Leptonica  1.82.0
Image processing and image analysis suite
projective.c File Reference
#include <string.h>
#include <math.h>
#include "allheaders.h"

Go to the source code of this file.

Functions

PIXpixProjectiveSampledPta (PIX *pixs, PTA *ptad, PTA *ptas, l_int32 incolor)
 
PIXpixProjectiveSampled (PIX *pixs, l_float32 *vc, l_int32 incolor)
 
PIXpixProjectivePta (PIX *pixs, PTA *ptad, PTA *ptas, l_int32 incolor)
 
PIXpixProjective (PIX *pixs, l_float32 *vc, l_int32 incolor)
 
PIXpixProjectivePtaColor (PIX *pixs, PTA *ptad, PTA *ptas, l_uint32 colorval)
 
PIXpixProjectiveColor (PIX *pixs, l_float32 *vc, l_uint32 colorval)
 
PIXpixProjectivePtaGray (PIX *pixs, PTA *ptad, PTA *ptas, l_uint8 grayval)
 
PIXpixProjectiveGray (PIX *pixs, l_float32 *vc, l_uint8 grayval)
 
PIXpixProjectivePtaWithAlpha (PIX *pixs, PTA *ptad, PTA *ptas, PIX *pixg, l_float32 fract, l_int32 border)
 
l_ok getProjectiveXformCoeffs (PTA *ptas, PTA *ptad, l_float32 **pvc)
 
l_ok projectiveXformSampledPt (l_float32 *vc, l_int32 x, l_int32 y, l_int32 *pxp, l_int32 *pyp)
 
l_ok projectiveXformPt (l_float32 *vc, l_int32 x, l_int32 y, l_float32 *pxp, l_float32 *pyp)
 

Variables

l_float32 AlphaMaskBorderVals [2]
 

Detailed Description


     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, once the coefficients are known, we use the
     equations "backwards": for each point (x,y) in the dest image,
     these two equations are used to compute the corresponding point
     (x',y') in the src.  That computed point in the src is then used
     to determine the corresponding dest pixel value in one of two ways:

      ~ sampling: simply 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.

Definition in file projective.c.

Function Documentation

◆ getProjectiveXformCoeffs()

l_ok getProjectiveXformCoeffs ( PTA ptas,
PTA ptad,
l_float32 **  pvc 
)

getProjectiveXformCoeffs()

Parameters
[in]ptassource 4 points; unprimed
[in]ptadtransformed 4 points; primed
[out]pvcvector of coefficients of transform
Returns
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.

Definition at line 778 of file projective.c.

References gaussjordan(), and ptaGetPt().

Referenced by fpixProjectivePta(), and pixProjectiveSampledPta().

◆ pixProjective()

PIX* pixProjective ( PIX pixs,
l_float32 *  vc,
l_int32  incolor 
)

pixProjective()

Parameters
[in]pixsall depths; colormap ok
[in]vcvector of 8 coefficients for projective transform
[in]incolorL_BRING_IN_WHITE, L_BRING_IN_BLACK
Returns
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 357 of file projective.c.

◆ pixProjectiveColor()

PIX* pixProjectiveColor ( PIX pixs,
l_float32 *  vc,
l_uint32  colorval 
)

pixProjectiveColor()

Parameters
[in]pixs32 bpp
[in]vcvector of 8 coefficients for projective transform
[in]colorvale.g., 0 to bring in BLACK, 0xffffff00 for WHITE
Returns
pixd, or NULL on error

Definition at line 454 of file projective.c.

References pixGetData(), and pixGetDimensions().

◆ pixProjectiveGray()

PIX* pixProjectiveGray ( PIX pixs,
l_float32 *  vc,
l_uint8  grayval 
)

pixProjectiveGray()

Parameters
[in]pixs8 bpp
[in]vcvector of 8 coefficients for projective transform
[in]grayval0 to bring in BLACK, 255 for WHITE
Returns
pixd, or NULL on error

Definition at line 558 of file projective.c.

References pixGetDimensions().

◆ pixProjectivePta()

PIX* pixProjectivePta ( PIX pixs,
PTA ptad,
PTA ptas,
l_int32  incolor 
)

pixProjectivePta()

Parameters
[in]pixsall depths; colormap ok
[in]ptad4 pts of final coordinate space
[in]ptas4 pts of initial coordinate space
[in]incolorL_BRING_IN_WHITE, L_BRING_IN_BLACK
Returns
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 287 of file projective.c.

References L_BRING_IN_BLACK, L_BRING_IN_WHITE, and ptaGetCount().

◆ pixProjectivePtaColor()

PIX* pixProjectivePtaColor ( PIX pixs,
PTA ptad,
PTA ptas,
l_uint32  colorval 
)

pixProjectivePtaColor()

Parameters
[in]pixs32 bpp
[in]ptad4 pts of final coordinate space
[in]ptas4 pts of initial coordinate space
[in]colorvale.g., 0 to bring in BLACK, 0xffffff00 for WHITE
Returns
pixd, or NULL on error

Definition at line 413 of file projective.c.

◆ pixProjectivePtaGray()

PIX* pixProjectivePtaGray ( PIX pixs,
PTA ptad,
PTA ptas,
l_uint8  grayval 
)

pixProjectivePtaGray()

Parameters
[in]pixs8 bpp
[in]ptad4 pts of final coordinate space
[in]ptas4 pts of initial coordinate space
[in]grayval0 to bring in BLACK, 255 for WHITE
Returns
pixd, or NULL on error

Definition at line 516 of file projective.c.

◆ pixProjectivePtaWithAlpha()

PIX* pixProjectivePtaWithAlpha ( PIX pixs,
PTA ptad,
PTA ptas,
PIX pixg,
l_float32  fract,
l_int32  border 
)

pixProjectivePtaWithAlpha()

Parameters
[in]pixs32 bpp rgb
[in]ptad4 pts of final coordinate space
[in]ptas4 pts of initial coordinate space
[in]pixg[optional] 8 bpp, for alpha channel, can be null
[in]fractbetween 0.0 and 1.0, with 0.0 fully transparent and 1.0 fully opaque
[in]borderof pixels added to capture transformed source pixels
Returns
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.

Definition at line 647 of file projective.c.

References pixGetDimensions().

◆ pixProjectiveSampled()

PIX* pixProjectiveSampled ( PIX pixs,
l_float32 *  vc,
l_int32  incolor 
)

pixProjectiveSampled()

Parameters
[in]pixsall depths
[in]vcvector of 8 coefficients for projective transform
[in]incolorL_BRING_IN_WHITE, L_BRING_IN_BLACK
Returns
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.

Definition at line 194 of file projective.c.

References L_BRING_IN_BLACK, L_BRING_IN_WHITE, pixCreateTemplate(), and pixGetDimensions().

Referenced by pixProjectiveSampledPta().

◆ pixProjectiveSampledPta()

PIX* pixProjectiveSampledPta ( PIX pixs,
PTA ptad,
PTA ptas,
l_int32  incolor 
)

pixProjectiveSampledPta()

Parameters
[in]pixsall depths
[in]ptad4 pts of final coordinate space
[in]ptas4 pts of initial coordinate space
[in]incolorL_BRING_IN_WHITE, L_BRING_IN_BLACK
Returns
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.

Definition at line 144 of file projective.c.

References getProjectiveXformCoeffs(), L_BRING_IN_BLACK, L_BRING_IN_WHITE, pixProjectiveSampled(), and ptaGetCount().

◆ projectiveXformPt()

l_ok projectiveXformPt ( l_float32 *  vc,
l_int32  x,
l_int32  y,
l_float32 *  pxp,
l_float32 *  pyp 
)

projectiveXformPt()

Parameters
[in]vcvector of 8 coefficients
[in]x,yinitial point
[out]pxp,pyptransformed point
Returns
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 912 of file projective.c.

Referenced by fpixProjective().

◆ projectiveXformSampledPt()

l_ok projectiveXformSampledPt ( l_float32 *  vc,
l_int32  x,
l_int32  y,
l_int32 *  pxp,
l_int32 *  pyp 
)

projectiveXformSampledPt()

Parameters
[in]vcvector of 8 coefficients
[in]x,yinitial point
[out]pxp,pyptransformed point
Returns
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 874 of file projective.c.