How do we computer SSD (Sum of Squared Differences)

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Emmanuel 2014-9-20

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评论： Image Analyst 2018-7-29

Hello!

I am having two images f and g, where g contains a block which is also present in a. How can detect the block in a using SSd? How is SSD computed. Please help!

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Emmanuel 2014-9-22

Sorry! my bad..Its actually "f". g contains the template of f and hence g is smaller than f

nikhil kumar 2017-7-26

Refer to this link http://www.cs.toronto.edu/~guerzhoy/320/lec/patches_filters.pdf

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Matt J 2014-9-20

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If g is a template of the block you're searching for, the minimum SSD match is equivalent to the maximum non-normalized correlation match,

correlation=conv2(f,rot90(g,2),'same');
[i,j]=find(correlation=max(correlation(:)));

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Matt J 2014-9-20

编辑：Matt J 2014-9-20

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Let f_ij be the sub-block of f located at coordinate (i,j). We consider blocks the same size as the template g. The SSD search criterion is to find the sub-block f_ij minimizing the squared difference with g

min_ij 0.5*norm(f_ij(:)-g(:))^2

Expanding the norm gives the equivalent

min_ij 0.5*norm(f_ij(:))^2 -dot(f_ij(:),g(:)) + 0.5*norm(g(:))^2

The final term is constant and can be ignored. Negating the remaining terms, this is equivalent to the maximization,

max_ij dot(f_ij(:),g(:)) - 0.5*norm(f_ij(:))^2

The first term can be computed for all (i,j) and organized as an image by taking the cross-correlation of f with g. The cross-correlation is likewise, the convolution of f with a rotated version of g.

The second term can likewise be obtained as the convolution

fEnergy=conv2(f.^2,ones(size(g))/2,'same');

All of this is just to say that an SSD search can be broken down into a series of convolutions/correlations... It's of questionable usefulness of course, and would often be outperformed by normalized cross-correlation, except when your template is very accurate.

Mohammad Al Nagdawi 2018-7-29

from the best on my knowledge the state of the art similarity measure unable to find similarity for such images that will lead to correct registration. I tried Mutual information, Jefferey divergence. conv2, RMSE, and PSNR are helpful only for monomodal images. Can you suggest a nonexistent solution I will build and try?

Image Analyst 2018-7-29

Then you'll have to develop your own. One that preprocesses the images to get something that can be used for registration, like one that finds the outer circle and center, and being robust enough to handle that gradient.

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