The purpose of this paper is to extend the Buneman construction of partially labelled trees to the general case. This extension is related with the characterization of median graphs by Mulder and Schrijver. In the first section, we construct a graph G(H) associated with a copair hypergraph H on a finite set X and define the notion of a median graph with latent vertices (called X-median graph). ...

Let M(m; n) be the complexity of checking whether a graph G with m edges and n vertices is a median graph. We show that the complexity of checking whether G is triangle-free is at most M(m; m). Conversely, we prove that the complexity of checking whether a given graph is a median graph is at most O(m log n)+T(m log n; n), where T(m; n) is the complexity of nding all triangles of the graph. This...

Currently, the threshold T must be entered manually, based on given or estimated values for the SNR of the degraded image. Future work will look at ways to automate this process. Also, we found that at very low SNR, the AMP median filter introduces a few speckles into the restored image. We suspect that this may be due to incorrect adaption in regions of exceptionally high noise levels. Further...

For J ≥ 2 independent groups, the paper deals with testing the global hypothesis that all J groups have a common population median or identical quantiles, with an emphasis on the quartiles. Classic rank-based methods are sometimes suggested for comparing medians, but it is well known that under general conditions they do not adequately address this goal. Extant methods based on the usual sample...

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...

This paper describes the definition and testing of a new type of median filter for images. The topological median filter implements some existing ideas and some new ideas on fuzzy connectedness to improve, over a conventional median filter, the extraction of edges in noise. The concept of alpha-connectivity is defined and used to create an algorithm for computing the degree of connectedness of ...

In this paper, we introduce iterative mean and median filtering schemes for smoothing noisy 3D shapes given as triangle meshes. Our main idea consists of applying mean and median filtering schemes to mesh normals and then update the mesh vertex position in order to fit the mesh to the modified normals. We also give a quantitative evaluation of the proposed mesh filtering schemes and compare the...

Novel matrix-valued imaging techniques such as diffusion tensor magnetic resonance imaging require the development of edgepreserving nonlinear filters. In this paper we introduce a median filter for such tensor-valued data. We show that it inherits a number of favourable properties from scalar-valued median filtering, and we present experiments on synthetic as well as on real-world images that ...

Median tilters operate by selecting the middle valve of an ascending-ordered scqucncc of numbers. These numbers are taken from a moving window on the data to be processed. The operation can be used in seismic data processing to reject glitches on data as well as enhance disconbnuiries in the dara. This paper reviews the definibons and some of the properties of median filters. The median filter ...