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A Riemannian weighted filter for edge-sensitive image smoothing

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Publication details

Journal18th International Conference on Pattern Recognition, Vol 1, Proceedings
DatePublished - 2006
Number of pages5
Pages (from-to)594-598
Original languageEnglish


This paper describes a new method for image smoothing. We view the image features as residing on a differential manifold, and we work with a representation based on the exponential map for this manifold (i.e. the map from the manifold to a plane that preserves geodesic distances). On the exponential map we characterise the features using a Riemannian weighted mean. We show how both gradient descent and Newton's method can be used to find the mean. Based on this weighted mean, we develop an edge-preserving filter that combines Gaussian and median filters of gray-scale images. We demonstrate our algorithm both on direction fields from shape-from-shading and tensor-valued images.

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