[Octave-bug-tracker] [bug #43218] imshear causes more signal spread than expected and inconsistent vertical offset

[anonymous]

Follow-up Comment #1, bug #43218 (project octave):

To improve the accuracy of shearing, I wrote the following imshear variant. It
currently is limited to the crop option (i.e., BBOX = 'crop' in imshear).



function MM = imgshear(M, AXIS, ALPHA)

        % -- Custom Function: imgshear(M, AXIS, ALPHA)
        %     Shear M along AXIS ('x' or 'y') by ALPHA (i.e., slope of shear)
        %
        %     The returned matrix is sheared and cropped to the same dimensions
        %     as the original matrix. For now, this custom function is preferred
        %     over imshear in the Octave Forge image package because imshear
        %     spreads the signal more than expected and has an inconsistent
        %     vertical offset, as described in the Octave bug tracker item 
#42318
        %     at http://savannah.gnu.org/bugs/?group=octave
        
        % initialize
        MM = M;
        
        % if shearing slope is nonzero
        if (ALPHA ~= 0)
                [h,w] = size(M);

                % if shearing is vertical
                if (AXIS == 'y')
                
                        % add vertical margin
                        if (ALPHA > 0)
                                hMargin = ceil((w-1)*ALPHA);
                                M = [M; zeros(hMargin,w,class(M))];
                                iBase = h;
                        else
                                hMargin = ceil((w-1)*(-ALPHA))+1;
                                M = [zeros(hMargin,w,class(M)); M];
                                iBase = h + hMargin;
                        endif;
                        
                        % for each sheared column
                        for col=2:w
                                hOffset = (col-1)*ALPHA;
                                iDel = ceil(hOffset);
                                iBottom = iBase + iDel;
                                iTop = iBottom - h + 1;
                                c1 = abs(iDel - hOffset);
                                c0 = 1 - c1;
                                MM(:,col) = c0*M(iTop:iBottom,col) + 
c1*M(iTop-1:iBottom-1,col);
                        endfor; % each sheared column

                % else if shearing is horizontal
                elseif (AXIS == 'x')
                
                        % add horizontal margin
                        if (ALPHA > 0)
                                wMargin = ceil((h-1)*ALPHA);
                                M = [zeros(h,wMargin,class(M)) M];
                                jBase = wMargin + 1;
                        else
                                wMargin = ceil((h-1)*(-ALPHA))+1;
                                M = [M zeros(h,wMargin,class(M))];
                                jBase = 1;
                        endif;
                        
                        % for each sheared row
                        for row=h-1:-1:1
                                wOffset = (h-row)*(-ALPHA);
                                jDel = floor(wOffset);
                                jLeft = jBase + jDel;
                                jRight = jLeft + w - 1;
                                c1 = abs(jDel - wOffset);
                                c0 = 1 - c1;
                                MM(row,:) = c0*M(row,jLeft:jRight) + 
c1*M(row,jLeft+1:jRight+1);
                        endfor; % each sheared column
                endif;  % shearing direction specified
        endif;  % shearing slope is nonzero
endfunction;



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