Image Classification using Combination of Topological Features and Neural Networks

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.

Combining recurrent and residual learning for deforestation monitoring using multitemporal SAR images

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.

Fourier Analysis and q-Gaussian Functions: Analytical and Numerical Results

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.

Convexity Analysis of Snake Models Based on Hamiltonian Formulation

This paper presents a convexity analysis for the dynamic snake model based on the Potential Energy functional and the Hamiltonian formulation of the classical mechanics. First we see the snake model as a dynamical system whose singular points are the borders we seek. Next we show that a necessary condition for a singular point to be an attractor is that the energy functional is strictly convex in a neighborhood of it, that means, if the singular point is a local minimum of the potential energy. As a consequence of this analysis, a local expression relating the dynamic parameters and the rate of convergence arises. Such results link the convexity analysis of the potential energy and the dynamic snake model and point forward to the necessity of a physical quantity whose convexity analysis is related to the dynamic and which incorporate the velocity space. Such a quantity is exactly the (conservative) Hamiltonian of the system.