Robust image denoising and smoothing with generalised spatial-tonal Averages

This article investigates image filtering and smoothing from the perspective of a recent generalisation of the notion of aggregation functions in fuzzy systems, called pre-aggregation functions. Mixture functions describing a broad class of robust spatial-tonal filters and smoothers are derived using penalty-based methods. Several existing filters are re-derived using this approach and several novel filters are proposed, which are able to better handle filtering in contexts where the pixel to be filtered is itself an outlier in the local neighbourhood. The proposed class of Robust Bilateral Filters formalises and generalises a recent result of Chaudhury, who noted that using a filtered version of an image to compute tonal weights for a Bilateral Filter gave more robust denoising. Filter performance is validated using standard test images and quantified using peak signal-to-noise ratio and visual similarity, finding novel filters that exceed the performance of the standard Bilateral Filter.