Edel García-Reyes

Javier Lamar-Leon, Rocio Gonzalez-Diaz, Edel Garcia-Reyes

In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of the object that models the motion. Two topological signatures are compared simply by the angle between the corresponding vectors. With respect to gait recognition, we have tested our method using only the lowest fourth part of the body's silhouette. In this way, the impact of variations in the upper part of the body, which are very frequent in real scenarios, decreases considerably. We have also tested our method using other periodic motions such as running or jumping. Finally, we formally prove that our method is robust to small perturbations in the input data and does not depend on the number of periods contained in the periodic motion sequence.

Yenisel Plasencia-Calaña, Mauricio Orozco-Alzate, Heydi Méndez-Vázquez et al.

Classification in the dissimilarity space has become a very active research area since it provides a possibility to learn from data given in the form of pairwise non-metric dissimilarities, which otherwise would be difficult to cope with. The selection of prototypes is a key step for the further creation of the space. However, despite previous efforts to find good prototypes, how to select the best representation set remains an open issue. In this paper we proposed scalable methods to select the set of prototypes out of very large datasets. The methods are based on genetic algorithms, dissimilarity-based hashing, and two different unsupervised and supervised scalable criteria. The unsupervised criterion is based on the Minimum Spanning Tree of the graph created by the prototypes as nodes and the dissimilarities as edges. The supervised criterion is based on counting matching labels of objects and their closest prototypes. The suitability of these type of algorithms is analyzed for the specific case of dissimilarity representations. The experimental results showed that the methods select good prototypes taking advantage of the large datasets, and they do so at low runtimes.

J. Lamar-Leon, Raul Alonso-Baryolo, Edel Garcia-Reyes et al.

Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. In this paper, we present a persistent homology-based method to extract topological features (the so-called {\it topological gait signature}) from the the body silhouettes of a gait sequence. % It has been used before in several conference papers of the same authors for human identification, gender classification, carried object detection and monitoring human activities at distance. % The novelty of this paper is the study of the stability of the topological gait signature under small perturbations and the number of gait cycles contained in a gait sequence. In other words, we show that the topological gait signature is robust to the presence of noise in the body silhouettes and to the number of gait cycles contained in a given gait sequence. % We also show that computing our topological gait signature of only the lowest fourth part of the body silhouette, we avoid the upper body movements that are unrelated to the natural dynamic of the gait, caused for example by carrying a bag or wearing a coat.