QGIS API Documentation 3.27.0-Master (a46f227e17)
qgsleastsquares.cpp
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1/***************************************************************************
2 qgsleastsquares.cpp
3 --------------------------------------
4 Date : Sun Sep 16 12:03:37 AKDT 2007
5 Copyright : (C) 2007 by Gary E. Sherman
6 Email : sherman at mrcc dot com
7 ***************************************************************************
8 * *
9 * This program is free software; you can redistribute it and/or modify *
10 * it under the terms of the GNU General Public License as published by *
11 * the Free Software Foundation; either version 2 of the License, or *
12 * (at your option) any later version. *
13 * *
14 ***************************************************************************/
15
16#include "qgsleastsquares.h"
17#include "qgsconfig.h"
18#include "qgsexception.h"
19
20#include <QObject>
21
22#include <cmath>
23#include <stdexcept>
24
25#ifdef HAVE_GSL
26#include <gsl/gsl_linalg.h>
27#include <gsl/gsl_blas.h>
28#endif
29
30void QgsLeastSquares::linear( const QVector<QgsPointXY> &sourceCoordinates,
31 const QVector<QgsPointXY> &destinationCoordinates,
32 QgsPointXY &origin, double &pixelXSize, double &pixelYSize )
33{
34 const int n = destinationCoordinates.size();
35 if ( n < 2 )
36 {
37 throw std::domain_error( QObject::tr( "Fit to a linear transform requires at least 2 points." ).toLocal8Bit().constData() );
38 }
39
40 double sumPx( 0 ), sumPy( 0 ), sumPx2( 0 ), sumPy2( 0 ), sumPxMx( 0 ), sumPyMy( 0 ), sumMx( 0 ), sumMy( 0 );
41 for ( int i = 0; i < n; ++i )
42 {
43 sumPx += sourceCoordinates.at( i ).x();
44 sumPy += sourceCoordinates.at( i ).y();
45 sumPx2 += std::pow( sourceCoordinates.at( i ).x(), 2 );
46 sumPy2 += std::pow( sourceCoordinates.at( i ).y(), 2 );
47 sumPxMx += sourceCoordinates.at( i ).x() * destinationCoordinates.at( i ).x();
48 sumPyMy += sourceCoordinates.at( i ).y() * destinationCoordinates.at( i ).y();
49 sumMx += destinationCoordinates.at( i ).x();
50 sumMy += destinationCoordinates.at( i ).y();
51 }
52
53 const double deltaX = n * sumPx2 - std::pow( sumPx, 2 );
54 const double deltaY = n * sumPy2 - std::pow( sumPy, 2 );
55
56 const double aX = ( sumPx2 * sumMx - sumPx * sumPxMx ) / deltaX;
57 const double aY = ( sumPy2 * sumMy - sumPy * sumPyMy ) / deltaY;
58 const double bX = ( n * sumPxMx - sumPx * sumMx ) / deltaX;
59 const double bY = ( n * sumPyMy - sumPy * sumMy ) / deltaY;
60
61 origin.setX( aX );
62 origin.setY( aY );
63
64 pixelXSize = std::fabs( bX );
65 pixelYSize = std::fabs( bY );
66}
67
68
69void QgsLeastSquares::helmert( const QVector<QgsPointXY> &sourceCoordinates,
70 const QVector<QgsPointXY> &destinationCoordinates,
71 QgsPointXY &origin, double &pixelSize,
72 double &rotation )
73{
74#ifndef HAVE_GSL
75 ( void )sourceCoordinates;
76 ( void )destinationCoordinates;
77 ( void )origin;
78 ( void )pixelSize;
79 ( void )rotation;
80 throw QgsNotSupportedException( QObject::tr( "Calculating a helmert transformation requires a QGIS build based GSL" ) );
81#else
82 const int n = destinationCoordinates.size();
83 if ( n < 2 )
84 {
85 throw std::domain_error( QObject::tr( "Fit to a Helmert transform requires at least 2 points." ).toLocal8Bit().constData() );
86 }
87
88 double A = 0;
89 double B = 0;
90 double C = 0;
91 double D = 0;
92 double E = 0;
93 double F = 0;
94 double G = 0;
95 double H = 0;
96 double I = 0;
97 double J = 0;
98 for ( int i = 0; i < n; ++i )
99 {
100 A += sourceCoordinates.at( i ).x();
101 B += sourceCoordinates.at( i ).y();
102 C += destinationCoordinates.at( i ).x();
103 D += destinationCoordinates.at( i ).y();
104 E += destinationCoordinates.at( i ).x() * sourceCoordinates.at( i ).x();
105 F += destinationCoordinates.at( i ).y() * sourceCoordinates.at( i ).y();
106 G += std::pow( sourceCoordinates.at( i ).x(), 2 );
107 H += std::pow( sourceCoordinates.at( i ).y(), 2 );
108 I += destinationCoordinates.at( i ).x() * sourceCoordinates.at( i ).y();
109 J += sourceCoordinates.at( i ).x() * destinationCoordinates.at( i ).y();
110 }
111
112 /* The least squares fit for the parameters { a, b, x0, y0 } is the solution
113 to the matrix equation Mx = b, where M and b is given below. I *think*
114 that this is correct but I derived it myself late at night. Look at
115 helmert.jpg if you suspect bugs. */
116
117 double MData[] = { A, -B, ( double ) n, 0.,
118 B, A, 0., ( double ) n,
119 G + H, 0., A, B,
120 0., G + H, -B, A
121 };
122
123 double bData[] = { C, D, E + F, J - I };
124
125 // we want to solve the equation M*x = b, where x = [a b x0 y0]
126 gsl_matrix_view M = gsl_matrix_view_array( MData, 4, 4 );
127 const gsl_vector_view b = gsl_vector_view_array( bData, 4 );
128 gsl_vector *x = gsl_vector_alloc( 4 );
129 gsl_permutation *p = gsl_permutation_alloc( 4 );
130 int s;
131 gsl_linalg_LU_decomp( &M.matrix, p, &s );
132 gsl_linalg_LU_solve( &M.matrix, p, &b.vector, x );
133 gsl_permutation_free( p );
134
135 origin.setX( gsl_vector_get( x, 2 ) );
136 origin.setY( gsl_vector_get( x, 3 ) );
137 pixelSize = std::sqrt( std::pow( gsl_vector_get( x, 0 ), 2 ) +
138 std::pow( gsl_vector_get( x, 1 ), 2 ) );
139 rotation = std::atan2( gsl_vector_get( x, 1 ), gsl_vector_get( x, 0 ) );
140#endif
141}
142
143#if 0
144void QgsLeastSquares::affine( QVector<QgsPointXY> mapCoords,
145 QVector<QgsPointXY> pixelCoords )
146{
147 int n = mapCoords.size();
148 if ( n < 4 )
149 {
150 throw std::domain_error( QObject::tr( "Fit to an affine transform requires at least 4 points." ).toLocal8Bit().constData() );
151 }
152
153 double A = 0, B = 0, C = 0, D = 0, E = 0, F = 0,
154 G = 0, H = 0, I = 0, J = 0, K = 0;
155 for ( int i = 0; i < n; ++i )
156 {
157 A += pixelCoords[i].x();
158 B += pixelCoords[i].y();
159 C += mapCoords[i].x();
160 D += mapCoords[i].y();
161 E += std::pow( pixelCoords[i].x(), 2 );
162 F += std::pow( pixelCoords[i].y(), 2 );
163 G += pixelCoords[i].x() * pixelCoords[i].y();
164 H += pixelCoords[i].x() * mapCoords[i].x();
165 I += pixelCoords[i].y() * mapCoords[i].y();
166 J += pixelCoords[i].x() * mapCoords[i].y();
167 K += mapCoords[i].x() * pixelCoords[i].y();
168 }
169
170 /* The least squares fit for the parameters { a, b, c, d, x0, y0 } is the
171 solution to the matrix equation Mx = b, where M and b is given below.
172 I *think* that this is correct but I derived it myself late at night.
173 Look at affine.jpg if you suspect bugs. */
174
175 double MData[] = { A, B, 0, 0, ( double ) n, 0,
176 0, 0, A, B, 0, ( double ) n,
177 E, G, 0, 0, A, 0,
178 G, F, 0, 0, B, 0,
179 0, 0, E, G, 0, A,
180 0, 0, G, F, 0, B
181 };
182
183 double bData[] = { C, D, H, K, J, I };
184
185 // we want to solve the equation M*x = b, where x = [a b c d x0 y0]
186 gsl_matrix_view M = gsl_matrix_view_array( MData, 6, 6 );
187 gsl_vector_view b = gsl_vector_view_array( bData, 6 );
188 gsl_vector *x = gsl_vector_alloc( 6 );
189 gsl_permutation *p = gsl_permutation_alloc( 6 );
190 int s;
191 gsl_linalg_LU_decomp( &M.matrix, p, &s );
192 gsl_linalg_LU_solve( &M.matrix, p, &b.vector, x );
193 gsl_permutation_free( p );
194
195}
196#endif
197
203void normalizeCoordinates( const QVector<QgsPointXY> &coords, QVector<QgsPointXY> &normalizedCoords,
204 double normalizeMatrix[9], double denormalizeMatrix[9] )
205{
206 // Calculate center of gravity
207 double cogX = 0.0, cogY = 0.0;
208 for ( int i = 0; i < coords.size(); i++ )
209 {
210 cogX += coords[i].x();
211 cogY += coords[i].y();
212 }
213 cogX *= 1.0 / coords.size();
214 cogY *= 1.0 / coords.size();
215
216 // Calculate mean distance to origin
217 double meanDist = 0.0;
218 for ( int i = 0; i < coords.size(); i++ )
219 {
220 const double X = ( coords[i].x() - cogX );
221 const double Y = ( coords[i].y() - cogY );
222 meanDist += std::sqrt( X * X + Y * Y );
223 }
224 meanDist *= 1.0 / coords.size();
225
226 const double OOD = meanDist * M_SQRT1_2;
227 const double D = 1.0 / OOD;
228 normalizedCoords.resize( coords.size() );
229 for ( int i = 0; i < coords.size(); i++ )
230 {
231 normalizedCoords[i] = QgsPointXY( ( coords[i].x() - cogX ) * D, ( coords[i].y() - cogY ) * D );
232 }
233
234 normalizeMatrix[0] = D;
235 normalizeMatrix[1] = 0.0;
236 normalizeMatrix[2] = -cogX * D;
237 normalizeMatrix[3] = 0.0;
238 normalizeMatrix[4] = D;
239 normalizeMatrix[5] = -cogY * D;
240 normalizeMatrix[6] = 0.0;
241 normalizeMatrix[7] = 0.0;
242 normalizeMatrix[8] = 1.0;
243
244 denormalizeMatrix[0] = OOD;
245 denormalizeMatrix[1] = 0.0;
246 denormalizeMatrix[2] = cogX;
247 denormalizeMatrix[3] = 0.0;
248 denormalizeMatrix[4] = OOD;
249 denormalizeMatrix[5] = cogY;
250 denormalizeMatrix[6] = 0.0;
251 denormalizeMatrix[7] = 0.0;
252 denormalizeMatrix[8] = 1.0;
253}
254
255// Fits a homography to the given corresponding points, and
256// return it in H (row-major format).
257void QgsLeastSquares::projective( const QVector<QgsPointXY> &sourceCoordinates,
258 const QVector<QgsPointXY> &destinationCoordinates,
259 double H[9] )
260{
261#ifndef HAVE_GSL
262 ( void )sourceCoordinates;
263 ( void )destinationCoordinates;
264 ( void )H;
265 throw QgsNotSupportedException( QObject::tr( "Calculating a projective transformation requires a QGIS build based GSL" ) );
266#else
267 Q_ASSERT( sourceCoordinates.size() == destinationCoordinates.size() );
268
269 if ( destinationCoordinates.size() < 4 )
270 {
271 throw std::domain_error( QObject::tr( "Fitting a projective transform requires at least 4 corresponding points." ).toLocal8Bit().constData() );
272 }
273
274 QVector<QgsPointXY> sourceCoordinatesNormalized;
275 QVector<QgsPointXY> destinationCoordinatesNormalized;
276
277 double normSource[9], denormSource[9];
278 double normDest[9], denormDest[9];
279 normalizeCoordinates( sourceCoordinates, sourceCoordinatesNormalized, normSource, denormSource );
280 normalizeCoordinates( destinationCoordinates, destinationCoordinatesNormalized, normDest, denormDest );
281
282 // GSL does not support a full SVD, so we artificially add a linear dependent row
283 // to the matrix in case the system is underconstrained.
284 const uint m = std::max( 9u, ( uint )destinationCoordinatesNormalized.size() * 2u );
285 const uint n = 9;
286 gsl_matrix *S = gsl_matrix_alloc( m, n );
287
288 for ( int i = 0; i < destinationCoordinatesNormalized.size(); i++ )
289 {
290 gsl_matrix_set( S, i * 2, 0, sourceCoordinatesNormalized[i].x() );
291 gsl_matrix_set( S, i * 2, 1, sourceCoordinatesNormalized[i].y() );
292 gsl_matrix_set( S, i * 2, 2, 1.0 );
293
294 gsl_matrix_set( S, i * 2, 3, 0.0 );
295 gsl_matrix_set( S, i * 2, 4, 0.0 );
296 gsl_matrix_set( S, i * 2, 5, 0.0 );
297
298 gsl_matrix_set( S, i * 2, 6, -destinationCoordinatesNormalized[i].x()*sourceCoordinatesNormalized[i].x() );
299 gsl_matrix_set( S, i * 2, 7, -destinationCoordinatesNormalized[i].x()*sourceCoordinatesNormalized[i].y() );
300 gsl_matrix_set( S, i * 2, 8, -destinationCoordinatesNormalized[i].x() * 1.0 );
301
302 gsl_matrix_set( S, i * 2 + 1, 0, 0.0 );
303 gsl_matrix_set( S, i * 2 + 1, 1, 0.0 );
304 gsl_matrix_set( S, i * 2 + 1, 2, 0.0 );
305
306 gsl_matrix_set( S, i * 2 + 1, 3, sourceCoordinatesNormalized[i].x() );
307 gsl_matrix_set( S, i * 2 + 1, 4, sourceCoordinatesNormalized[i].y() );
308 gsl_matrix_set( S, i * 2 + 1, 5, 1.0 );
309
310 gsl_matrix_set( S, i * 2 + 1, 6, -destinationCoordinatesNormalized[i].y()*sourceCoordinatesNormalized[i].x() );
311 gsl_matrix_set( S, i * 2 + 1, 7, -destinationCoordinatesNormalized[i].y()*sourceCoordinatesNormalized[i].y() );
312 gsl_matrix_set( S, i * 2 + 1, 8, -destinationCoordinatesNormalized[i].y() * 1.0 );
313 }
314
315 if ( destinationCoordinatesNormalized.size() == 4 )
316 {
317 // The GSL SVD routine only supports matrices with rows >= columns (m >= n)
318 // Unfortunately, we can't use the SVD of the transpose (i.e. S^T = (U D V^T)^T = V D U^T)
319 // to work around this, because the solution lies in the right nullspace of S, and
320 // gsl only supports a thin SVD of S^T, which does not return these vectors.
321
322 // HACK: duplicate last row to get a 9x9 equation system
323 for ( int j = 0; j < 9; j++ )
324 {
325 gsl_matrix_set( S, 8, j, gsl_matrix_get( S, 7, j ) );
326 }
327 }
328
329 // Solve Sh = 0 in the total least squares sense, i.e.
330 // with Sh = min and |h|=1. The solution "h" is given by the
331 // right singular eigenvector of S corresponding, to the smallest
332 // singular value (via SVD).
333 gsl_matrix *V = gsl_matrix_alloc( n, n );
334 gsl_vector *singular_values = gsl_vector_alloc( n );
335 gsl_vector *work = gsl_vector_alloc( n );
336
337 // V = n x n
338 // U = m x n (thin SVD) U D V^T
339 gsl_linalg_SV_decomp( S, V, singular_values, work );
340
341 // Columns of V store the right singular vectors of S
342 for ( unsigned int i = 0; i < n; i++ )
343 {
344 H[i] = gsl_matrix_get( V, i, n - 1 );
345 }
346
347 gsl_matrix *prodMatrix = gsl_matrix_alloc( 3, 3 );
348
349 gsl_matrix_view Hmatrix = gsl_matrix_view_array( H, 3, 3 );
350 const gsl_matrix_view normSourceMatrix = gsl_matrix_view_array( normSource, 3, 3 );
351 const gsl_matrix_view denormDestMatrix = gsl_matrix_view_array( denormDest, 3, 3 );
352
353 // Change coordinate frame of image and pre-image from normalized to destination and source coordinates.
354 // H' = denormalizeMapCoords*H*normalizePixelCoords
355 gsl_blas_dgemm( CblasNoTrans, CblasNoTrans, 1.0, &Hmatrix.matrix, &normSourceMatrix.matrix, 0.0, prodMatrix );
356 gsl_blas_dgemm( CblasNoTrans, CblasNoTrans, 1.0, &denormDestMatrix.matrix, prodMatrix, 0.0, &Hmatrix.matrix );
357
358 gsl_matrix_free( prodMatrix );
359 gsl_matrix_free( S );
360 gsl_matrix_free( V );
361 gsl_vector_free( singular_values );
362 gsl_vector_free( work );
363#endif
364}
static void helmert(const QVector< QgsPointXY > &sourceCoordinates, const QVector< QgsPointXY > &destinationCoordinates, QgsPointXY &origin, double &pixelSize, double &rotation)
Transforms the point at origin in-place, using a helmert transformation calculated from the list of s...
static void projective(const QVector< QgsPointXY > &sourceCoordinates, const QVector< QgsPointXY > &destinationCoordinates, double H[9])
Calculates projective parameters from the list of source and destination Ground Control Points (GCPs)...
static void linear(const QVector< QgsPointXY > &sourceCoordinates, const QVector< QgsPointXY > &destinationCoordinates, QgsPointXY &origin, double &pixelXSize, double &pixelYSize)
Transforms the point at origin in-place, using a linear transformation calculated from the list of so...
Custom exception class which is raised when an operation is not supported.
Definition: qgsexception.h:118
A class to represent a 2D point.
Definition: qgspointxy.h:59
void setX(double x) SIP_HOLDGIL
Sets the x value of the point.
Definition: qgspointxy.h:122
void setY(double y) SIP_HOLDGIL
Sets the y value of the point.
Definition: qgspointxy.h:132
void normalizeCoordinates(const QVector< QgsPointXY > &coords, QVector< QgsPointXY > &normalizedCoords, double normalizeMatrix[9], double denormalizeMatrix[9])
Scales the given coordinates so that the center of gravity is at the origin and the mean distance to ...