Mercurial > hgrepos > Python2 > PyMuPDF

annotate mupdf-source/thirdparty/tesseract/src/ccstruct/quadlsq.cpp @ 43:202a1f38a622

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FIX: New added code snippets did not yet account for the changed return values from "_fromto()"
author Franz Glasner <fzglas.hg@dom66.de>
date Sat, 11 Oct 2025 17:15:08 +0200
parents b50eed0cc0ef
children
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2
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1 /**********************************************************************
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2 * File: quadlsq.cpp (Formerly qlsq.c)
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3 * Description: Code for least squares approximation of quadratics.
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4 * Author: Ray Smith
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5 *
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6 * (C) Copyright 1993, 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 "quadlsq.h"
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21 #include "tprintf.h"
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23 #include <cmath>
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24 #include <cstdio>
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26 namespace tesseract {
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28 // Minimum variance in least squares before backing off to a lower degree.
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29 const long double kMinVariance = 1.0L / 1024;
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31 /**********************************************************************
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32 * QLSQ::clear
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33 *
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34 * Function to initialize a QLSQ.
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35 **********************************************************************/
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37 void QLSQ::clear() { // initialize
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38 a = 0.0;
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39 b = 0.0;
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40 c = 0.0;
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41 n = 0; // No elements.
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42 sigx = 0.0; // Zero accumulators.
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43 sigy = 0.0;
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44 sigxx = 0.0;
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45 sigxy = 0.0;
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46 sigyy = 0.0;
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47 sigxxx = 0.0;
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48 sigxxy = 0.0;
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49 sigxxxx = 0.0;
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50 }
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52 /**********************************************************************
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53 * QLSQ::add
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54 *
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55 * Add an element to the accumulator.
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56 **********************************************************************/
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58 void QLSQ::add(double x, double y) {
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59 n++; // Count elements.
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60 sigx += x; // Update accumulators.
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61 sigy += y;
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62 sigxx += x * x;
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63 sigxy += x * y;
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64 sigyy += y * y;
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65 sigxxx += static_cast<long double>(x) * x * x;
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66 sigxxy += static_cast<long double>(x) * x * y;
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67 sigxxxx += static_cast<long double>(x) * x * x * x;
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68 }
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70 /**********************************************************************
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71 * QLSQ::remove
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72 *
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73 * Delete an element from the accumulator.
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74 **********************************************************************/
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75
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76 void QLSQ::remove(double x, double y) {
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77 if (n <= 0) {
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78 tprintf("Can't remove an element from an empty QLSQ accumulator!\n");
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79 return;
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80 }
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81 n--; // Count elements.
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82 sigx -= x; // Update accumulators.
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83 sigy -= y;
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84 sigxx -= x * x;
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85 sigxy -= x * y;
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86 sigyy -= y * y;
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87 sigxxx -= static_cast<long double>(x) * x * x;
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88 sigxxy -= static_cast<long double>(x) * x * y;
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89 sigxxxx -= static_cast<long double>(x) * x * x * x;
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90 }
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91
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92 /**********************************************************************
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93 * QLSQ::fit
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94 *
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95 * Fit the given degree of polynomial and store the result.
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96 * This creates a quadratic of the form axx + bx + c, but limited to
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97 * the given degree.
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98 **********************************************************************/
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99
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100 void QLSQ::fit(int degree) {
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101 long double x_variance =
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102 static_cast<long double>(sigxx) * n - static_cast<long double>(sigx) * sigx;
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103
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104 // Note: for computational efficiency, we do not normalize the variance,
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105 // covariance and cube variance here as they are in the same order in both
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106 // nominators and denominators. However, we need be careful in value range
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107 // check.
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108 if (x_variance < kMinVariance * n * n || degree < 1 || n < 2) {
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109 // We cannot calculate b reliably so forget a and b, and just work on c.
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110 a = b = 0.0;
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111 if (n >= 1 && degree >= 0) {
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112 c = sigy / n;
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113 } else {
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114 c = 0.0;
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115 }
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116 return;
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117 }
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118 long double top96 = 0.0; // Accurate top.
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119 long double bottom96 = 0.0; // Accurate bottom.
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120 long double cubevar = sigxxx * n - static_cast<long double>(sigxx) * sigx;
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121 long double covariance =
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122 static_cast<long double>(sigxy) * n - static_cast<long double>(sigx) * sigy;
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123
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124 if (n >= 4 && degree >= 2) {
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125 top96 = cubevar * covariance;
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126 top96 += x_variance * (static_cast<long double>(sigxx) * sigy - sigxxy * n);
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127
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128 bottom96 = cubevar * cubevar;
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129 bottom96 -= x_variance * (sigxxxx * n - static_cast<long double>(sigxx) * sigxx);
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130 }
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131 if (bottom96 >= kMinVariance * n * n * n * n) {
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132 // Denominators looking good
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133 a = top96 / bottom96;
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134 top96 = covariance - cubevar * a;
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135 b = top96 / x_variance;
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136 } else {
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137 // Forget a, and concentrate on b.
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138 a = 0.0;
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139 b = covariance / x_variance;
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140 }
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141 c = (sigy - a * sigxx - b * sigx) / n;
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142 }
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143
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144 } // namespace tesseract