Guest Editorial: Scale Space and Variational Methods

This special issue reflects recent developments in mathematical image processing and analysis. Advanced mathematical concepts and methods, including convex, non-convex and non-smooth optimization, differential geometry, variational methods, spatiotemporal scale space, nonlinear diffusion, are used to model complex situations in image analysis, medical imaging and computer vision problems. This special issue comprises seven paperswhich represent state-of-the-art research on these topics and are outlined in the next paragraphs. In “DynamicTextureRecognitionUsingTime-Causal and Time-Recursive Spatio-Temporal Receptive Fields,” Y. Jansson and T. Lindeberg extend classical Gaussian scale space, constructions to time-causal scale space, and use it to develop new, comparable to state-of-the-art, video descriptors for dynamic texture recognition with potential applications to video analysis problems. Diffusion has been a major topic in image analysis for the last three decades, with its connection to scale space, thoroughly explored. Many questions regarding nonlinear diffusion are still open. In this context, M. Welk, J. Weickert and G. Gilboa propose a novel approach for forward– backward space-discrete, time-continuous diffusion in “A Discrete Theory and Efficient Algorithms for Forward– Backward Diffusion Filtering” where they establish some well-posedness results which carry over to the fully discrete case, and efficient algorithms are proposed. In “Design and Processing of Invertible Orientation Scores of 3D Images,” M.H.J. Janssen, A.J.E.M. Janssen, E.J. Bekkers, J. Oliván Bescós and R. Duits extend 2D