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
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
|
// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2021 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Bicubic interpolation with analytic differentiation
//
// We will use estimation of 2d shift as a sample problem for bicubic
// interpolation.
//
// Let us define f(x, y) = x * x - y * x + y * y
// And optimize cost function sum_i [f(x_i + s_x, y_i + s_y) - v_i]^2
//
// Bicubic interpolation of f(x, y) will be exact, thus we can expect close to
// perfect convergence
#include <utility>
#include "ceres/ceres.h"
#include "ceres/cubic_interpolation.h"
#include "glog/logging.h"
using Grid = ceres::Grid2D<double>;
using Interpolator = ceres::BiCubicInterpolator<Grid>;
// Cost-function using analytic interface of BiCubicInterpolator
struct AnalyticBiCubicCost : public ceres::CostFunction {
EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
bool Evaluate(double const* const* parameters,
double* residuals,
double** jacobians) const override {
Eigen::Map<const Eigen::Vector2d> shift(parameters[0]);
const Eigen::Vector2d point = point_ + shift;
double* f = residuals;
double* dfdr = nullptr;
double* dfdc = nullptr;
if (jacobians && jacobians[0]) {
dfdc = jacobians[0];
dfdr = dfdc + 1;
}
interpolator_.Evaluate(point.y(), point.x(), f, dfdr, dfdc);
if (residuals) {
*f -= value_;
}
return true;
}
AnalyticBiCubicCost(const Interpolator& interpolator,
Eigen::Vector2d point,
double value)
: point_(std::move(point)), value_(value), interpolator_(interpolator) {
set_num_residuals(1);
*mutable_parameter_block_sizes() = {2};
}
static ceres::CostFunction* Create(const Interpolator& interpolator,
const Eigen::Vector2d& point,
double value) {
return new AnalyticBiCubicCost(interpolator, point, value);
}
const Eigen::Vector2d point_;
const double value_;
const Interpolator& interpolator_;
};
// Function for input data generation
static double f(const double& x, const double& y) {
return x * x - y * x + y * y;
}
int main(int argc, char** argv) {
google::InitGoogleLogging(argv[0]);
// Problem sizes
const int kGridRowsHalf = 9;
const int kGridColsHalf = 11;
const int kGridRows = 2 * kGridRowsHalf + 1;
const int kGridCols = 2 * kGridColsHalf + 1;
const int kPoints = 4;
const Eigen::Vector2d shift(1.234, 2.345);
const std::array<Eigen::Vector2d, kPoints> points = {
Eigen::Vector2d{-2., -3.},
Eigen::Vector2d{-2., 3.},
Eigen::Vector2d{2., 3.},
Eigen::Vector2d{2., -3.}};
// Data is a row-major array of kGridRows x kGridCols values of function
// f(x, y) on the grid, with x in {-kGridColsHalf, ..., +kGridColsHalf},
// and y in {-kGridRowsHalf, ..., +kGridRowsHalf}
double data[kGridRows * kGridCols];
for (int i = 0; i < kGridRows; ++i) {
for (int j = 0; j < kGridCols; ++j) {
// Using row-major order
int index = i * kGridCols + j;
double y = i - kGridRowsHalf;
double x = j - kGridColsHalf;
data[index] = f(x, y);
}
}
const Grid grid(data,
-kGridRowsHalf,
kGridRowsHalf + 1,
-kGridColsHalf,
kGridColsHalf + 1);
const Interpolator interpolator(grid);
Eigen::Vector2d shift_estimate(3.1415, 1.337);
ceres::Problem problem;
problem.AddParameterBlock(shift_estimate.data(), 2);
for (const auto& p : points) {
const Eigen::Vector2d shifted = p + shift;
const double v = f(shifted.x(), shifted.y());
problem.AddResidualBlock(AnalyticBiCubicCost::Create(interpolator, p, v),
nullptr,
shift_estimate.data());
}
ceres::Solver::Options options;
options.minimizer_progress_to_stdout = true;
ceres::Solver::Summary summary;
ceres::Solve(options, &problem, &summary);
std::cout << summary.BriefReport() << '\n';
std::cout << "Bicubic interpolation with analytic derivatives:\n";
std::cout << "Estimated shift: " << shift_estimate.transpose()
<< ", ground-truth: " << shift.transpose()
<< " (error: " << (shift_estimate - shift).transpose() << ")"
<< std::endl;
CHECK_LT((shift_estimate - shift).norm(), 1e-9);
return 0;
}
|
