Morphological filters, which rely on data ranking rather than level, have received much less attention. This is despite their inherent insensitivity They exist outside the current trends in machine learning since they cannot be represented with convolutions. But they are inherently insensitive to the extent of an edge edge, which should makes make them good candidates for edge-preserving filtering. It has recently been demonstrated that the bitonic filter, filtering, a morphological filter based on 'opening' and 'closing' operations, can perform nearly as performs better than both well as anisotropic diffusion and non-local means for noisy natural images. This is despite images with various amounts the use of a local added noise. 'structuring element' which does not automatically adjust to the data around each pixel. Hence there is good reason to expect that local variation of the shape of this structuring element will significantly improve performance. However, there has been very little work on locally-varying morphological filters, partly perhaps due to difficulties in both implementation and analysis. The aim of this project is to investigate such filters, which could encompass implementation efficiency, what is the best shape of the structuring elements, or what determines the local orientation of the structuring elements.

The initial bitonic filter just used a circular mask at every pixel. In the structurally-varying bitonic filter, this was replaced with a locally varying mask. This hugely improved the filter performance, despite the possible mask shapes being constrained to a small range of ellipses. Hence it is the aim of this project to investigate such a filter with a greater variation of mask shapes: the problem is that, if the mask shape is allowed to exactlymatch the image features, it will start to match the noise rather than the actual structure in the image. So what is the optimal amount of mask variation, and how should the mask shape be constrained for best noise performance?