Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 1, pp. 5-14 (2015)

Note on the Riemannian geometry of image processing

Howard E. Brandt

United States Army Research Laboratory, Maryland

Abstract: A brief review is given of the Riemannian geometry of image processing. Methods are exposited for treating images as Riemannian manifolds in general embedding spaces for application to linear and nonlinear scale-space image processing. In particular, the Beltrami operator approach to obtaining a nonlinear differential equation for processing of gray-scale images is treated in some detail. A minor error is found in earlier work appearing in the literature.

Keywords: Image processing, scale space, Riemannian geometry, Beltrami flow, harmonic map.

Classification (MSC2000): 68U10

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