Ali Alsam and Hans Jakob Rivertz
non-linear-smoothing, edge preservation, scale-space
The identification of edges is a prerequisite in edge preserving image smoothing algorithms. It is, however, known that the more accurate the results need to be the more costly the calculation of the edges is. Edges are typically identified by the eigen analysis of the gradient matrix at each pixel and image scale. In this paper we introduce the following observation: Smoothing a function in the direction of a large gradient results in an increase in the magnitude of adjacent gradients. Based on this observation, we introduce a constrained diffusion algorithm that is fast and results in clear edge preservation. The basic approach is based on the condition that if smoothing an image pixel in a given direction, towards one of its eight neighbors, result in an increase in the magnitude of the gradients in any other direction then the diffusion is stopped. Experimental results validate the approach.
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