Image Smoothing and Differentiation with Minimal-Curvature Filters

Abstract
The fundamental problem of smoothing and differentiating of noisy images has been previously approached in two different ways: 1) Minimization of a smoothness functional, a theoretically well understood procedure but one that involves the solution of a very large system of equations involving all the pixels of the image, for each image. 2) Use of small scale, ready made filters for local smoothing. The process is computationally cheap but generally ad hoc and not very reliable. This paper offers a way to combine the advantages of the two approaches. We construct general filters for local windows of the image, derived from maximization of smoothness of 'regularization' theory. In this way the theoretically robust minimization process becomes suitable for practical implementation, possibly in real time, and is readily adaptable to local image properties. Filters for more reliable derivatives are also being derived. (RRH)

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