On the Dynamic Time Warping of Cyclic Sequences for Shape Retrieval

In the last years, in shape retrieval, methods based on Dynamic Time Warping and sequences where each point of the contour is represented by elements of several dimensions have had a significant presence. In this approach each point of the closed contour contains information with respect to the other ones, this global information is very discriminant. The current state-of-the-art shape retrieval is based on the analysis of these distances to learn better ones. These methods are robust to noise and invariant to transformations, but, they obtain the invariance to the starting point with a brute force cyclic alignment which has a high computational time. In this work, we present the Cyclic Dynamic Time Warping. It can obtain the cyclic alignment in O(n2 log n) time, where n is the size of both sequences. Experimental results show that our proposal is a better alternative than the brute force cyclic alignment and other heuristics for obtaining this invariance

Circular pattern matching with k mismatches

The k-mismatch problem consists in computing the Hamming distance between a pattern P of length m and every length-m substring of a text T of length n, if this distance is no more than k. In many real-world applications, any cyclic shift of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P. This is the circular pattern m

Circular pattern matching with k mismatches

We consider the circular pattern matching with k mismatches (k-CPM) problem in which one is to compute the minimal Hamming distance of every length-m substring of T and any cyclic rotation of P, if this distance is no more than k. It is a variation of the well-studied k-mismatch problem. A multitude of papers has been devoted