homography.h

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/* Copyright (C) 2013-2016, The Regents of The University of Michigan.
All rights reserved.
This software was developed in the APRIL Robotics Lab under the
direction of Edwin Olson, ebolson@umich.edu. This software may be
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*/

#pragma once

#include "matd.h"
#include "zarray.h"

#ifdef __cplusplus
extern "C" {
#endif

// correspondences is a list of float[4]s, consisting of the points x
// and y concatenated. We will compute a homography such that y = Hx
// Specifically, float [] { a, b, c, d } where x = [a b], y = [c d].


#define HOMOGRAPHY_COMPUTE_FLAG_INVERSE 1
#define HOMOGRAPHY_COMPUTE_FLAG_SVD 0

matd_t *homography_compute(zarray_t *correspondences, int flags);

//void homography_project(const matd_t *H, double x, double y, double *ox, double *oy);
static inline void homography_project(const matd_t *H, double x, double y, double *ox, double *oy)
{
    double xx = MATD_EL(H, 0, 0)*x + MATD_EL(H, 0, 1)*y + MATD_EL(H, 0, 2);
    double yy = MATD_EL(H, 1, 0)*x + MATD_EL(H, 1, 1)*y + MATD_EL(H, 1, 2);
    double zz = MATD_EL(H, 2, 0)*x + MATD_EL(H, 2, 1)*y + MATD_EL(H, 2, 2);

    *ox = xx / zz;
    *oy = yy / zz;
}

// assuming that the projection matrix is:
// [ fx 0  cx 0 ]
// [  0 fy cy 0 ]
// [  0  0  1 0 ]
//
// And that the homography is equal to the projection matrix times the model matrix,
// recover the model matrix (which is returned). Note that the third column of the model
// matrix is missing in the expresison below, reflecting the fact that the homography assumes
// all points are at z=0 (i.e., planar) and that the element of z is thus omitted.
// (3x1 instead of 4x1).
//
// [ fx 0  cx 0 ] [ R00  R01  TX ]    [ H00 H01 H02 ]
// [  0 fy cy 0 ] [ R10  R11  TY ] =  [ H10 H11 H12 ]
// [  0  0  1 0 ] [ R20  R21  TZ ] =  [ H20 H21 H22 ]
//                [  0    0    1 ]
//
// fx*R00 + cx*R20 = H00   (note, H only known up to scale; some additional adjustments required; see code.)
// fx*R01 + cx*R21 = H01
// fx*TX  + cx*TZ  = H02
// fy*R10 + cy*R20 = H10
// fy*R11 + cy*R21 = H11
// fy*TY  + cy*TZ  = H12
// R20 = H20
// R21 = H21
// TZ  = H22
matd_t *homography_to_pose(const matd_t *H, double fx, double fy, double cx, double cy);

// Similar to above
// Recover the model view matrix assuming that the projection matrix is:
//
// [ F  0  A  0 ]     (see glFrustrum)
// [ 0  G  B  0 ]
// [ 0  0  C  D ]
// [ 0  0 -1  0 ]

matd_t *homography_to_model_view(const matd_t *H, double F, double G, double A, double B, double C, double D);

#ifdef __cplusplus
}
#endif