2次元フーリエ変換,フーリエ逆変換
YouTube で見た以下のビデオが面白かったので,似たようなものを OpenCV のサンプルとして作ってみました.cv::dft,cv::idft を利用しています.処理の詳細は,ビデオをご覧ください.
C++
001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 | #include <iostream> #include <cv.h> #include <highgui.h> using namespace cv; using namespace std; // class declaration class DftIdftApp { public : DftIdftApp( const string filename); ~DftIdftApp(){}; void calcMagImage(); void showOrgImage(){imshow(org_win, src_img);} void showMagImage(){imshow(mag_win, mag_img);} void showIDFTImage(){imshow(idft_win, idft_img);} void shiftDFT(Mat &src, Mat &dst); void calcIDFT( bool all= false ); void clear(){idft_img.setTo(0);} static void onMouse( int event, int x, int y, int flags, void * param); private : Mat src_img, mag_img; Mat Re_img, Im_img, Complex_img; Mat zero, dft_src, dft_dst, dft_dst_p; Mat idft_img; vector<Mat> mv; string org_win, mag_win, idft_win; int src_cols, src_rows, dft_cols, dft_rows; }; // constructor DftIdftApp::DftIdftApp( const string filename) :org_win( "Original" ), mag_win( "Magnitude" ), idft_win( "IDTF" ) { src_img = imread(filename, 0); if (!src_img.data) return ; Size s_size = src_img.size(); src_cols = s_size.width; src_rows = s_size.height; Re_img = Mat(s_size, CV_64F); Im_img = Mat::zeros(s_size, CV_64F); Complex_img = Mat(s_size, CV_64FC2); src_img.convertTo(Re_img, CV_64F); mv.push_back(Re_img); mv.push_back(Im_img); merge(mv, Complex_img); idft_img = zero = Mat::zeros(s_size, CV_64F); namedWindow(org_win, CV_WINDOW_AUTOSIZE); namedWindow(mag_win, CV_WINDOW_AUTOSIZE); namedWindow(idft_win, CV_WINDOW_AUTOSIZE); cvSetMouseCallback(mag_win.c_str(), DftIdftApp::onMouse, this ); } // calc magnitude image void DftIdftApp::calcMagImage() { dft_rows = getOptimalDFTSize(src_rows); dft_cols = getOptimalDFTSize(src_cols); dft_src = Mat::zeros(dft_rows, dft_cols, CV_64FC2); Mat roi(dft_src, Rect(0, 0, src_cols, src_rows)); Complex_img.copyTo(roi); dft(dft_src, dft_dst); dft_dst_p = Mat::zeros(dft_dst.size(), dft_dst.type()); //split(dft_dst.mul(dft_dst), mv); //sqrt(mv[0]+mv[1], mv[0]); split(dft_dst, mv); magnitude(mv[0], mv[1], mv[0]); log (mv[0]+1, mv[0]); // for ver. 2.1 or later shiftDFT(mv[0], mv[0]); //double min, max; //minMaxLoc(mv[0], &min, &max); //mag_img = mv[0]*1.0/(max-min) - 1.0*min/(max-min); normalize(mv[0], mag_img, 0, 1, CV_MINMAX); } // swap 1,3 and 2,4 quadrants respectively void DftIdftApp::shiftDFT(Mat &src, Mat& dst) { Mat tmp; int cx = src.cols/2; int cy = src.rows/2; for ( int i=0; i<=cx; i+=cx) { Mat qs(src, Rect(i^cx,0,cx,cy)); Mat qd(dst, Rect(i,cy,cx,cy)); qs.copyTo(tmp); qd.copyTo(qs); tmp.copyTo(qd); } } // mouse event callback void DftIdftApp::onMouse( int event, int x, int y, int flags, void * param) { DftIdftApp *app = static_cast <DftIdftApp*>(param); Mat &dft_dst = app->dft_dst; Mat &dft_dst_p = app->dft_dst_p; Mat &mag_img = app->mag_img; int cx = app->src_cols/2; int cy = app->src_rows/2; int mx=x, my=y; int w = app->dft_cols; int h = app->dft_rows; switch (event) { case CV_EVENT_MOUSEMOVE: if ((flags&CV_EVENT_FLAG_LBUTTON)==0) return ; case CV_EVENT_LBUTTONUP: if (flags&CV_EVENT_FLAG_CTRLKEY) { // LeftButton+CTRL int step = 5; for ( int j=-step; j<=step; j++) { my = y+j + ((y+j)<cy ? cy:-cy); if (y+j<0 || y+j>=h) continue ; double *from = dft_dst.ptr< double >(my); double *to = dft_dst_p.ptr< double >(my); double *mag = mag_img.ptr< double >(y+j); for ( int i=-step; i<=step; i++) { mx = x+i + ((x+i)<cx ? cx:-cx); if (x+i<0 || x+i>=w) break ; to[(mx)*2+0] = from[(mx)*2+0]; to[(mx)*2+1] = from[(mx)*2+1]; mag[x+i] = 0; } } } else { // LeftButton mx += x<cx ? cx:-cx; my += y<cy ? cy:-cy; double *from = dft_dst.ptr< double >(my); double *to = dft_dst_p.ptr< double >(my); double *mag = mag_img.ptr< double >(y); to[(mx)*2+0] = from[(mx)*2+0]; to[(mx)*2+1] = from[(mx)*2+1]; mag[x] = 0; } break ; default : return ; } app->calcIDFT(); } // Inverse Discrete Fourier Transforma void DftIdftApp::calcIDFT( bool all) { if (all) { dft_dst.copyTo(dft_dst_p); mag_img.setTo(0); } double min, max; idft(dft_dst_p, dft_src); split(dft_src, mv); minMaxLoc(mv[0], &min, &max); idft_img = Mat(mv[0]*1.0/max, Rect(0, 0, src_cols, src_rows)); } int main( int argc, char *argv[]) { const string filename = argc > 1 ? argv[1] : "../image/Fourier.png" ; DftIdftApp app(filename); cout << "Usage: click or drag on Magnitude Image.\n" << "Hot keys: \n" "\tESC - quit the program\n" "\ta - select all pixels\n" "\tr - restore original images\n" "\tleft mouse button - select one pixel\n" "\tCTRL+left mouse button - select a pixel and neighbors\n" ; app.showOrgImage(); app.calcMagImage(); while (1) { int c = waitKey(10); switch (( char )c) { case '\x1b' : // exit return 0; case 'a' : // IDFT all app.calcIDFT( true ); break ; case 'r' : // reset app.clear(); app.calcMagImage(); break ; } app.showIDFTImage(); app.showMagImage(); } return 0; } |
実行結果例
(1)動画(サンプル実行の例)
(2)静止画
(左)対数パワースペクトル, (右)IDFT結果 左画像の黒い領域は,選択された(IDFTの対象となる)周波数,方向の正弦波を表します.この領域は,対数パワースペクトル画像上をマウスでクリック,ドラッグなどすることで選択できます.多くの正弦波を重ね合わせることで,より元の画像に近づく様子が分かります.