New Bi-, Tri-, and Fourlateral Filters for Color and Hyperspectral Images Filtering

In the paper, we investigate effectiveness of modified bilateral and new tri-, and fourlateral denoising filters for grey, color, and hyperspectral image procession. Conventional bilateral filter performs merely weighted averaging of the local neighborhood pixels. The weight includes two components: spatial and radiometric ones. The first component measures the geometric distances between the center pixel and local neighborhood ones. The second component measures the radiometric distance between the values of the center pixel and local neighborhood ones. Noise affects all pixels even onto the centre one used as a reference for the tonal filtering. Thus, the noise affecting the centre pixel has a disproportionate effect onto the result. This suggests the first modification: the center pixel is replaced by the weighted average (with some estimate of the true value) of the neighborhood pixels contained in a window around it. The second modification uses the matrix-valued weights. They include four components: spatial, radiometric, inter-channel weights, and radiometric inter-channel ones. The fourth weight measures the radiometric distance (for grey-level images) between the inter-channel values of the center scalar-valued channel pixel and local neighborhood channel ones.