Shape Retrieval Using Normalized Fourier Descriptors Based Signatures and Cyclic Dynamic Time Warping

Abstract

The WARP system defines a dissimilarity measure between shapes described by their contours which is based on Dynamic Time Warping of Fourier Descriptors based signatures. These signatures are invariant to translation, scaling, rotation, and selection of the starting point. However, identical shapes present ambiguous signatures and similar shapes may yield significantly different signatures. Differences affect rotation and starting-point of the signatures, which may lead to poor performance in classification and shape retrieval tasks. We propose a different signature method to provide true rotation invariance and a Cyclic Dynamic Time Warping dissimilarity measure to achieve true startingpoint invariance in shape comparisons. This work has been supported by the Spanish Ministerio de Ciencia y Tecnología and FEDER under grant TIC2002-02684.

A Heuristic Based on the Intrinsic Dimensionality for Reducing the Number of Cyclic DTW Comparisons in Shape Classification and Retrieval Using AESA

“…Hence the necessity to use cyclic sequences and then CDTW (Cyclic DTW) arises. In [10], an algorithm is proposed to calculate the CDTW in time O(n 2 log n) (being n the size of the sequences). Although this algorithm considerably reduces the cost, with the shape descriptors mentioned before, the local distance or dissimilarity [10] between the components of the sequence has too much weight on the final cost, due to its dimensionality.…”

“…In [10], an algorithm is proposed to calculate the CDTW in time O(n 2 log n) (being n the size of the sequences). Although this algorithm considerably reduces the cost, with the shape descriptors mentioned before, the local distance or dissimilarity [10] between the components of the sequence has too much weight on the final cost, due to its dimensionality. Thus, in recognition tasks to use solutions that avoid the computation of CDTW over all the prototypes of the database is necessary, i.e., to avoid an exhaustive search.…”

“…In this work, they do not use the algorithm of [10], but they make clusters of sequences based on their similarity, treating every possible starting point as a different sequence and using indexing methods with lower bounds of these clusters. This solution seems to be suitable just for shape descriptors with only one dimension (such as the curvature) and not for much more dimensions [2][3][4][5][6][7][8].…”