Mercurial > hgrepos > Python2 > PyMuPDF

annotate mupdf-source/thirdparty/tesseract/src/ccstruct/linlsq.cpp @ 2:b50eed0cc0ef upstream

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ADD: MuPDF v1.26.7: the MuPDF source as downloaded by a default build of PyMuPDF 1.26.4. The directory name has changed: no version number in the expanded directory now.
author Franz Glasner <fzglas.hg@dom66.de>
date Mon, 15 Sep 2025 11:43:07 +0200
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children
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1 /**********************************************************************
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2 * File: linlsq.cpp (Formerly llsq.c)
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3 * Description: Linear Least squares fitting code.
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4 * Author: Ray Smith
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5 *
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6 * (C) Copyright 1991, Hewlett-Packard Ltd.
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7 ** Licensed under the Apache License, Version 2.0 (the "License");
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8 ** you may not use this file except in compliance with the License.
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9 ** You may obtain a copy of the License at
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10 ** http://www.apache.org/licenses/LICENSE-2.0
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11 ** Unless required by applicable law or agreed to in writing, software
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12 ** distributed under the License is distributed on an "AS IS" BASIS,
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13 ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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14 ** See the License for the specific language governing permissions and
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15 ** limitations under the License.
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16 *
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17 **********************************************************************/
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19 #include "linlsq.h"
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20 #include <cmath> // for std::sqrt
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21 #include <cstdio>
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22 #include "errcode.h"
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24 namespace tesseract {
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26 constexpr ERRCODE EMPTY_LLSQ("Can't delete from an empty LLSQ");
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28 /**********************************************************************
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29 * LLSQ::clear
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30 *
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31 * Function to initialize a LLSQ.
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32 **********************************************************************/
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34 void LLSQ::clear() { // initialize
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35 total_weight = 0.0; // no elements
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36 sigx = 0.0; // update accumulators
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37 sigy = 0.0;
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38 sigxx = 0.0;
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39 sigxy = 0.0;
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40 sigyy = 0.0;
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41 }
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43 /**********************************************************************
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44 * LLSQ::add
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45 *
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46 * Add an element to the accumulator.
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47 **********************************************************************/
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49 void LLSQ::add(double x, double y) { // add an element
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50 total_weight++; // count elements
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51 sigx += x; // update accumulators
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52 sigy += y;
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53 sigxx += x * x;
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54 sigxy += x * y;
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55 sigyy += y * y;
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56 }
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57 // Adds an element with a specified weight.
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58 void LLSQ::add(double x, double y, double weight) {
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59 total_weight += weight;
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60 sigx += x * weight; // update accumulators
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61 sigy += y * weight;
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62 sigxx += x * x * weight;
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63 sigxy += x * y * weight;
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64 sigyy += y * y * weight;
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65 }
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66 // Adds a whole LLSQ.
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67 void LLSQ::add(const LLSQ &other) {
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68 total_weight += other.total_weight;
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69 sigx += other.sigx; // update accumulators
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70 sigy += other.sigy;
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71 sigxx += other.sigxx;
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72 sigxy += other.sigxy;
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73 sigyy += other.sigyy;
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74 }
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75
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76 /**********************************************************************
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77 * LLSQ::remove
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78 *
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79 * Delete an element from the acculuator.
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80 **********************************************************************/
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81
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82 void LLSQ::remove(double x, double y) { // delete an element
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83 if (total_weight <= 0.0) { // illegal
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84 EMPTY_LLSQ.error("LLSQ::remove", ABORT);
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85 }
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86 total_weight--; // count elements
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87 sigx -= x; // update accumulators
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88 sigy -= y;
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89 sigxx -= x * x;
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90 sigxy -= x * y;
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91 sigyy -= y * y;
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92 }
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93
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94 /**********************************************************************
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95 * LLSQ::m
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96 *
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97 * Return the gradient of the line fit.
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98 **********************************************************************/
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99
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100 double LLSQ::m() const { // get gradient
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101 double covar = covariance();
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102 double x_var = x_variance();
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103 if (x_var != 0.0) {
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104 return covar / x_var;
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105 } else {
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106 return 0.0; // too little
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107 }
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108 }
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109
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110 /**********************************************************************
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111 * LLSQ::c
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112 *
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113 * Return the constant of the line fit.
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114 **********************************************************************/
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115
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116 double LLSQ::c(double m) const { // get constant
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117 if (total_weight > 0.0) {
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118 return (sigy - m * sigx) / total_weight;
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119 } else {
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120 return 0; // too little
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121 }
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122 }
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123
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124 /**********************************************************************
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125 * LLSQ::rms
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126 *
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127 * Return the rms error of the fit.
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128 **********************************************************************/
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129
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130 double LLSQ::rms(double m, double c) const { // get error
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131 double error; // total error
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132
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133 if (total_weight > 0) {
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134 error = sigyy + m * (m * sigxx + 2 * (c * sigx - sigxy)) + c * (total_weight * c - 2 * sigy);
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135 if (error >= 0) {
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136 error = std::sqrt(error / total_weight); // sqrt of mean
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137 } else {
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138 error = 0;
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139 }
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140 } else {
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141 error = 0; // too little
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142 }
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143 return error;
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144 }
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145
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146 /**********************************************************************
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147 * LLSQ::pearson
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148 *
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149 * Return the pearson product moment correlation coefficient.
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150 **********************************************************************/
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151
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parents:
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152 double LLSQ::pearson() const { // get correlation
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parents:
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153 double r = 0.0; // Correlation is 0 if insufficient data.
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154
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diff changeset
155 double covar = covariance();
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156 if (covar != 0.0) {
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157 double var_product = x_variance() * y_variance();
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158 if (var_product > 0.0) {
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159 r = covar / std::sqrt(var_product);
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160 }
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161 }
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162 return r;
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163 }
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parents:
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164
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parents:
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165 // Returns the x,y means as an FCOORD.
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parents:
diff changeset
166 FCOORD LLSQ::mean_point() const {
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parents:
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167 if (total_weight > 0.0) {
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parents:
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168 return FCOORD(sigx / total_weight, sigy / total_weight);
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parents:
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169 } else {
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parents:
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170 return FCOORD(0.0f, 0.0f);
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171 }
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172 }
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173
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parents:
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174 // Returns the sqrt of the mean squared error measured perpendicular from the
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parents:
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175 // line through mean_point() in the direction dir.
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176 //
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177 // Derivation:
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178 // Lemma: Let v and x_i (i=1..N) be a k-dimensional vectors (1xk matrices).
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179 // Let % be dot product and ' be transpose. Note that:
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180 // Sum[i=1..N] (v % x_i)^2
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parents:
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181 // = v * [x_1' x_2' ... x_N'] * [x_1' x_2' .. x_N']' * v'
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182 // If x_i have average 0 we have:
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183 // = v * (N * COVARIANCE_MATRIX(X)) * v'
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parents:
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184 // Expanded for the case that k = 2, where we treat the dimensions
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parents:
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185 // as x_i and y_i, this is:
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Franz Glasner <fzglas.hg@dom66.de>
parents:
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186 // = v * (N * [VAR(X), COV(X,Y); COV(X,Y) VAR(Y)]) * v'
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parents:
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187 // Now, we are trying to calculate the mean squared error, where v is
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parents:
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188 // perpendicular to our line of interest:
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parents:
diff changeset
189 // Mean squared error
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Franz Glasner <fzglas.hg@dom66.de>
parents:
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190 // = E [ (v % (x_i - x_avg))) ^2 ]
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
191 // = Sum (v % (x_i - x_avg))^2 / N
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Franz Glasner <fzglas.hg@dom66.de>
parents:
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192 // = v * N * [VAR(X) COV(X,Y); COV(X,Y) VAR(Y)] / N * v'
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
193 // = v * [VAR(X) COV(X,Y); COV(X,Y) VAR(Y)] * v'
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
194 // = code below
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
195 double LLSQ::rms_orth(const FCOORD &dir) const {
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
196 FCOORD v = !dir;
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Franz Glasner <fzglas.hg@dom66.de>
parents:
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197 v.normalise();
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parents:
diff changeset
198 return std::sqrt(x_variance() * v.x() * v.x() + 2 * covariance() * v.x() * v.y() +
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
199 y_variance() * v.y() * v.y());
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
200 }
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Franz Glasner <fzglas.hg@dom66.de>
parents:
diff changeset
201
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Franz Glasner <fzglas.hg@dom66.de>
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202 // Returns the direction of the fitted line as a unit vector, using the
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203 // least mean squared perpendicular distance. The line runs through the
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204 // mean_point, i.e. a point p on the line is given by:
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205 // p = mean_point() + lambda * vector_fit() for some real number lambda.
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206 // Note that the result (0<=x<=1, -1<=y<=-1) is directionally ambiguous
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207 // and may be negated without changing its meaning.
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208 // Fitting a line m + ๐œ†v to a set of N points Pi = (xi, yi), where
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209 // m is the mean point (๐, ๐‚) and
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210 // v is the direction vector (cos๐œƒ, sin๐œƒ)
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211 // The perpendicular distance of each Pi from the line is:
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212 // (Pi - m) x v, where x is the scalar cross product.
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213 // Total squared error is thus:
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214 // E = โˆ‘((xi - ๐)sin๐œƒ - (yi - ๐‚)cos๐œƒ)ยฒ
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215 // = โˆ‘(xi - ๐)ยฒsinยฒ๐œƒ - 2โˆ‘(xi - ๐)(yi - ๐‚)sin๐œƒ cos๐œƒ + โˆ‘(yi - ๐‚)ยฒcosยฒ๐œƒ
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216 // = NVar(xi)sinยฒ๐œƒ - 2NCovar(xi, yi)sin๐œƒ cos๐œƒ + NVar(yi)cosยฒ๐œƒ (Eq 1)
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217 // where Var(xi) is the variance of xi,
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218 // and Covar(xi, yi) is the covariance of xi, yi.
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219 // Taking the derivative wrt ๐œƒ and setting to 0 to obtain the min/max:
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220 // 0 = 2NVar(xi)sin๐œƒ cos๐œƒ -2NCovar(xi, yi)(cosยฒ๐œƒ - sinยฒ๐œƒ) -2NVar(yi)sin๐œƒ cos๐œƒ
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221 // => Covar(xi, yi)(cosยฒ๐œƒ - sinยฒ๐œƒ) = (Var(xi) - Var(yi))sin๐œƒ cos๐œƒ
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222 // Using double angles:
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223 // 2Covar(xi, yi)cos2๐œƒ = (Var(xi) - Var(yi))sin2๐œƒ (Eq 2)
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224 // So ๐œƒ = 0.5 atan2(2Covar(xi, yi), Var(xi) - Var(yi)) (Eq 3)
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225
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226 // Because it involves 2๐œƒ , Eq 2 has 2 solutions 90 degrees apart, but which
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227 // is the min and which is the max? From Eq1:
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228 // E/N = Var(xi)sinยฒ๐œƒ - 2Covar(xi, yi)sin๐œƒ cos๐œƒ + Var(yi)cosยฒ๐œƒ
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229 // and 90 degrees away, using sin/cos equivalences:
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230 // E'/N = Var(xi)cosยฒ๐œƒ + 2Covar(xi, yi)sin๐œƒ cos๐œƒ + Var(yi)sinยฒ๐œƒ
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231 // The second error is smaller (making it the minimum) iff
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232 // E'/N < E/N ie:
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233 // (Var(xi) - Var(yi))(cosยฒ๐œƒ - sinยฒ๐œƒ) < -4Covar(xi, yi)sin๐œƒ cos๐œƒ
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234 // Using double angles:
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235 // (Var(xi) - Var(yi))cos2๐œƒ < -2Covar(xi, yi)sin2๐œƒ (InEq 1)
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236 // But atan2(2Covar(xi, yi), Var(xi) - Var(yi)) picks 2๐œƒ such that:
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237 // sgn(cos2๐œƒ) = sgn(Var(xi) - Var(yi)) and sgn(sin2๐œƒ) = sgn(Covar(xi, yi))
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238 // so InEq1 can *never* be true, making the atan2 result *always* the min!
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239 // In the degenerate case, where Covar(xi, yi) = 0 AND Var(xi) = Var(yi),
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240 // the 2 solutions have equal error and the inequality is still false.
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241 // Therefore the solution really is as trivial as Eq 3.
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242
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243 // This is equivalent to returning the Principal Component in PCA, or the
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244 // eigenvector corresponding to the largest eigenvalue in the covariance
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245 // matrix. However, atan2 is much simpler! The one reference I found that
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246 // uses this formula is http://web.mit.edu/18.06/www/Essays/tlsfit.pdf but
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247 // that is still a much more complex derivation. It seems Pearson had already
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248 // found this simple solution in 1901.
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249 // http://books.google.com/books?id=WXwvAQAAIAAJ&pg=PA559
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250 FCOORD LLSQ::vector_fit() const {
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251 double x_var = x_variance();
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252 double y_var = y_variance();
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253 double covar = covariance();
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254 double theta = 0.5 * atan2(2.0 * covar, x_var - y_var);
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255 FCOORD result(cos(theta), sin(theta));
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256 return result;
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257 }
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258
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259 } // namespace tesseract