Abstract
Median filters for scalar-valued data are well-known tools for image denoising and analysis. They preserve discontinuities and are robust under noise. We generalise median filtering to matrix-valued data using a minimisation approach. Experiments on DT-MRI and fluid dynamics tensor data demonstrate that tensor-valued median filtering shares important properties of its scalar-valued counterpart, including the robustness as well as the existence of non-trivial steady states (root signals).
A straightforward extension of the definition allows the introduction of matrix-valued mid-range filters and, more general, M-smoothers. Mid-range filters can also serve as a building block in constructing further (e.g. supremum-based) tensor image filters.
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Welk, M., Feddern, C., Burgeth, B., Weickert, J. (2006). Tensor Median Filtering and M-Smoothing. In: Weickert, J., Hagen, H. (eds) Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31272-2_21
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DOI: https://doi.org/10.1007/3-540-31272-2_21
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