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Pattern Recognition, International Conference on (2006)
Hong Kong
Aug. 20, 2006 to Aug. 24, 2006
ISSN: 1051-4651
ISBN: 0-7695-2521-0
pp: 594-598
Fan Zhang , University of York, York, YO10 5DD, UK
Edwin R. Hancock , University of York, York, YO10 5DD, UK
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.

F. Zhang and E. R. Hancock, "A Riemannian Weighted Filter for Edge-sensitive Image Smoothing," 2006 18th International Conference on Pattern Recognition(ICPR), Hong Kong, 2006, pp. 594-598.
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