/*
* Copyright (c) 2011-2013, Peter Abeles. All Rights Reserved.
*
* This file is part of BoofCV (http://boofcv.org).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package boofcv.alg.geo;
import boofcv.struct.geo.AssociatedPair;
import boofcv.struct.geo.AssociatedTriple;
import georegression.struct.point.Point2D_F64;
import org.ejml.data.DenseMatrix64F;
import java.util.List;
/**
* Lists of operations used by various multi-view algorithms, but not of use to the typical user.
*
* @author Peter Abeles
*/
public class LowLevelMultiViewOps {
/**
*
* Computes a normalization matrix used to reduce numerical errors inside of linear estimation algorithms.
* Pixels coordinates are poorly scaled for linear algebra operations resulting in excessive numerical error.
* This function computes a transform which will minimize numerical error by properly scaling the pixels.
*
*
*
* N = [ 1/σ_x 0 -μ_x/σ_x ]
* [ 0 1/σ_y 0 -μ_y/σ_y ]
* [ 0 0 1 ]
*
*
*
* Y. Ma, S. Soatto, J. Kosecka, and S. S. Sastry, "An Invitation to 3-D Vision" Springer-Verlad, 2004
*
*
* @param points Input: List of observed points. Not modified.
* @param N Output: 3x3 normalization matrix for first set of points. Modified.
*/
public static void computeNormalization(List points, DenseMatrix64F N )
{
double meanX1 = 0;
double meanY1 = 0;
for( Point2D_F64 p : points ) {
meanX1 += p.x;
meanY1 += p.y;
}
meanX1 /= points.size();
meanY1 /= points.size();
double stdX1 = 0;
double stdY1 = 0;
for( Point2D_F64 p : points ) {
double dx = p.x - meanX1;
double dy = p.y - meanY1;
stdX1 += dx*dx;
stdY1 += dy*dy;
}
stdX1 = Math.sqrt(stdX1/points.size());
stdY1 = Math.sqrt(stdY1/points.size());
N.zero();
N.set(0, 0, 1.0 / stdX1);
N.set(1, 1, 1.0 / stdY1);
N.set(0, 2, -meanX1 / stdX1);
N.set(1, 2, -meanY1 / stdY1);
N.set(2, 2, 1.0);
}
/**
*
* Computes two normalization matrices for each set of point correspondences in the list of
* {@link boofcv.struct.geo.AssociatedPair}. Same as {@link #computeNormalization(java.util.List, org.ejml.data.DenseMatrix64F)},
* but for two views.
*
*
* @param points Input: List of observed points that are to be normalized. Not modified.
* @param N1 Output: 3x3 normalization matrix for first set of points. Modified.
* @param N2 Output: 3x3 normalization matrix for second set of points. Modified.
*/
public static void computeNormalization(List points, DenseMatrix64F N1, DenseMatrix64F N2)
{
double meanX1 = 0; double meanY1 = 0;
double meanX2 = 0; double meanY2 = 0;
for( AssociatedPair p : points ) {
meanX1 += p.p1.x; meanY1 += p.p1.y;
meanX2 += p.p2.x; meanY2 += p.p2.y;
}
meanX1 /= points.size(); meanY1 /= points.size();
meanX2 /= points.size(); meanY2 /= points.size();
double stdX1 = 0; double stdY1 = 0;
double stdX2 = 0; double stdY2 = 0;
for( AssociatedPair p : points ) {
double dx = p.p1.x - meanX1;
double dy = p.p1.y - meanY1;
stdX1 += dx*dx;
stdY1 += dy*dy;
dx = p.p2.x - meanX2;
dy = p.p2.y - meanY2;
stdX2 += dx*dx;
stdY2 += dy*dy;
}
stdX1 = Math.sqrt(stdX1/points.size()); stdY1 = Math.sqrt(stdY1/points.size());
stdX2 = Math.sqrt(stdX2/points.size()); stdY2 = Math.sqrt(stdY2/points.size());
N1.zero(); N2.zero();
N1.set(0,0,1.0/stdX1);
N1.set(1,1,1.0/stdY1);
N1.set(0,2,-meanX1/stdX1);
N1.set(1,2,-meanY1/stdY1);
N1.set(2,2,1.0);
N2.set(0,0,1.0/stdX2);
N2.set(1,1,1.0/stdY2);
N2.set(0,2,-meanX2/stdX2);
N2.set(1,2,-meanY2/stdY2);
N2.set(2,2,1.0);
}
/**
*
* Computes three normalization matrices for each set of point correspondences in the list of
* {@link boofcv.struct.geo.AssociatedTriple}. Same as {@link #computeNormalization(java.util.List, org.ejml.data.DenseMatrix64F)},
* but for three views.
*
*
* @param points Input: List of observed points that are to be normalized. Not modified.
* @param N1 Output: 3x3 normalization matrix for first set of points. Modified.
* @param N2 Output: 3x3 normalization matrix for second set of points. Modified.
* @param N3 Output: 3x3 normalization matrix for third set of points. Modified.
*/
public static void computeNormalization( List points,
DenseMatrix64F N1, DenseMatrix64F N2, DenseMatrix64F N3 )
{
double meanX1 = 0; double meanY1 = 0;
double meanX2 = 0; double meanY2 = 0;
double meanX3 = 0; double meanY3 = 0;
for( AssociatedTriple p : points ) {
meanX1 += p.p1.x; meanY1 += p.p1.y;
meanX2 += p.p2.x; meanY2 += p.p2.y;
meanX3 += p.p3.x; meanY3 += p.p3.y;
}
meanX1 /= points.size(); meanY1 /= points.size();
meanX2 /= points.size(); meanY2 /= points.size();
meanX3 /= points.size(); meanY3 /= points.size();
double stdX1 = 0; double stdY1 = 0;
double stdX2 = 0; double stdY2 = 0;
double stdX3 = 0; double stdY3 = 0;
for( AssociatedTriple p : points ) {
double dx = p.p1.x - meanX1; double dy = p.p1.y - meanY1;
stdX1 += dx*dx; stdY1 += dy*dy;
dx = p.p2.x - meanX2; dy = p.p2.y - meanY2;
stdX2 += dx*dx; stdY2 += dy*dy;
dx = p.p3.x - meanX3; dy = p.p3.y - meanY3;
stdX3 += dx*dx; stdY3 += dy*dy;
}
stdX1 = Math.sqrt(stdX1/points.size()); stdY1 = Math.sqrt(stdY1/points.size());
stdX2 = Math.sqrt(stdX2/points.size()); stdY2 = Math.sqrt(stdY2/points.size());
stdX3 = Math.sqrt(stdX3/points.size()); stdY3 = Math.sqrt(stdY3/points.size());
N1.zero(); N2.zero(); N3.zero();
N1.set(0,0,1.0/stdX1);
N1.set(1,1,1.0/stdY1);
N1.set(0,2,-meanX1/stdX1);
N1.set(1,2,-meanY1/stdY1);
N1.set(2,2,1.0);
N2.set(0,0,1.0/stdX2);
N2.set(1,1,1.0/stdY2);
N2.set(0,2,-meanX2/stdX2);
N2.set(1,2,-meanY2/stdY2);
N2.set(2,2,1.0);
N3.set(0,0,1.0/stdX3);
N3.set(1,1,1.0/stdY3);
N3.set(0,2,-meanX3/stdX3);
N3.set(1,2,-meanY3/stdY3);
N3.set(2,2,1.0);
}
/**
* Given the normalization matrix computed from {@link #computeNormalization(java.util.List, org.ejml.data.DenseMatrix64F)}
* normalize the point.
*
* @param N Normalization matrix.
* @param orig Unnormalized coordinate in pixels.
* @param normed Normalized coordinate.
*/
public static void applyPixelNormalization(DenseMatrix64F N, Point2D_F64 orig, Point2D_F64 normed) {
normed.x = orig.x * N.data[0] + N.data[2];
normed.y = orig.y * N.data[4] + N.data[5];
}
}
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