robotics专项课程Perception Assignment 2: Image Projection(图像投影)

文档中错误更正：1. 公式（14）中x3=1

                            2. A为8x9矩阵

                            3. reshape后H矩阵需转置

function [ H ] = est_homography(video_pts, logo_pts)
% est_homography estimates the homography to transform each of the
% video_pts into the logo_pts
% Inputs:
%     video_pts: a 4x2 matrix of corner points in the video
%     logo_pts: a 4x2 matrix of logo points that correspond to video_pts
% Outputs:
%     H: a 3x3 homography matrix such that logo_pts ~ H*video_pts

A = zeros(8,9);
for i = 1:4
    A(2*i-1,:)= [-video_pts(i,1) -video_pts(i,2) -1 0 0 0 video_pts(i,1)*logo_pts(i,1) video_pts(i,2)*logo_pts(i,1) logo_pts(i,1)];
    A(2*i, :) = [0 0 0 -video_pts(i,1) -video_pts(i,2)  -1  video_pts(i,1)*logo_pts(i,2) video_pts(i,2)*logo_pts(i,2) logo_pts(i,2)];
end
[U, S, V] = svd(A);

H = zeros(3,3);
H = reshape(V(:,9),3,3);
H = H';

end

function [ warped_pts ] = warp_pts( video_pts, logo_pts, sample_pts)
% warp_pts computes the homography that warps the points inside
% video_pts to those inside logo_pts. It then uses this
% homography to warp the points in sample_pts to points in the logo
% image
% Inputs:
%     video_pts: a 4x2 matrix of (x,y) coordinates of corners in the
%         video frame
%     logo_pts: a 4x2 matrix of (x,y) coordinates of corners in
%         the logo image
%     sample_pts: a nx2 matrix of (x,y) coordinates of points in the video
%         video that need to be warped to corresponding points in the
%         logo image
% Outputs:
%     warped_pts: a nx2 matrix of (x,y) coordinates of points obtained
%         after warping the sample_pts

% Complete est_homography first!
[ H ] = est_homography(video_pts, logo_pts);

[nrows,ncols] = size(sample_pts);
warped_pts = zeros(nrows,ncols);
for i = 1:nrows
    factor = H(3,1)*sample_pts(i,1)+H(3,2)*sample_pts(i,2)+H(3,3);
    x = (H(1,1)*sample_pts(i,1)+H(1,2)*sample_pts(i,2)+H(1,3))/factor;
    y = (H(2,1)*sample_pts(i,1)+H(2,2)*sample_pts(i,2)+H(2,3))/factor;
    warped_pts(i,:) = [x y];
end
end