Page History

Smearing of the 2-D array can be done by averaging for each array element ower neighbour elements with weights

{latex}\LARGE
\( \tilde A_{i,j} = \frac{\sum_{m=-N,n=-N}^{N,N}  A_{i+m,j+n} w_{|m|,|n|}}{\sum_{m=-N,n=-N}^{N,N} w_{|m|,|n|}}, \)
{latex}

with weights defined by the Gaussian function

{latex}\LARGE
\( w_{|m|,|n|}(\sigma) = \exp(-\frac{m^2+n^2}{2\sigma^2}), \)
{latex}

where i, j, m, and n are the pixel indexes, and the Gaussian widths, ?, is also expressed in terms of number of pixels.