Gilson A. Giraldi

Josildo Pereira da Silva, Antônio Lopes Apolinário Júnior, Gilson A. Giraldi

Dynamic NURBS, also called D-NURBS, is a known dynamic version of the nonuniform rational B-spline (NURBS) which integrates free-form shape representation and a physically-based model in a unified framework. More recently, computer aided design (CAD) and finite element (FEM) community realized the need to unify CAD and FEM descriptions which motivates a review of D-NURBS concepts. Therefore, in this paper we describe D-NURBS theory in the context of 1D shape deformations. We start with a revision of NURBS for parametric representation of curve spaces. Then, the Lagrangian mechanics is introduced in order to complete the theoretical background. Next, the D-NURBS framework for 1D curve spaces is presented as well as some details about constraints and numerical implementations. In the experimental results, we focus on parameters choice and computational cost.

Liliane Rodrigues de Almeida, Gilson A. Giraldi, Marcelo Bernardes Vieira

In the last decades, some literature appeared using the Lie groups theory to solve problems in computer vision. On the other hand, Lie algebraic representations of the transformations therein were introduced to overcome the difficulties behind group structure by mapping the transformation groups to linear spaces. In this paper we focus on application of Lie groups and Lie algebras to find the rigid transformation that best register two surfaces represented by point clouds. The so called pairwise rigid registration can be formulated by comparing intrinsic second-order orientation tensors that encode local geometry. These tensors can be (locally) represented by symmetric non-negative definite matrices. In this paper we interpret the obtained tensor field as a multivariate normal model. So, we start with the fact that the space of Gaussians can be equipped with a Lie group structure, that is isomorphic to a subgroup of the upper triangular matrices. Consequently, the associated Lie algebra structure enables us to handle Gaussians, and consequently, to compare orientation tensors, with Euclidean operations. We apply this methodology to variants of the Iterative Closest Point (ICP), a known technique for pairwise registration. We compare the obtained results with the original implementations that apply the comparative tensor shape factor (CTSF), which is a similarity notion based on the eigenvalues of the orientation tensors. We notice that the similarity measure in tensor spaces directly derived from Lie's approach is not invariant under rotations, which is a problem in terms of rigid registration. Despite of this, the performed computational experiments show promising results when embedding orientation tensor fields in Lie algebras.

Carlos E. Thomaz, Vagner Amaral, Gilson A. Giraldi et al.

Research on human face processing using eye movements has provided evidence that we recognize face images successfully focusing our visual attention on a few inner facial regions, mainly on the eyes, nose and mouth. To understand how we accomplish this process of coding high-dimensional faces so efficiently, this paper proposes and implements a multivariate extraction method that combines face images variance with human spatial attention maps modeled as feature- and pattern-based information sources. It is based on a unified multidimensional representation of the well-known face-space concept. The spatial attention maps are summary statistics of the eye-tracking fixations of a number of participants and trials to frontal and well-framed face images during separate gender and facial expression recognition tasks. Our experimental results carried out on publicly available face databases have indicated that we might emulate the human extraction system as a pattern-based computational method rather than a feature-based one to properly explain the proficiency of the human system in recognizing visual face information.