Abstract: Non-linear dimensionality reduction techniques are affected by two critical aspects: (i) the design of the adjacency graphs, and (ii) the embedding of new test data-the out-of-sample problem. For the first aspect, the proposed solutions, in general, were heuristically driven. For the second aspect, the difficulty resides in finding an accurate mapping that transfers unseen data samples into an existing manifold. Past works addressing these two aspects were heavily parametric in the sense that the optimal performance is only achieved for a suitable parameter choice that should be known in advance. In this paper, we demonstrate that the sparse representation theory not only serves for automatic graph construction as shown in recent works, but also represents an accurate alternative for out-of-sample embedding. Considering for a case study the Laplacian Eigenmaps, we applied our method to the face recognition problem. To evaluate the effectiveness of the proposed out-of-sample embedding, experiments are conducted using the K-nearest neighbor (KNN) and Kernel Support Vector Machines (KSVM) classifiers on six public face datasets. The experimental results show that the proposed model is able to achieve high categorization effectiveness as well as high consistency with non-linear embeddings/manifolds obtained in batch modes.

Abstract: PR4883, PII: S0031-3203(13)00327-0
Two-dimensional shape models have been successfully applied to solve many problems in computer vision, such as object tracking, recognition, and segmentation. Typically, 2D shape models are learned from a discrete set of image landmarks (corresponding to projection of 3D points of an object), after applying Generalized Procustes Analysis (GPA) to remove 2D rigid transformations. However, the
standard GPA process suffers from three main limitations. Firstly, the 2D training samples do not necessarily cover a uniform sampling of all the 3D transformations of an object. This can bias the estimate of the shape model. Secondly, it can be computationally expensive to learn the shape model by sampling 3D transformations. Thirdly, standard GPA methods use only one reference shape, which can might be insufficient to capture large structural variability of some objects.
To address these drawbacks, this paper proposes continuous generalized Procrustes analysis (CGPA).
CGPA uses a continuous formulation that avoids the need to generate 2D projections from all the rigid 3D transformations. It builds an efficient (in space and time) non-biased 2D shape model from a set of 3D model of objects. A major challenge in CGPA is the need to integrate over the space of 3D rotations, especially when the rotations are parameterized with Euler angles. To address this problem, we introduce the use of the Haar measure. Finally, we extended CGPA to incorporate several reference shapes. Experimental results on synthetic and real experiments show the benefits of CGPA over GPA.

Abstract: Intestinal contractions are one of the most important events to diagnose motility pathologies of the small intestine. When visualized by wireless capsule endoscopy (WCE), the sequence of frames that represents a contraction is characterized by a clear wrinkle structure in the central frames that corresponds to the folding of the intestinal wall. In this paper we present a new method to robustly detect wrinkle frames in full WCE videos by using a new mid-level image descriptor that is based on a centrality measure proposed for graphs. We present an extended validation, carried out in a very large database, that shows that the proposed method achieves state of the art performance for this task.