MORPHOLOGY-BASED NOISE REDUCTION: STRUCTURAL VARIATION AND THRESHOLDING IN THE BITONIC FILTER
The bitonic filter was recently developed to embody the novel concept of using signal bitonicity to differentiate from noise. This is a combined linear/morphological operator, and the use of data ranking leads to good noise-reduction performance across smooth and disjoint signals alike. However, for processing images, the spatial extent of the bitonic filter was locally constrained to a fixed circular mask. Since natural images tend to have structure which varies over the image, a novel structurally varying bitonic filter is presented, in which the mask is locally adaptive to the signal in the image, but does not follow patterns in the noise. This new filter includes novel robust structurally varying morphological operations, for which an efficient implementation is also developed, and a novel formulation of non-iterative directional Gaussian filtering. Data thresholds are also integrated with the morphological operations, increasing noise reduction for low noise levels, and enabling the filter to be embodied in a multi-resolution framework for better performance at high noise levels. The structurally varying bitonic filter is presented in detail without presuming prior knowledge of morphological filtering, and compared to a number of high-performance linear noise-reduction filters, to set this novel concept in context. These are all tested over a very wide range of noise levels, on a fairly broad set of images, using conventional performance measures. The new filter is a considerable improvement on the fixed-mask bitonic, outperforms anisotropic diffusion and image-guided filtering at all but extremely low noise levels, non-local means at all noise levels, but not the block-matching 3D filter, except for very high noise. Nevertheless, the structurally varying bitonic tends to have less characteristic residual noise in regions of smooth signal, and very good preservation of signal edges, though with some loss of small scale detail when compared to the block-matching 3D filter. The efficient implementation means that processing time, though slower than the fixed-mask bitonic filter, remains competitive.
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