 0 0 x4 y4 x4*y4 1
These eight equations are solved here for the coefficients C.
These eight coefficients can then be used to find the mapping (x,y) --> (x',y'):
x' = c[0]x + c[1]y + c[2]xy + c[3] y' = c[4]x + c[5]y + c[6]xy + c[7]
that are implemented in bilinearXformSampledPt() and bilinearXFormPt().
Definition at line 798 of file bilinear.c.
References CALLOC, ERROR_INT, FREE, gaussjordan(), NULL, PROCNAME, ptaGetPt(), x1, x2, x3, x4, y1, y2, y3, and y4.
Referenced by pixBilinearPtaColor(), pixBilinearPtaGray(), and pixBilinearSampledPta().
| l_int32 bilinearXformSampledPt | ( | l_float32 * | vc, |
| l_int32 | x, | ||
| l_int32 | y, | ||
| l_int32 * | pxp, | ||
| l_int32 * | pyp | ||
| ) |
Input: vc (vector of 8 coefficients) (x, y) (initial point) (&xp, &yp) (<return> transformed point) Return: 0 if OK; 1 on error
Notes: (1) This finds the nearest pixel coordinates of the transformed point. (2) It does not check ptrs for returned data!
Definition at line 889 of file bilinear.c.
References ERROR_INT, and PROCNAME.
Referenced by pixBilinearSampled().
Input: vc (vector of 8 coefficients) (x, y) (initial point) (&xp, &yp) (<return> transformed point) Return: 0 if OK; 1 on error
Notes: (1) This computes the floating point location of the transformed point. (2) It does not check ptrs for returned data!
Definition at line 920 of file bilinear.c.
References ERROR_INT, and PROCNAME.
Referenced by pixBilinearColor(), and pixBilinearGray().
1.7.3