% IMTRANS - Homogeneous transformation of an image. % % Applies a geometric transform to an image % % [newim, newT] = imTrans(im, T, region, sze); % % Arguments: % im - The image to be transformed. % T - The 3x3 homogeneous transformation matrix. % region - An optional 4 element vector specifying % [minrow maxrow mincol maxcol] to transform. % This defaults to the whole image if you omit it % or specify it as an empty array []. % sze - An optional desired size of the transformed image % (this is the maximum No of rows or columns). % This defaults to the maximum of the rows and columns % of the original image. % % Returns: % newim - The transformed image. % newT - The transformation matrix that relates transformed image % coordinates to the reference coordinates for use in a % function such as DIGIPLANE. % % The region argument is used when one is inverting a perspective % transformation of a plane and the vanishing line of the plane lies within % the image. Attempts to transform any part of the vanishing line will % position you at infinity. Accordingly one should specify a region that % excludes any part of the vanishing line. % % The sze parameter is optionally used to control the size of the % output image. When inverting a perpective or affine transformation % the scale parameter is unknown/arbitrary, and without specifying % it explicitly the transformed image can end up being very small % or very large. % % Problems: If your transformed image ends up as being two small bits of % image separated by a large black area then the chances are that you have % included the vanishing line of the plane within the specified region to % transform. If your image degenerates to a very thin triangular shape % part of your region is probably very close to the vanishing line of the % plane. % Copyright (c) 2000-2005 Peter Kovesi % School of Computer Science & Software Engineering % The University of Western Australia % http://www.csse.uwa.edu.au/ % % Permission is hereby granted, free of charge, to any person obtaining a copy % of this software and associated documentation files (the "Software"), to deal % in the Software without restriction, subject to the following conditions: % % The above copyright notice and this permission notice shall be included in % all copies or substantial portions of the Software. % % The Software is provided "as is", without warranty of any kind. % April 2000 - original version. % July 2001 - transformation of region boundaries corrected. % May 2016 - Minor tidying function [newim, newT] = imTrans(im, T, region, sze); if isa(im,'uint8') im = double(im); % Make sure image is double end % Set up default region and transformed image size values [rows, cols, chan] = size(im); if ~exist('region', 'var') || isempty(region) region = [1 rows 1 cols]; end if ~exist('sze', 'var') || isempty(sze) sze = max([rows, cols]); end if chan == 3 % Transform red, green, blue components separately im = im/255; [r, newT] = transformImage(im(:,:,1), T, region, sze); [g, newT] = transformImage(im(:,:,2), T, region, sze); [b, newT] = transformImage(im(:,:,3), T, region, sze); newim = repmat(uint8(0),[size(r),3]); newim(:,:,1) = uint8(round(r*255)); newim(:,:,2) = uint8(round(g*255)); newim(:,:,3) = uint8(round(b*255)); else % Assume the image is greyscale [newim, newT] = transformImage(im, T, region, sze); end %------------------------------------------------------------ % The internal function that does all the work function [newim, newT] = transformImage(im, T, region, sze); [rows, cols] = size(im); % Cut the image down to the specified region im = im(region(1):region(2), region(3):region(4)); [rows, cols] = size(im); % Find where corners go - this sets the bounds on the final image B = bounds(T,region); nrows = B(2) - B(1); ncols = B(4) - B(3); % Determine any rescaling needed s = sze/max(nrows,ncols); S = [s 0 0 % Scaling matrix 0 s 0 0 0 1]; T = S*T; Tinv = inv(T); % Recalculate the bounds of the new (scaled) image to be generated B = bounds(T,region); nrows = B(2) - B(1); ncols = B(4) - B(3); % Construct a transformation matrix that relates transformed image % coordinates to the reference coordinates for use in a function such as % DIGIPLANE. This transformation is just an inverse of a scaling and % origin shift. newT=inv(S - [0 0 B(3); 0 0 B(1); 0 0 0]); % Set things up for the image transformation. newim = zeros(nrows,ncols); [xi,yi] = meshgrid(1:ncols,1:nrows); % All possible xy coords in the image. % Transform these xy coords to determine where to interpolate values % from. Note we have to work relative to x=B(3) and y=B(1). sxy = homoTrans(Tinv, [xi(:)'+B(3) ; yi(:)'+B(1) ; ones(1,ncols*nrows)]); xi = reshape(sxy(1,:),nrows,ncols); yi = reshape(sxy(2,:),nrows,ncols); [x,y] = meshgrid(1:cols,1:rows); x = x+region(3)-1; % Offset x and y relative to region origin. y = y+region(1)-1; newim = interp2(x,y,double(im),xi,yi); % Interpolate values from source image. %% Plot bounding region %P = [region(3) region(4) region(4) region(3) % region(1) region(1) region(2) region(2) % 1 1 1 1 ]; %B = round(homoTrans(T,P)); %Bx = B(1,:); %By = B(2,:); %Bx = Bx-min(Bx); Bx(5)=Bx(1); %By = By-min(By); By(5)=By(1); %show(newim,2), axis xy %line(Bx,By,'Color',[1 0 0],'LineWidth',2); %% end plot bounding region %--------------------------------------------------------------------- % % Internal function to find where the corners of a region, R % defined by [minrow maxrow mincol maxcol] are transformed to % by transform T and returns the bounds, B in the form % [minrow maxrow mincol maxcol] function B = bounds(T, R) P = [R(3) R(4) R(4) R(3) % homogeneous coords of region corners R(1) R(1) R(2) R(2) 1 1 1 1 ]; PT = round(homoTrans(T,P)); B = [min(PT(2,:)) max(PT(2,:)) min(PT(1,:)) max(PT(1,:))]; % minrow maxrow mincol maxcol