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 <span id="projectnumber">3.03</span>
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<div class="title">/usr/local/google/home/jbreiden/tesseract-ocr-read-only/ccstruct/linlsq.h</div> </div>
102
<div class="contents">
103
<a href="a00753.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/**********************************************************************</span>
104
<a name="l00002"></a>00002 <span class="comment"> * File: linlsq.h (Formerly llsq.h)</span>
105
<a name="l00003"></a>00003 <span class="comment"> * Description: Linear Least squares fitting code.</span>
106
<a name="l00004"></a>00004 <span class="comment"> * Author: Ray Smith</span>
107
<a name="l00005"></a>00005 <span class="comment"> * Created: Thu Sep 12 08:44:51 BST 1991</span>
108
<a name="l00006"></a>00006 <span class="comment"> *</span>
109
<a name="l00007"></a>00007 <span class="comment"> * (C) Copyright 1991, Hewlett-Packard Ltd.</span>
110
<a name="l00008"></a>00008 <span class="comment"> ** Licensed under the Apache License, Version 2.0 (the "License");</span>
111
<a name="l00009"></a>00009 <span class="comment"> ** you may not use this file except in compliance with the License.</span>
112
<a name="l00010"></a>00010 <span class="comment"> ** You may obtain a copy of the License at</span>
113
<a name="l00011"></a>00011 <span class="comment"> ** http://www.apache.org/licenses/LICENSE-2.0</span>
114
<a name="l00012"></a>00012 <span class="comment"> ** Unless required by applicable law or agreed to in writing, software</span>
115
<a name="l00013"></a>00013 <span class="comment"> ** distributed under the License is distributed on an "AS IS" BASIS,</span>
116
<a name="l00014"></a>00014 <span class="comment"> ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span>
117
<a name="l00015"></a>00015 <span class="comment"> ** See the License for the specific language governing permissions and</span>
118
<a name="l00016"></a>00016 <span class="comment"> ** limitations under the License.</span>
119
<a name="l00017"></a>00017 <span class="comment"> *</span>
120
<a name="l00018"></a>00018 <span class="comment"> **********************************************************************/</span>
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<a name="l00019"></a>00019
122
<a name="l00020"></a>00020 <span class="preprocessor">#ifndef TESSERACT_CCSTRUCT_LINLSQ_H_</span>
123
<a name="l00021"></a>00021 <span class="preprocessor"></span><span class="preprocessor">#define TESSERACT_CCSTRUCT_LINLSQ_H_</span>
124
<a name="l00022"></a>00022 <span class="preprocessor"></span>
125
<a name="l00023"></a>00023 <span class="preprocessor">#include "<a class="code" href="a00775.html">points.h</a>"</span>
126
<a name="l00024"></a>00024 <span class="preprocessor">#include "<a class="code" href="a00844.html">params.h</a>"</span>
127
<a name="l00025"></a>00025
128
<a name="l00026"></a><a class="code" href="a00454.html">00026</a> <span class="keyword">class </span><a class="code" href="a00454.html">LLSQ</a> {
129
<a name="l00027"></a>00027 <span class="keyword">public</span>:
130
<a name="l00028"></a><a class="code" href="a00454.html#ae5fcf7b887f023364e62be5a591175a4">00028</a> <a class="code" href="a00454.html#ae5fcf7b887f023364e62be5a591175a4">LLSQ</a>() { <span class="comment">// constructor</span>
131
<a name="l00029"></a>00029 <a class="code" href="a00454.html#a9f7b92005193802bc03539a6ae48a27a">clear</a>(); <span class="comment">// set to zeros</span>
132
<a name="l00030"></a>00030 }
133
<a name="l00031"></a>00031 <span class="keywordtype">void</span> <a class="code" href="a00454.html#a9f7b92005193802bc03539a6ae48a27a">clear</a>(); <span class="comment">// initialize</span>
134
<a name="l00032"></a>00032
135
<a name="l00033"></a>00033 <span class="comment">// Adds an element with a weight of 1.</span>
136
<a name="l00034"></a>00034 <span class="keywordtype">void</span> <a class="code" href="a00454.html#aa439294be0539828cf042f8941125b3c">add</a>(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y);
137
<a name="l00035"></a>00035 <span class="comment">// Adds an element with a specified weight.</span>
138
<a name="l00036"></a>00036 <span class="keywordtype">void</span> <a class="code" href="a00454.html#aa439294be0539828cf042f8941125b3c">add</a>(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y, <span class="keywordtype">double</span> weight);
139
<a name="l00037"></a>00037 <span class="comment">// Adds a whole LLSQ.</span>
140
<a name="l00038"></a>00038 <span class="keywordtype">void</span> <a class="code" href="a00454.html#aa439294be0539828cf042f8941125b3c">add</a>(<span class="keyword">const</span> <a class="code" href="a00454.html">LLSQ</a>& other);
141
<a name="l00039"></a>00039 <span class="comment">// Deletes an element with a weight of 1.</span>
142
<a name="l00040"></a>00040 <span class="keywordtype">void</span> <span class="keyword">remove</span>(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y);
143
<a name="l00041"></a><a class="code" href="a00454.html#ae9282d47723a9741da7fa97cd5fd8025">00041</a> <a class="code" href="a00831.html#aba1f582fd0168f3ff9225d8c90fa9eb8">inT32</a> <a class="code" href="a00454.html#ae9282d47723a9741da7fa97cd5fd8025">count</a>()<span class="keyword"> const </span>{ <span class="comment">// no of elements</span>
144
<a name="l00042"></a>00042 <span class="keywordflow">return</span> <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(total_weight + 0.5);
145
<a name="l00043"></a>00043 }
146
<a name="l00044"></a>00044
147
<a name="l00045"></a>00045 <span class="keywordtype">double</span> <a class="code" href="a00454.html#ad3aed3a5a46cf180dd80893c1034aa9e">m</a>() <span class="keyword">const</span>; <span class="comment">// get gradient</span>
148
<a name="l00046"></a>00046 <span class="keywordtype">double</span> <a class="code" href="a00454.html#af66af81c0276216acfa659178189019f">c</a>(<span class="keywordtype">double</span> <a class="code" href="a00454.html#ad3aed3a5a46cf180dd80893c1034aa9e">m</a>) <span class="keyword">const</span>; <span class="comment">// get constant</span>
149
<a name="l00047"></a>00047 <span class="keywordtype">double</span> <a class="code" href="a00454.html#adb169c39429f6f206130e463c557af67">rms</a>(<span class="keywordtype">double</span> <a class="code" href="a00454.html#ad3aed3a5a46cf180dd80893c1034aa9e">m</a>, <span class="keywordtype">double</span> <a class="code" href="a00454.html#af66af81c0276216acfa659178189019f">c</a>) <span class="keyword">const</span>; <span class="comment">// get error</span>
150
<a name="l00048"></a>00048 <span class="keywordtype">double</span> <a class="code" href="a00454.html#a8537176180a1cd3ff9c3b1f97d1ffb78">pearson</a>() <span class="keyword">const</span>; <span class="comment">// get correlation coefficient.</span>
151
<a name="l00049"></a>00049
152
<a name="l00050"></a>00050 <span class="comment">// Returns the x,y means as an FCOORD.</span>
153
<a name="l00051"></a>00051 <a class="code" href="a00375.html">FCOORD</a> <a class="code" href="a00454.html#ac786685f62b271ca20aa719a8a03aa3d">mean_point</a>() <span class="keyword">const</span>;
154
<a name="l00052"></a>00052
155
<a name="l00053"></a>00053 <span class="comment">// Returns the average sum of squared perpendicular error from a line</span>
156
<a name="l00054"></a>00054 <span class="comment">// through mean_point() in the direction dir.</span>
157
<a name="l00055"></a>00055 <span class="keywordtype">double</span> <a class="code" href="a00454.html#af047401ce847d873866f6018d15d4a95">rms_orth</a>(<span class="keyword">const</span> <a class="code" href="a00375.html">FCOORD</a> &dir) <span class="keyword">const</span>;
158
<a name="l00056"></a>00056
159
<a name="l00057"></a>00057 <span class="comment">// Returns the direction of the fitted line as a unit vector, using the</span>
160
<a name="l00058"></a>00058 <span class="comment">// least mean squared perpendicular distance. The line runs through the</span>
161
<a name="l00059"></a>00059 <span class="comment">// mean_point, i.e. a point p on the line is given by:</span>
162
<a name="l00060"></a>00060 <span class="comment">// p = mean_point() + lambda * vector_fit() for some real number lambda.</span>
163
<a name="l00061"></a>00061 <span class="comment">// Note that the result (0<=x<=1, -1<=y<=-1) is directionally ambiguous</span>
164
<a name="l00062"></a>00062 <span class="comment">// and may be negated without changing its meaning, since a line is only</span>
165
<a name="l00063"></a>00063 <span class="comment">// unique to a range of pi radians.</span>
166
<a name="l00064"></a>00064 <span class="comment">// Modernists prefer to think of this as an Eigenvalue problem, but</span>
167
<a name="l00065"></a>00065 <span class="comment">// Pearson had the simple solution in 1901.</span>
168
<a name="l00066"></a>00066 <span class="comment">//</span>
169
<a name="l00067"></a>00067 <span class="comment">// Note that this is equivalent to returning the Principal Component in PCA,</span>
170
<a name="l00068"></a>00068 <span class="comment">// or the eigenvector corresponding to the largest eigenvalue in the</span>
171
<a name="l00069"></a>00069 <span class="comment">// covariance matrix.</span>
172
<a name="l00070"></a>00070 <a class="code" href="a00375.html">FCOORD</a> <a class="code" href="a00454.html#a1e15590443e86960c79ae5785f850d6d">vector_fit</a>() <span class="keyword">const</span>;
173
<a name="l00071"></a>00071
174
<a name="l00072"></a>00072 <span class="comment">// Returns the covariance.</span>
175
<a name="l00073"></a><a class="code" href="a00454.html#a36d6bf1e469425fc4f9b97521aee481e">00073</a> <span class="keywordtype">double</span> <a class="code" href="a00454.html#a36d6bf1e469425fc4f9b97521aee481e">covariance</a>()<span class="keyword"> const </span>{
176
<a name="l00074"></a>00074 <span class="keywordflow">if</span> (total_weight > 0.0)
177
<a name="l00075"></a>00075 <span class="keywordflow">return</span> (sigxy - sigx * sigy / total_weight) / total_weight;
178
<a name="l00076"></a>00076 <span class="keywordflow">else</span>
179
<a name="l00077"></a>00077 <span class="keywordflow">return</span> 0.0;
180
<a name="l00078"></a>00078 }
181
<a name="l00079"></a><a class="code" href="a00454.html#a27994b02b1ea16d8e3a6c951c90205dd">00079</a> <span class="keywordtype">double</span> <a class="code" href="a00454.html#a27994b02b1ea16d8e3a6c951c90205dd">x_variance</a>()<span class="keyword"> const </span>{
182
<a name="l00080"></a>00080 <span class="keywordflow">if</span> (total_weight > 0.0)
183
<a name="l00081"></a>00081 <span class="keywordflow">return</span> (sigxx - sigx * sigx / total_weight) / total_weight;
184
<a name="l00082"></a>00082 <span class="keywordflow">else</span>
185
<a name="l00083"></a>00083 <span class="keywordflow">return</span> 0.0;
186
<a name="l00084"></a>00084 }
187
<a name="l00085"></a><a class="code" href="a00454.html#a3e386f3db4343cca32ac4a4f028c6ea4">00085</a> <span class="keywordtype">double</span> <a class="code" href="a00454.html#a3e386f3db4343cca32ac4a4f028c6ea4">y_variance</a>()<span class="keyword"> const </span>{
188
<a name="l00086"></a>00086 <span class="keywordflow">if</span> (total_weight > 0.0)
189
<a name="l00087"></a>00087 <span class="keywordflow">return</span> (sigyy - sigy * sigy / total_weight) / total_weight;
190
<a name="l00088"></a>00088 <span class="keywordflow">else</span>
191
<a name="l00089"></a>00089 <span class="keywordflow">return</span> 0.0;
192
<a name="l00090"></a>00090 }
193
<a name="l00091"></a>00091
194
<a name="l00092"></a>00092 <span class="keyword">private</span>:
195
<a name="l00093"></a>00093 <span class="keywordtype">double</span> total_weight; <span class="comment">// no of elements or sum of weights.</span>
196
<a name="l00094"></a>00094 <span class="keywordtype">double</span> sigx; <span class="comment">// sum of x</span>
197
<a name="l00095"></a>00095 <span class="keywordtype">double</span> sigy; <span class="comment">// sum of y</span>
198
<a name="l00096"></a>00096 <span class="keywordtype">double</span> sigxx; <span class="comment">// sum x squared</span>
199
<a name="l00097"></a>00097 <span class="keywordtype">double</span> sigxy; <span class="comment">// sum of xy</span>
200
<a name="l00098"></a>00098 <span class="keywordtype">double</span> sigyy; <span class="comment">// sum y squared</span>
201
<a name="l00099"></a>00099 };
202
<a name="l00100"></a>00100
203
<a name="l00101"></a>00101
204
<a name="l00102"></a>00102 <span class="comment">// Returns the median value of the vector, given that the values are</span>
205
<a name="l00103"></a>00103 <span class="comment">// circular, with the given modulus. Values may be signed or unsigned,</span>
206
<a name="l00104"></a>00104 <span class="comment">// eg range from -pi to pi (modulus 2pi) or from 0 to 2pi (modulus 2pi).</span>
207
<a name="l00105"></a>00105 <span class="comment">// NOTE that the array is shuffled, but the time taken is linear.</span>
208
<a name="l00106"></a>00106 <span class="comment">// An assumption is made that most of the values are spread over no more than</span>
209
<a name="l00107"></a>00107 <span class="comment">// half the range, but wrap-around is accounted for if the median is near</span>
210
<a name="l00108"></a>00108 <span class="comment">// the wrap-around point.</span>
211
<a name="l00109"></a>00109 <span class="comment">// Cannot be a member of GenericVector, as it makes heavy used of LLSQ.</span>
212
<a name="l00110"></a>00110 <span class="comment">// T must be an integer or float/double type.</span>
213
<a name="l00111"></a><a class="code" href="a00753.html#abde6267e843aeeea5089d458c465dee2">00111</a> <span class="keyword">template</span><<span class="keyword">typename</span> T> T <a class="code" href="a00753.html#abde6267e843aeeea5089d458c465dee2">MedianOfCircularValues</a>(T modulus, <a class="code" href="a00403.html">GenericVector<T></a>* v) {
214
<a name="l00112"></a>00112 <a class="code" href="a00454.html">LLSQ</a> stats;
215
<a name="l00113"></a>00113 T halfrange = <span class="keyword">static_cast<</span>T<span class="keyword">></span>(modulus / 2);
216
<a name="l00114"></a>00114 <span class="keywordtype">int</span> num_elements = v-><a class="code" href="a00403.html#a111b51dd0bf1324cfb69ef70703d8e70">size</a>();
217
<a name="l00115"></a>00115 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_elements; ++i) {
218
<a name="l00116"></a>00116 stats.<a class="code" href="a00454.html#aa439294be0539828cf042f8941125b3c">add</a>((*v)[i], (*v)[i] + halfrange);
219
<a name="l00117"></a>00117 }
220
<a name="l00118"></a>00118 <span class="keywordtype">bool</span> offset_needed = stats.<a class="code" href="a00454.html#a3e386f3db4343cca32ac4a4f028c6ea4">y_variance</a>() < stats.<a class="code" href="a00454.html#a27994b02b1ea16d8e3a6c951c90205dd">x_variance</a>();
221
<a name="l00119"></a>00119 <span class="keywordflow">if</span> (offset_needed) {
222
<a name="l00120"></a>00120 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_elements; ++i) {
223
<a name="l00121"></a>00121 (*v)[i] += halfrange;
224
<a name="l00122"></a>00122 }
225
<a name="l00123"></a>00123 }
226
<a name="l00124"></a>00124 <span class="keywordtype">int</span> median_index = v-><a class="code" href="a00403.html#a5c4218ef833d0fe5db9b9749abd81ea5">choose_nth_item</a>(num_elements / 2);
227
<a name="l00125"></a>00125 <span class="keywordflow">if</span> (offset_needed) {
228
<a name="l00126"></a>00126 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_elements; ++i) {
229
<a name="l00127"></a>00127 (*v)[i] -= halfrange;
230
<a name="l00128"></a>00128 }
231
<a name="l00129"></a>00129 }
232
<a name="l00130"></a>00130 <span class="keywordflow">return</span> (*v)[median_index];
233
<a name="l00131"></a>00131 }
234
<a name="l00132"></a>00132
235
<a name="l00133"></a>00133
236
<a name="l00134"></a>00134 <span class="preprocessor">#endif // TESSERACT_CCSTRUCT_LINLSQ_H_</span>
237
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