1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
|
// Copyright (c) 2011 libmv authors.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
#ifndef LIBMV_MULTIVIEW_HOMOGRAPHY_H_
#define LIBMV_MULTIVIEW_HOMOGRAPHY_H_
#include "libmv/numeric/numeric.h"
namespace libmv {
/**
* 2D homography transformation estimation.
*
* This function estimates the homography transformation from a list of 2D
* correspondences which represents either:
*
* - 3D points on a plane, with a general moving camera.
* - 3D points with a rotating camera (pure rotation).
* - 3D points + different planar projections
*
* \param x1: The first 2xN or 3xN matrix of euclidean or homogeneous points.
* \param x2: The second 2xN or 3xN matrix of euclidean or homogeneous points.
* \param H: The 3x3 homography transformation matrix (8 dof) such that
* <pre>
* x2 = H * x1 with |a b c|
* H = |d e f|
* |g h 1|
* </pre>
* \param expected_precision: The expected precision in order for instance
* to accept almost homography matrices.
*
* \return True if the transformation estimation has succeeded.
* \note There must be at least 4 non-colinear points.
*/
bool Homography2DFromCorrespondencesLinear(const Mat &x1,
const Mat &x2,
Mat3 *H,
double expected_precision =
EigenDouble::dummy_precision());
/**
* This structure contains options that controls how the homography
* estimation operates.
*
* Defaults should be suitable for a wide range of use cases, but
* better performance and accuracy might require tweaking/
*/
struct EstimateHomographyOptions {
// Default constructor which sets up a options for generic usage.
EstimateHomographyOptions(void);
// Normalize correspondencies before estimating the homography
// in order to increase estimation stability.
//
// Normaliztion will make it so centroid od correspondences
// is the coordinate origin and their average distance from
// the origin is sqrt(2).
//
// See:
// - R. Hartley and A. Zisserman. Multiple View Geometry in Computer
// Vision. Cambridge University Press, second edition, 2003.
// - https://www.cs.ubc.ca/grads/resources/thesis/May09/Dubrofsky_Elan.pdf
bool use_normalization;
// Maximal number of iterations for the refinement step.
int max_num_iterations;
// Expected average of symmetric geometric distance between
// actual destination points and original ones transformed by
// estimated homography matrix.
//
// Refinement will finish as soon as average of symmetric
// geometric distance is less or equal to this value.
//
// This distance is measured in the same units as input points are.
double expected_average_symmetric_distance;
};
/**
* 2D homography transformation estimation.
*
* This function estimates the homography transformation from a list of 2D
* correspondences by doing algebraic estimation first followed with result
* refinement.
*/
bool EstimateHomography2DFromCorrespondences(
const Mat &x1,
const Mat &x2,
const EstimateHomographyOptions &options,
Mat3 *H);
/**
* 3D Homography transformation estimation.
*
* This function can be used in order to estimate the homography transformation
* from a list of 3D correspondences.
*
* \param[in] x1 The first 4xN matrix of homogeneous points
* \param[in] x2 The second 4xN matrix of homogeneous points
* \param[out] H The 4x4 homography transformation matrix (15 dof) such that
* <pre>
* x2 = H * x1 with |a b c d|
* H = |e f g h|
* |i j k l|
* |m n o 1|
* </pre>
* \param[in] expected_precision The expected precision in order for instance
* to accept almost homography matrices.
*
* \return true if the transformation estimation has succeeded
*
* \note Need at least 5 non coplanar points
* \note Points coordinates must be in homogeneous coordinates
*/
bool Homography3DFromCorrespondencesLinear(const Mat &x1,
const Mat &x2,
Mat4 *H,
double expected_precision =
EigenDouble::dummy_precision());
/**
* Calculate symmetric geometric cost:
*
* D(H * x1, x2)^2 + D(H^-1 * x2, x1)
*/
double SymmetricGeometricDistance(const Mat3 &H,
const Vec2 &x1,
const Vec2 &x2);
} // namespace libmv
#endif // LIBMV_MULTIVIEW_HOMOGRAPHY_H_
|
