For reducing impulsive noise without degrading image contours, median ltering is a powerful tool. In multi-band images, as for example color images or vector eld obtained by optic ow computation, a vector median lter can be used. Vector median lters are deened on the basis of a suitable distance, the best performing distance being the euclidean. Euclidean distance is computed by using the eucli...

We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore useless as a distance measure in this case. We study basic properties of this quantity, and find interesting relationships between the TRE and the trace norm ...

Massive data streams are now fundamental to many data processing applications. For example, Internet routers produce large scale diagnostic data streams. Such streams are rarely stored in traditional databases, and instead must be processed “on the fly” as they are produced. Similarly, sensor networks produce multiple data streams of observations from their sensors. There is growing focus on ma...

Introducing contravariant trace-densities for quantum states, we restore one-to-one correspondence between quantum operations described by normal CP maps and their trace densities as Hermitian-positive operatorvalued contravariant kernels. The CB-norm distance between two quantum operations is explicitly expressed in terms of these densities as the supremum over the input states. A larger C-dis...

In this work we propose an lp-norm data fidelity constraint for training the autoencoder. Usually the Euclidean distance is used for this purpose; we generalize the l2-norm to the lp-norm; smaller values of p make the problem robust to outliers. The ensuing optimization problem is solved using the Augmented Lagrangian approach. The proposed lp -norm Autoencoder has been tested on benchmark deep...

In order to derive the offset curves by using cubic Bézier curves with a linear field of normal vectors (the so-called LN Bézier curves) more efficiently, three methods for approximating degree n Bézier curves by cubic LN Bézier curves are considered, which includes two traditional methods and one new method based on Hausdorff distance. The approximation based on shifting control points is equi...

W ABSTRACT e describe a bisection method to determine the 2-norm and Frobenius norm-g distance from a given matrix A to the nearest matrix with an eigenvalue on the ima inary axis. If A is stable in the sense that its eigenvalues lie in the open left half e plane, then this distance measures how "nearly unstable" A is. Each step provides ither a rigorous upper bound or a rigorous lower bound on...

The Wilkinson distance of a matrix A is the two-norm of the smallest perturbation E so that A + E has a multiple eigenvalue. Malyshev derived a singular value optimization characterization for the Wilkinson distance. In this work we generalize the definition of the Wilkinson distance as the two-norm of the smallest perturbation so that the perturbed matrix has an eigenvalue of prespecified alge...

We present techniques to efficiently compute the distance under max-norm between a point and a wide class of geometric primitives. We reduce the distance computation to an optimization problem and use our framework to design efficient algorithms for convex polytopes, quadrics and triangulated models. We extend them to handle large models using bounding volume hierarchies, and use rasterization ...

We present techniques to efficiently compute the distance under max-norm between a point and a wide class of geometric primitives. We formulate the distance computation as an optimization problem and use this framework to design efficient algorithms for convex polytopes, algebraic primitives and triangulated models. We extend them to handle large models using bounding volume hierarchies, and us...