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A frequent problem in low-level vision consists of eliminating noise and small-scale details from an image while still preserving or even enhancing the edge structure. Nonlinear anisotropic diiusion ltering may be one possibility to achieve these goals. The objective of the present paper is to review the author's results on a scale-space interpretation of a(More)
We study an energy functional for computing optical flow that combines three assumptions: a brightness constancy assumption, a gradient constancy assumption, and a discontinuity-preserving spatio-temporal smoothness constraint. In order to allow for large displacements, linearisations in the two data terms are strictly avoided. We present a consistent(More)
The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional(More)
Nonlinear diffusion filtering in image processing is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a discrete nonlinear diffusion scale-space framework we present semi-implicit schemes which are stable for all time steps. These novel schemes(More)
Differential methods belong to the most widely used techniques for optic flow computation in image sequences. They can be classified into local methods such as the Lucas–Kanade technique or Bigün's structure tensor method, and into global methods such as the Horn/Schunck approach and its extensions. Often local methods are more robust under noise, while(More)
Soft wavelet shrinkage, total variation (TV) diffusion, TV regularization, and a dynamical system called SIDEs are four useful techniques for discontinuity preserving denoising of signals and images. In this paper we investigate under which circumstances these methods are equivalent in the one-dimensional case. First, we prove that Haar wavelet shrinkage on(More)
Although variational methods are among the most accurate techniques for estimating the optical flow, they have not yet entered the field of real-time vision. Main reason is the great popularity of standard numerical schemes that are easy to implement, however, at the expense of being too slow for real-time performance. In our paper we address this problem(More)