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.

Carla Nascimento Neves, Raul Queiroz Feitosa, Mabel X. Ortega Adarme et al.

With its vast expanse, exceeding that of Western Europe by twice, the Amazon rainforest stands as the largest forest of the Earth, holding immense importance in global climate regulation. Yet, deforestation detection from remote sensing data in this region poses a critical challenge, often hindered by the persistent cloud cover that obscures optical satellite data for much of the year. Addressing this need, this paper proposes three deep-learning models tailored for deforestation monitoring, utilizing SAR (Synthetic Aperture Radar) multitemporal data moved by its independence on atmospheric conditions. Specifically, the study proposes three novel recurrent fully convolutional network architectures-namely, RRCNN-1, RRCNN-2, and RRCNN-3, crafted to enhance the accuracy of deforestation detection. Additionally, this research explores replacing a bitemporal with multitemporal SAR sequences, motivated by the hypothesis that deforestation signs quickly fade in SAR images over time. A comprehensive assessment of the proposed approaches was conducted using a Sentinel-1 multitemporal sequence from a sample site in the Brazilian rainforest. The experimental analysis confirmed that analyzing a sequence of SAR images over an observation period can reveal deforestation spots undetectable in a pair of images. Notably, experimental results underscored the superiority of the multitemporal approach, yielding approximately a five percent enhancement in F1-Score across all tested network architectures. Particularly the RRCNN-1 achieved the highest accuracy and also boasted half the processing time of its closest counterpart.

Mariana Dória Prata Lima, Gilson Antonio Giraldi, Gastão Florêncio Miranda Junior

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA, the concepts of complexes and filtration are building blocks. Firstly, a filtration is constructed from some complex. Then, persistent homology classes are computed, and their evolution along the filtration is visualized through the persistence diagram. Additionally, we applied vectorization techniques to the persistence diagram to make this topological information compatible with machine learning algorithms. This was carried out with the aim of classifying images from multiple classes in the MNIST dataset. Our approach inserts topological features into deep learning approaches composed by single and two-streams neural networks architectures based on a multi-layer perceptron (MLP) and a convolutional neral network (CNN) taylored for multi-class classification in the MNIST dataset. In our analysis, we evaluated the obtained results and compared them with the outcomes achieved through the baselines that are available in the TensorFlow library. The main conclusion is that topological information may increase neural network accuracy in multi-class classification tasks with the price of computational complexity of persistent homology calculation. Up to the best of our knowledge, it is the first work that combines deep learning features and the combination of topological features for multi-class classification tasks.

Leandro C. Souza, Bruno C. Guingo, Gilson Giraldi et al.

Since classical machine learning has become a powerful tool for developing data-driven algorithms, quantum machine learning is expected to similarly impact the development of quantum algorithms. The literature reflects a mutually beneficial relationship between machine learning and quantum computing, where progress in one field frequently drives improvements in the other. Motivated by the fertile connection between machine learning and quantum computing enabled by parameterized quantum circuits, we use a resource-efficient and scalable Single-Qubit Quantum Neural Network (SQQNN) for both regression and classification tasks. The SQQNN leverages parameterized single-qubit unitary operators and quantum measurements to achieve efficient learning. To train the model, we use gradient descent for regression tasks. For classification, we introduce a novel training method inspired by the Taylor series, which can efficiently find a global minimum in a single step. This approach significantly accelerates training compared to iterative methods. Evaluated across various applications, the SQQNN exhibits virtually error-free and strong performance in regression and classification tasks, including the MNIST dataset. These results demonstrate the versatility, scalability, and suitability of the SQQNN for deployment on near-term quantum devices.

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.

Paulo Sérgio Silva Rodrigues, Gilson Antonio Giraldi

It is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In this paper we collect theoretical elements to follow this avenue but using the q-Gaussian kernel that is a nonextensive generalization of the Gaussian one. Firstly, we review some theoretical elements behind the one-dimensional q-Gaussian and its Fourier transform. Then, we consider the two-dimensional q-Gaussian and we highlight the issues behind its analytical Fourier transform computation. We analyze the q-Gaussian kernel in the space and Fourier domains using the concepts of space window, cut-off frequency, and the Heisenberg inequality.