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// Copyright (c) 2009 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.
//
#include "libmv/multiview/panography.h"
namespace libmv {
static bool Build_Minimal2Point_PolynomialFactor(
const Mat& x1,
const Mat& x2,
double* P) { // P must be a double[4]
assert(2 == x1.rows());
assert(2 == x1.cols());
assert(x1.rows() == x2.rows());
assert(x1.cols() == x2.cols());
// Setup the variable of the input problem:
Vec xx1 = (x1.col(0)).transpose();
Vec yx1 = (x1.col(1)).transpose();
double a12 = xx1.dot(yx1);
Vec xx2 = (x2.col(0)).transpose();
Vec yx2 = (x2.col(1)).transpose();
double b12 = xx2.dot(yx2);
double a1 = xx1.squaredNorm();
double a2 = yx1.squaredNorm();
double b1 = xx2.squaredNorm();
double b2 = yx2.squaredNorm();
// Build the 3rd degre polynomial in F^2.
//
// f^6 * p + f^4 * q + f^2* r + s = 0;
//
// Coefficients in ascending powers of alpha, i.e. P[N]*x^N.
// Run panography_coeffs.py to get the below coefficients.
P[0] = b1 * b2 * a12 * a12 - a1 * a2 * b12 * b12;
P[1] = -2 * a1 * a2 * b12 + 2 * a12 * b1 * b2 + b1 * a12 * a12 +
b2 * a12 * a12 - a1 * b12 * b12 - a2 * b12 * b12;
P[2] = b1 * b2 - a1 * a2 - 2 * a1 * b12 - 2 * a2 * b12 + 2 * a12 * b1 +
2 * a12 * b2 + a12 * a12 - b12 * b12;
P[3] = b1 + b2 - 2 * b12 - a1 - a2 + 2 * a12;
// If P[3] equal to 0 we get ill conditionned data
return (P[3] != 0.0);
}
// This implements a minimal solution (2 points) for panoramic stitching:
//
// http://www.cs.ubc.ca/~mbrown/minimal/minimal.html
//
// [1] M. Brown and R. Hartley and D. Nister. Minimal Solutions for Panoramic
// Stitching. CVPR07.
void F_FromCorrespondance_2points(const Mat& x1,
const Mat& x2,
vector<double>* fs) {
// Build Polynomial factor to get squared focal value.
double P[4];
Build_Minimal2Point_PolynomialFactor(x1, x2, &P[0]);
// Solve it by using F = f^2 and a Cubic polynomial solver
//
// F^3 * p + F^2 * q + F^1 * r + s = 0
//
double roots[3];
int num_roots = SolveCubicPolynomial(P, roots);
for (int i = 0; i < num_roots; ++i) {
if (roots[i] > 0.0) {
fs->push_back(sqrt(roots[i]));
}
}
}
// Compute the 3x3 rotation matrix that fits two 3D point clouds in the least
// square sense. The method is from:
//
// K. Arun,T. Huand and D. Blostein. Least-squares fitting of 2 3-D point
// sets. IEEE Transactions on Pattern Analysis and Machine Intelligence,
// 9:698-700, 1987.
void GetR_FixedCameraCenter(const Mat& x1,
const Mat& x2,
const double focal,
Mat3* R) {
assert(3 == x1.rows());
assert(2 <= x1.cols());
assert(x1.rows() == x2.rows());
assert(x1.cols() == x2.cols());
// Build simplified K matrix
Mat3 K(Mat3::Identity() * 1.0 / focal);
K(2, 2) = 1.0;
// Build the correlation matrix; equation (22) in [1].
Mat3 C = Mat3::Zero();
for (int i = 0; i < x1.cols(); ++i) {
Mat r1i = (K * x1.col(i)).normalized();
Mat r2i = (K * x2.col(i)).normalized();
C += r2i * r1i.transpose();
}
// Solve for rotation. Equations (24) and (25) in [1].
Eigen::JacobiSVD<Mat> svd(C, Eigen::ComputeThinU | Eigen::ComputeThinV);
Mat3 scale = Mat3::Identity();
scale(2, 2) =
((svd.matrixU() * svd.matrixV().transpose()).determinant() > 0.0) ? 1.0
: -1.0;
(*R) = svd.matrixU() * scale * svd.matrixV().transpose();
}
} // namespace libmv
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