introduction

images are not just functions (intensity).
it also contains location properties.

1D correlation

the filter is normalized and then is used to compute cross -correlation.
why the peak value is at index 60?
because positve value in signal [50,70] multiply positive value in filter, and negative value in signal [50,70] multiply negative value in filter. At last, we sum them up.

cross-correlation in matlab

%% matlab cross-correlation
fruit = rgb2gray(imread('../pics/fruit.png'));
apple = rgb2gray(imread('../pics/apple.png'));
% imshowpair(fruit,apple, 'montage');
c = normxcorr2(apple, fruit);
figure;
surf(c);
shading flat;

% Find template 1D
% Function definition must be the very first piece of code here!
function index = find_template_1D(t, s)
    c = normxcorr2(t,s);
    [~,index] = max(c);

    index = index -size(t,2) + 1;

end

pkg load image; % after define function
% Test code:
s = [-1 0 0 1 1 1 0 -1 -1 0 1 0 0 -1];
t = [1 1 0];
disp('Signal:'), disp([1:size(s, 2); s]);
disp('Template:'), disp([1:size(t, 2); t]);

index = find_template_1D(t, s);
disp('Index:'), disp(index);

template matching

% Find template 2D
% NOTE: Function definition must be the very first piece of code here!
function [yIndex xIndex] = find_template_2D(template, img)
    % TODO: Find template in img and return [y x] location
    % NOTE: Turn off all output from inside the function before submitting!
    c = normxcorr2(template, img);
    [~,idx] = max(c(:));
    [yIndex, xIndex] = ind2sub(size(c), idx);
    xIndex = xIndex - size(template,2) + 1;
    yIndex = yIndex - size(template,1) + 1;
endfunction

pkg load image; % AFTER function definition

% Test code:
tablet = imread('tablet.png');
imshow(tablet);
glyph = tablet(75:165, 150:185);
imshow(glyph);

[y x] = find_template_2D(glyph, tablet);
% y row number 
% x column number
disp([y x]); % should be the top-left corner of template in tablet
colormap('gray'),imagesc(tablet);
hold on;
plot(x,y,'r+','markersize',16);
hold on;

but we have more powerful tools to detection face.