// // Interpolates a scale-space extremum's location and scale to subpixel // accuracy to form an image feature. Rejects features with low contrast. // Based on Section 4 of Lowe's paper. static bool adjustLocalExtrema( const vector<Mat>& dog_pyr, KeyPoint& kpt, int octv, int& layer, int& r, int& c, int nOctaveLayers, float contrastThreshold, float edgeThreshold, float sigma ) { const float img_scale = 1.f/(255*SIFT_FIXPT_SCALE); const float deriv_scale = img_scale*0.5f; const float second_deriv_scale = img_scale; const float cross_deriv_scale = img_scale*0.25f; float xi=0, xr=0, xc=0, contr=0; int i = 0; for( ; i < SIFT_MAX_INTERP_STEPS; i++ ) { int idx = octv*(nOctaveLayers+2) + layer; const Mat& img = dog_pyr[idx]; const Mat& prev = dog_pyr[idx-1]; const Mat& next = dog_pyr[idx+1]; Vec3f dD((img.at<sift_wt>(r, c+1) - img.at<sift_wt>(r, c-1))*deriv_scale, (img.at<sift_wt>(r+1, c) - img.at<sift_wt>(r-1, c))*deriv_scale, (next.at<sift_wt>(r, c) - prev.at<sift_wt>(r, c))*deriv_scale); float v2 = (float)img.at<sift_wt>(r, c)*2; float dxx = (img.at<sift_wt>(r, c+1) + img.at<sift_wt>(r, c-1) - v2)*second_deriv_scale; float dyy = (img.at<sift_wt>(r+1, c) + img.at<sift_wt>(r-1, c) - v2)*second_deriv_scale; float dss = (next.at<sift_wt>(r, c) + prev.at<sift_wt>(r, c) - v2)*second_deriv_scale; float dxy = (img.at<sift_wt>(r+1, c+1) - img.at<sift_wt>(r+1, c-1) - img.at<sift_wt>(r-1, c+1) + img.at<sift_wt>(r-1, c-1))*cross_deriv_scale; float dxs = (next.at<sift_wt>(r, c+1) - next.at<sift_wt>(r, c-1) - prev.at<sift_wt>(r, c+1) + prev.at<sift_wt>(r, c-1))*cross_deriv_scale; float dys = (next.at<sift_wt>(r+1, c) - next.at<sift_wt>(r-1, c) - prev.at<sift_wt>(r+1, c) + prev.at<sift_wt>(r-1, c))*cross_deriv_scale; Matx33f H(dxx, dxy, dxs, dxy, dyy, dys, dxs, dys, dss); Vec3f X = H.solve(dD, DECOMP_LU); xi = -X[2]; xr = -X[1]; xc = -X[0]; if( std::abs(xi) < 0.5f && std::abs(xr) < 0.5f && std::abs(xc) < 0.5f ) break; if( std::abs(xi) > (float)(INT_MAX/3) || std::abs(xr) > (float)(INT_MAX/3) || std::abs(xc) > (float)(INT_MAX/3) ) return false; c += cvRound(xc); r += cvRound(xr); layer += cvRound(xi); if( layer < 1 || layer > nOctaveLayers || c < SIFT_IMG_BORDER || c >= img.cols - SIFT_IMG_BORDER || r < SIFT_IMG_BORDER || r >= img.rows - SIFT_IMG_BORDER ) return false; } // ensure convergence of interpolation if( i >= SIFT_MAX_INTERP_STEPS ) return false; { int idx = octv*(nOctaveLayers+2) + layer; const Mat& img = dog_pyr[idx]; const Mat& prev = dog_pyr[idx-1]; const Mat& next = dog_pyr[idx+1]; Matx31f dD((img.at<sift_wt>(r, c+1) - img.at<sift_wt>(r, c-1))*deriv_scale, (img.at<sift_wt>(r+1, c) - img.at<sift_wt>(r-1, c))*deriv_scale, (next.at<sift_wt>(r, c) - prev.at<sift_wt>(r, c))*deriv_scale); float t = dD.dot(Matx31f(xc, xr, xi)); contr = img.at<sift_wt>(r, c)*img_scale + t * 0.5f; if( std::abs( contr ) * nOctaveLayers < contrastThreshold ) return false; // principal curvatures are computed using the trace and det of Hessian float v2 = img.at<sift_wt>(r, c)*2.f; float dxx = (img.at<sift_wt>(r, c+1) + img.at<sift_wt>(r, c-1) - v2)*second_deriv_scale; float dyy = (img.at<sift_wt>(r+1, c) + img.at<sift_wt>(r-1, c) - v2)*second_deriv_scale; float dxy = (img.at<sift_wt>(r+1, c+1) - img.at<sift_wt>(r+1, c-1) - img.at<sift_wt>(r-1, c+1) + img.at<sift_wt>(r-1, c-1)) * cross_deriv_scale; float tr = dxx + dyy; float det = dxx * dyy - dxy * dxy; if( det <= 0 || tr*tr*edgeThreshold >= (edgeThreshold + 1)*(edgeThreshold + 1)*det ) return false; } kpt.pt.x = (c + xc) * (1 << octv); kpt.pt.y = (r + xr) * (1 << octv); kpt.octave = octv + (layer << 8) + (cvRound((xi + 0.5)*255) << 16); kpt.size = sigma*powf(2.f, (layer + xi) / nOctaveLayers)*(1 << octv)*2; kpt.response = std::abs(contr); return true; }
Point3f Warp::transform(Point3f p) { Matx31f P = R * Matx31f(p.x, p.y, p.z); return Point3f(P(0), P(1), P(2)) + t; }