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## Sketch with least-squares

The original figure is here, and we wish to have a sketch of it, not by hand, but from a computer program. The program is given a bunch of lines with random lengths and orientations and it seeks a weight for each of the lines through a minimisation of the least-squares error between the original and the generated figure.

The resulting figure is as follows. The idea is from David Barber's page and here.

The MATLAB program is

% load the image yo = imread('a380.jpg'); Z = rgb2gray(yo); N = 2000; % number of lines [Ymax, Xmax] = size(Z); % width and height S = ceil(diag([Xmax Ymax])*rand(2,N)); % starting points for lines E = ceil(diag([Xmax Ymax])*rand(2,N)); % ending points for lines % for first run, initialise B=[]; % generating the lines (not optimised, very time consuming) for i = 1:N b = zeros(Ymax,Xmax); dx = E(1,i) - S(1,i); if dx>0 dy = E(2,i) - S(2,i); x = linspace(S(1,i),E(1,i),abs(dx)+1); y = round((x - S(1,i)) * dy / dx + S(2,i)); b(sub2ind(size(b), y, x)) = 1; B = [B b(:)]; end end disp('Lines generated...') %least squres B = sparse(B); %w = B\double(Z(:)); w = lsqr(B,double(Z(:))); imshow(reshape(B*w,Ymax,Xmax),[0 255])

— Last modified: *xiaoke 2014/06/20 13:46*