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Dr Graham Treece, Department of Engineering
F-GMT11-2: Noise reduction with image-sensitive morphological operators
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| This is a typical natural image of a boat, with some additional noise added. Removing such noise is a very common image processing operation. | There are many ways of doing this: one very recent approach uses morphological operations to process the data. These operations are based around a mask shape, which in this case is fixed to be circular over the whole image | Since the image structure varies over the image, it makes sense to allow this mask shape to also vary with the data. In this case more image features have been preserved, but there is also more noise around edges, since the mask shape is affected by noise as well as real structure. | In this case only a restricted set of elliptical shapes have been allowed. This reduces the impact of the noise, but it also starts to smooth over small features. Is there an optimal way of selecting possible mask shapes that preserves small features but does not match image noise? |
Digital image filters, which replace each pixel in an image with some combination of pixels from a local neighbourhood, are extremely useful in image processing. Of particular note are those which attempt to reduce noise levels in an image whilst preserving the location and extent of any feature gradients, or 'edges'. Multiple linear filters have been developed for this purpose, for instance anisotropic diffusion, non-local means and image-guided filtering. These are all able to automatically adjust
whichpixels are used in the local neighbourhood around each pixel to give the best reduced-noise new estimate.
Morphological filters, which rely on data ranking rather than level, have received much less attention. This is despite their inherent insensitivity to the extent of an edge which should make them good candidates for edge-preserving filtering. It has recently been demonstrated that the bitonic filter, a morphological filter based on 'opening' and 'closing' operations, can perform nearly as well as anisotropic diffusion and non-local means for noisy natural images. This is despite the use of a local '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.
This is an algorithmic development / software project, so experience of writing software is essential, though the development could also be done using Matlab.
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