Make a weight matrix sparce

Hi,

I have an image in size of 256x256.

I would like to implement an algorithem that use graph theory on this image so i want to calculate the weights matrix: for 2 pixcels x,y i want to calculate D(x,y)= exp(-|x-y|/sigma)

By theory, the matrix D should be in size of (256^2)x(256^2), but i understaned that this is not practical.

I read a paper said that in order to make the weight matrix sparse, it is possible to truncate the matrix to the 50 nearest neighbors.

Does anyone know how can i do it in matlab?

Or maybe another way to make the weight matrix sparse?

thanks,

Or

[Matt J]

Do you really need D, or do you simply need an algorithm that computes D*I(:) for a given image I? The latter is just a convolution operation, and can be done efficiently with FFTs.

[Matt J]

Also, do you absolutely have to define D as D(x,y)= exp(-|x-y|/sigma) ? If you instead use a Mahalanobis distance, D(x,y)= exp(-|x-y|^2/sigma^2), then D can be expressed as a Kronecker product

D=kron( exp(-(xi-yi)^2/sigma)   , exp(-(xj-yj)^2/sigma) )

which has a number of simplifying properties.