Matlab: Selecting a meshgrid subset and transform it with a conformal map

Preamble: - This is a very small part of a non-commercial art project with a fixed budget of 30 EUR but no strict due date or deadline. A sufficient time intervall would be completion in 1 weeks. - Making higher price bids than the budget or low price bids without reading the description and demanding more later is worthless and is only a waste of time for all stakeholders. - Demanding a milestone release without me inspecting and testing the Matlab code will not be accepted. THE TASK: Given is a RGB image (img), a gray mask (SF), and a complex valued function fz (like fz = 0.5*(z+(1./z))), that should be used to distort a region of img. A region in SF should be specified by a condition for example SF > 0. If an output-grid is generated the same size as SF a corresponding region can be specified in that grid and the transformation of the output-grid should be restricted to this grid subset: if the corresponding SF-pixel to a gridpoint satisfy the given condition transform gridpoint with fz; end Instead of iterating through the grid or using the slow arrayfun I tried to specify a sub-grid with [u, v] = find(SF>0); y_u = yo0(u); x_v = xo0(v); apply the conformal map to the sub-grid and separate real and imag fxiy = 0.5*((x_v+1i.*y_u)+(1./(x_v+1i.*y_u))); x_v = real(fxiy); y_u = imag(fxiy); and then exchange the transformed sub-grid in the original grid before generating the output image using interp2 (see complete Matlab code below as a low level conformal image mapping generalized from the Droste effect [login to view URL]). But the output image looks the same as the input image. The task is to find a fast (vectorinzing) solution to transform a subgrid with fz. [h_o,w_o,~] = size(SF); [h_i,w_i,~] = size(img); % GENERATE IN-GRID AND NORMALIZE [0 1] [xi,yi] = meshgrid(linspace(0,w_i+1,w_i),linspace(0,h_i+1,h_i)); xi = xi/w_i; yi = yi/h_i; % GENERATE OUT-GRID AND NORMALIZE [-1 1] [xo0,yo0] = meshgrid(1:w_o,1:h_o); xo0 = (xo0/w_o)*2 - 1; yo0 = (yo0/h_o)*2 - 1; % FIND GRID POINTS WHERE CORRESPONDING COORDINATE IN SF FULFILLS CONDITION [u, v] = find(SF>0); y_u = yo0(u); x_v = xo0(v); % APPLY fz TO THOSE GRID POINTS fxiy = 0.5*((x_v+1i.*y_u)+(1./(x_v+1i.*y_u))); % SEPARATE real & imag x_v = real(fxiy); y_u = imag(fxiy); % EXCHANGE MAPPED GRID POINTS xo1 = xo0; xo1(v) = x_v; yo1 = yo0; yo1(u) = y_u; % NORMALIZE OUT-GRID [0 1] xo1 = (xo1+1)/2; yo1 = (yo1+1)/2; % INTERPOLATE OUTPUT IMAGE img_out = zeros(h_o,w_o,3); for k = 1:3; img_out(:,:,k) = uint8(interp2(xi, yi, img(:,:,k), xo1, yo1, 'linear')); end;