An algorithm for multiresolution pyramid decomposition is described. At each stage, the smoothed (“lowpass”) image is obtained by combining morphological grayscale opening and closing. Using this technique, we avoid the systematic bias of traditional approaches, as illustrated by an example. As our application, we perform image enhancement by modifying the reconstruction scheme using a morpholo...

Abstract An m-factorization of a graph is a decomposition of its edge set into edge-disjoint m-regular spanning subgraphs (or factors). In this paper, we prove the existence of an isomorphic m-factorization of the Cartesian product of graphs each of which is decomposable into Hamiltonian even cycles. Moreover, each factor in the m-factorization is m-connected, and bipancyclic for m ≥ 4 and near...

To a given finite graph we associate three kinds of adic, or BratteliVershik, systems: stationary, symbol-count, and reinforced. We give conditions for the natural walk measure to be adic-invariant and identify the ergodic adicinvariant measures for some classes of examples. If the walk measure is adicinvariant we relate its ergodic decomposition to the vector of limiting edge traversal frequen...

This paper focuses on improved edge model based on Curvelet coefficients analysis. Curvelet transform is a powerful tool for multiresolution representation of object with anisotropic edge. Curvelet coefficients contributions have been analyzed using Scale Invariant Feature Transform (SIFT), commonly used to study local structure in images. The permutation of Curvelet coefficients from original ...

This paper considers the problem of maintaining a compact representation (O(n) space) of permutation graphs under vertex and edge modifications (insertion or deletion). That representation allows us to answer adjacency queries in O(1) time. The approach is based on a fully dynamic modular decomposition algorithm for permutation graphs that works in O(n) time per edge and vertex modification. We...

An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi) graph is a simple, complete, edge-colored (multi) graph lacking rainbow triangles. As has been previously shown for Gallai graphs, we show that Gallai multigraphs admit a simple iterative construction. Moreover, we show that Gallai multigraphs give rise to a surprising and highly structured decompos...

We consider the class of graphs for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees, and the natural generalization to matroids, where the cogirth is equal to the number of disjoint bases. We provide descriptions of such graphs and matroids, showing that such a graph (or matroid) has a unique decomposition. In the case of graphs, our results are releva...

| This paper addresses the problem of mobile robot self-localization given a polygonal map and a set of observed edge segments. The standard approach uses interpretation tree search with pruning heuristics to match observed edges to map edges. Our approach introduces a preprocessing step in which the map is decomposed into view-invariant regions (VIRs). The VIR decomposition captures informatio...

Proof: “⇒” Suppose D = (V,A) is a strongly connected graph obtained as an orientation of G = (V,E). Then, since ∀S ⊂ V , |δ D(S)| ≥ 1 and |δ − D(S)| ≥ 1, we have |δG(S)| ≥ 2. Therefore, G is 2-edge-connected. “⇐” Let G be a 2-edge-connected graph. Then G has an ear-decomposition. In other words, G is either a cycle C or G is obtained from a 2-edge-connected graph G by adding an ear P (a path) c...