Masked k-order statistic filters for 2D data

Morphological erosion, dilation, median filter and generic k-order statistic filter implementation

Masked k-order statistic filter for double data

refer to: F. Bellavia, D. Tegolo, C. Valenti, "Improving Harris corner selection strategy", IET Computer Vision 5(2), 2011. Only for academic or other non-commercial purposes.

With respect to standard matlab routines, any kernel mask can be used and it is faster for large kernel size (i.e. more than 30x30 kernel mask)

input:
im - input 2D matrix
ker - kernel binary mask
idx - k-order index, in range [1,sum(ker(:)))

Use idx=1 for min filter (graylevel erosion), idx=sum(ker(:))/2+0.5 for median filter, idx=sum(ker(:)) for max filter (graylevel dilation), any other value for k-selection filter, non integer values interpolate between values, i.e. 5.6 give 0.4*I(5)+0.6*I(6) where I(n) is the n-th values in the sorted order inside the kernel mask.

output:
r - result 2D matrix, of the same size of im, zero padding is used for the border.

The median filter implementation is based on:
W. Hardle, W. Steiger, "Algorithm AS 296: Optimal Median Smoothing", Journal of the Royal Statistical Society, Series C (Applied Statistics), pp. 258-264.