Laboratory 3

Dilation and Erosion

Original image

Image thresheld at 130

The m file used to generate the below images can be downloaded here

Image Result	Structuring Element
BW1 = imerode(imdilate(BW, SE1),SE1) imclose(BW, SE1)	SE1 = circularstruct(2)
BW2 = imdilate(imerode(BW, SE2),SE2) imopen(BW, SE2)	SE2 = ones(3)
BW3 = imerode(imdilate(BW, SE3),SE3) imclose(BW, SE3)	SE3 = ones(2, 5)
BW4 = imdilate(imerode(BW, SE4),SE4) imopen(BW, SE4)	SE4 = eye(5) | rot90(eye(5))

BW5 = imopen(imclose(BW, SE1), SE1)	BW6 = imclose(imopen(BW, SE1), SE1)

Locating Landmarks on a Multiple Choice Answer Sheet

Listing of locatelandmarks.m

% LOCATELANDMARKS - locates landmarks on SURF form
%
% Usage:  [tl, tr, bl, br] = locatelandmarks(im)
%
% Argument: im - Image to be processed, assumed binary.
%
% Returns:  tl, tr, bl, br
%              - Coordinates of the centroids of the top-left, top-right,
%                bottom-left and bottom-right landmarks respectively.  
%                These coordinates are returned as column vectors in the
%                form [row; col] for each landmark.
%
% The function should also display the image with the centroids of the 
% landmarks overlayed.
function [tl, tr, bl, br] = locatelandmarks(im)
    
    [rows,cols] = size(im);
    
    % initially define landmark coordinates to extremes
    tl=[rows;cols];
    tr=[rows;0   ];
    bl=[0   ;cols];
    br=[0   ;0   ];
    
    bw = ~im;
    
    % Note: 8 pixels is the minimum space between landmarks and adjacent blobs
    %       (TR landmark, surf10.png with a size of 1128x784 pixels)
    %       Hence SE is proportional to im size, scaled by 8/784
    
    a = 8/784; %scale factor
    
    SE = ones(a*rows, a*cols);
    
    % perform close-open morphology
    % Note: a close-open resulted in the landmarks having strighter sides
    %       compared to open-close 
    closeopen = imopen(imclose(bw,SE),SE);
    
    % Matrix with each pixel set to its x coordinate
    x = ones(rows,1)*[1:cols];
    % Matrix with each pixel set to its y coordinate
    y = [1:rows]'*ones(1,cols);
    
    % label all the blobs
    [L, num] = bwlabel(closeopen);
    
    % search the blobs to find centers, and then landmarks
    for i = 1:num
        img = L==i;
        area(i) = sum(sum(img));
        meanx = sum(sum(double(img).*x))/area(i);
        meany = sum(sum(double(img).*y))/area(i);
        
        % determine tl
        if tl(1)+tl(2) > meanx + meany
            tl = [meanx; meany];
            tlindex = i;
        end
        % determine tr
        if tr(1)-tr(2) > meanx - meany
            tr = [meanx; meany];
            trindex = i;
        end
        % determine br
        if br(1)+br(2) < meanx + meany
            br = [meanx; meany];
            brindex = i;
        end
        % determine bl
        if bl(1)-bl(2) < meanx - meany
            bl = [meanx; meany];
            blindex = i;
        end
    end
    
    % test for upside down form
    % Note: tl > bl and tr > br for correctly orientated forms
    if area(tlindex) < area(blindex) && area(trindex) < area(brindex)
        'warning: upside down form'
        locatelandmarks(imrotate(im,180));
        
    else imshow(im)
        hold;
        landmarks = [tl, tr, br, bl];    
        plot(landmarks(1,:), landmarks(2,:),'+r','MarkerSize',50,'LineWidth',2);
        hold;
end

Results of using locatelandmarks.m

Below tests the upsidedown detection

surf11.jpg	loacatelandmarks of surf11.jpg

Below tests different resolution forums

Original surf10.png	After using locatelandmarks on original surf10.png
After using locatelandmarks on 66.67% surf10.png	After using locatelandmarks on 166.67% surf10.png

Notes: I have tested both upside down forms and scaled forms.
I have used a SE that ovbiously works for all the provided surf forms, and I have tried to account for arbitary forms. The thing where my code would fail is if there was a low quality scan, and the landmarks where not so defined.