Image::Leptonica::Func::projective
version 0.04
projective.c
projective.c Projective (4 pt) image transformation using a sampled (to nearest integer) transform on each dest point PIX *pixProjectiveSampledPta() PIX *pixProjectiveSampled() Projective (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 *pixProjectivePta() PIX *pixProjective() PIX *pixProjectivePtaColor() PIX *pixProjectiveColor() PIX *pixProjectivePtaGray() PIX *pixProjectiveGray() Projective transform including alpha (blend) component PIX *pixProjectivePtaWithAlpha() Projective coordinate transformation l_int32 getProjectiveXformCoeffs() l_int32 projectiveXformSampledPt() l_int32 projectiveXformPt() A projective transform can be specified as a specific functional mapping between 4 points in the source and 4 points in the dest. It preserves straight lines, but is less stable than a bilinear transform, because it contains a division by a quantity that can get arbitrarily small.) We give both a projective coordinate transformation and two projective image transformations. 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 keystoning due to a projective transform in the imaging system. The projective transform is given by specifying two equations: x' = (ax + by + c) / (gx + hy + 1) y' = (dx + ey + f) / (gx + hy + 1) 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 where there is little scale change, (e.g., for rotation) area mapping is nearly equivalent to interpolation. Typical relative timing of pointwise transforms (sampled = 1.0): 8 bpp: sampled 1.0 interpolated 1.5 32 bpp: sampled 1.0 interpolated 1.6 Additionally, the computation time/pixel is nearly the same for 8 bpp and 32 bpp, for both sampled and interpolated.
l_int32 getProjectiveXformCoeffs ( PTA *ptas, PTA *ptad, l_float32 **pvc )
getProjectiveXformCoeffs() 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 projective transformation that takes 4 points (ptas) into 4 other points (ptad). These equations are: x1' = (c[0]*x1 + c[1]*y1 + c[2]) / (c[6]*x1 + c[7]*y1 + 1) y1' = (c[3]*x1 + c[4]*y1 + c[5]) / (c[6]*x1 + c[7]*y1 + 1) x2' = (c[0]*x2 + c[1]*y2 + c[2]) / (c[6]*x2 + c[7]*y2 + 1) y2' = (c[3]*x2 + c[4]*y2 + c[5]) / (c[6]*x2 + c[7]*y2 + 1) x3' = (c[0]*x3 + c[1]*y3 + c[2]) / (c[6]*x3 + c[7]*y3 + 1) y3' = (c[3]*x3 + c[4]*y3 + c[5]) / (c[6]*x3 + c[7]*y3 + 1) x4' = (c[0]*x4 + c[1]*y4 + c[2]) / (c[6]*x4 + c[7]*y4 + 1) y4' = (c[3]*x4 + c[4]*y4 + c[5]) / (c[6]*x4 + c[7]*y4 + 1) Multiplying both sides of each eqn by the denominator, we get 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 1 0 0 0 -x1*x1' -y1*x1' 0 0 0 x1 y1 1 -x1*y1' -y1*y1' x2 y2 1 0 0 0 -x2*x2' -y2*x2' 0 0 0 x2 y2 1 -x2*y2' -y2*y2' x3 y3 1 0 0 0 -x3*x3' -y3*x3' 0 0 0 x3 y3 1 -x3*y3' -y3*y3' x4 y4 1 0 0 0 -x4*x4' -y4*x4' 0 0 0 x4 y4 1 -x4*y4' -y4*y4' 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]) / (c[6]x + c[7]y + 1) y' = (c[3]x + c[4]y + c[5]) / (c[6]x + c[7]y + 1) that is implemented in projectiveXformSampled() and projectiveXFormInterpolated().
PIX * pixProjective ( PIX *pixs, l_float32 *vc, l_int32 incolor )
pixProjective() Input: pixs (all depths; colormap ok) vc (vector of 8 coefficients for projective 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
PIX * pixProjectiveColor ( PIX *pixs, l_float32 *vc, l_uint32 colorval )
pixProjectiveColor() Input: pixs (32 bpp) vc (vector of 8 coefficients for projective transformation) colorval (e.g., 0 to bring in BLACK, 0xffffff00 for WHITE) Return: pixd, or null on error
PIX * pixProjectiveGray ( PIX *pixs, l_float32 *vc, l_uint8 grayval )
pixProjectiveGray() Input: pixs (8 bpp) vc (vector of 8 coefficients for projective transformation) grayval (0 to bring in BLACK, 255 for WHITE) Return: pixd, or null on error
PIX * pixProjectivePta ( PIX *pixs, PTA *ptad, PTA *ptas, l_int32 incolor )
pixProjectivePta() 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
PIX * pixProjectivePtaColor ( PIX *pixs, PTA *ptad, PTA *ptas, l_uint32 colorval )
pixProjectivePtaColor() 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
PIX * pixProjectivePtaGray ( PIX *pixs, PTA *ptad, PTA *ptas, l_uint8 grayval )
pixProjectivePtaGray() 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
PIX * pixProjectivePtaWithAlpha ( PIX *pixs, PTA *ptad, PTA *ptas, PIX *pixg, l_float32 fract, l_int32 border )
pixProjectivePtaWithAlpha() Input: pixs (32 bpp rgb) ptad (4 pts of final coordinate space) ptas (4 pts of initial coordinate space) pixg (<optional> 8 bpp, for alpha channel, 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 @fract. Otherwise, it is cropped to pixs if required and @fract 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 projective transformation. This can be any non-negative number. (6) The input @ptad and @ptas are in a coordinate space before the border is added. Internally, we compensate for this before doing the projective 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. (8) A subtle use of gamma correction is to remove gamma correction before scaling and restore it afterwards. This is done by sandwiching this function between a gamma/inverse-gamma photometric transform: pixt = pixGammaTRCWithAlpha(NULL, pixs, 1.0 / gamma, 0, 255); pixd = pixProjectivePtaWithAlpha(pixt, ptad, ptas, NULL, fract, border); pixGammaTRCWithAlpha(pixd, pixd, gamma, 0, 255); pixDestroy(&pixt); This has the side-effect of producing artifacts in the very dark regions.
PIX * pixProjectiveSampled ( PIX *pixs, l_float32 *vc, l_int32 incolor )
pixProjectiveSampled() Input: pixs (all depths) vc (vector of 8 coefficients for projective 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 pixProjective(). See that function for relative timings between sampled and interpolated.
PIX * pixProjectiveSampledPta ( PIX *pixs, PTA *ptad, PTA *ptas, l_int32 incolor )
pixProjectiveSampledPta() 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 pixProjectivePta(). See that function for relative timings between sampled and interpolated.
l_int32 projectiveXformPt ( l_float32 *vc, l_int32 x, l_int32 y, l_float32 *pxp, l_float32 *pyp )
projectiveXformPt() 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!
l_int32 projectiveXformSampledPt ( l_float32 *vc, l_int32 x, l_int32 y, l_int32 *pxp, l_int32 *pyp )
projectiveXformSampledPt() 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!
Zakariyya Mughal <zmughal@cpan.org>
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.
To install Image::Leptonica, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Image::Leptonica
CPAN shell
perl -MCPAN -e shell install Image::Leptonica
For more information on module installation, please visit the detailed CPAN module installation guide.