计算机视觉14-第七章Shape(Structure)-From-Motion-I.ppt

三维运动估计 三维运动估计是指从二维图象序列来估计物体三维运动参数以及三维结构。 SFM (Shape From Motion) 三维刚体运动 1. 基于正交投影的三维运动估计 基于正交投影的三维运动估计 基于正交投影的三维运动估计 基于正交投影的三维运动估计 2 基于透视投影模型的三维运动估计 规范化焦距F=1,分子分母同除以Zk 3 基于外极线的三维运动估计 外极线方程几何意义 基于外极线的三维运动估计 基于外极线的三维运动估计 基于外极线的三维运动估计 基于外极线的三维运动估计 基本矩阵的性质 外极线方程的待求参数 5个未知的独立的参数，这也和运动参数的自由度数量相一致，即三个旋转自由度，二个平移自由度（或三个关于一个比例系数的平移自由度）. (1) 根据基本矩阵估计运动 (1) 根据基本矩阵估计运动 根据基本矩阵估计运动 (2) 直接根据外极线方程估计运动 Problem with 8-point algorithm ~10000 ~10000 ~10000 ~10000 ~100 ~100 1 ~100 ~100 ! Orders of magnitude difference between column of data matrix ? least-squares yields poor results Normalized 8-point algorithm Transform input by , Call 8-point on to obtain Normalized 8-point algorithm (0,0) (700,500) (700,0) (0,500) (1,-1) (0,0) (1,1) (-1,1) (-1,-1) normalized least squares yields good results Transform image to ~[-1,1]x[-1,1] Normalized 8-point algorithm A = [x2(1,:)‘.*x1(1,:) x2(1,:).*x1(2,:) x2(1,:) ... x2(2,:).*x1(1,:) x2(2,:).*x1(2,:) x2(2,:) ... x1(1,:) x1(2,:) ones(npts,1) ]; [U,D,V] = svd(A); E = reshape(V(:,9),3,3); [U,D,V] = svd(E); E = U*diag([D(1,1) D(2,2) 0])*V; % Denormalise E = T2*E*T1; [x1, T1] = normalise2dpts(x1); [x2, T2] = normalise2dpts(x2); Normalization function [newpts, T] = normalise2dpts(pts) c = mean(pts(1:2,:)); % Centroid newp(1,:) = pts(1,:)-c(1); % Shift origin to centroid. newp(2,:) = pts(2,:)-c(2); meandist = mean(sqrt(newp(1,:).^2 + newp(2,:).^2)); scale = sqrt(2)/meandist; T = [scale 0 -scale*c(1) 0 scale -scale*c(2) 0 0 1 ]; newpts = T*pts; RANSAC repeat select minimal sample (8 matches) compute solution(s) for F determine inliers until ?(#inliers,#samples)95% || too many times compute E based on all inliers 2. 估计运动参数 T: 根据基本矩阵的性质 R: 根据 理想情况下： 由于误差，改求： Structure from motion Structure