Odemir M. Bruno

Leonardo Scabini, Kallil M. Zielinski, Lucas C. Ribas et al.

Texture analysis is a classical yet challenging task in computer vision for which deep neural networks are actively being applied. Most approaches are based on building feature aggregation modules around a pre-trained backbone and then fine-tuning the new architecture on specific texture recognition tasks. Here we propose a new method named \textbf{R}andom encoding of \textbf{A}ggregated \textbf{D}eep \textbf{A}ctivation \textbf{M}aps (RADAM) which extracts rich texture representations without ever changing the backbone. The technique consists of encoding the output at different depths of a pre-trained deep convolutional network using a Randomized Autoencoder (RAE). The RAE is trained locally to each image using a closed-form solution, and its decoder weights are used to compose a 1-dimensional texture representation that is fed into a linear SVM. This means that no fine-tuning or backpropagation is needed. We explore RADAM on several texture benchmarks and achieve state-of-the-art results with different computational budgets. Our results suggest that pre-trained backbones may not require additional fine-tuning for texture recognition if their learned representations are better encoded.

Leonardo Scabini, Bernard De Baets, Odemir M. Bruno

The deep learning literature is continuously updated with new architectures and training techniques. However, weight initialization is overlooked by most recent research, despite some intriguing findings regarding random weights. On the other hand, recent works have been approaching Network Science to understand the structure and dynamics of Artificial Neural Networks (ANNs) after training. Therefore, in this work, we analyze the centrality of neurons in randomly initialized networks. We show that a higher neuronal strength variance may decrease performance, while a lower neuronal strength variance usually improves it. A new method is then proposed to rewire neuronal connections according to a preferential attachment (PA) rule based on their strength, which significantly reduces the strength variance of layers initialized by common methods. In this sense, PA rewiring only reorganizes connections, while preserving the magnitude and distribution of the weights. We show through an extensive statistical analysis in image classification that performance is improved in most cases, both during training and testing, when using both simple and complex architectures and learning schedules. Our results show that, aside from the magnitude, the organization of the weights is also relevant for better initialization of deep ANNs.

Mariane B. Neiva, Odemir M. Bruno

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several metrics of the graph. However, it is not always clear that this representation is unique, as the permutation of lines and rows in the matrix can represent the same graph. To address this issue, the proposed methodology employs a sorting algorithm to rearrange the elements of the adjacency matrix of a complex graph in a specific order. The resulting sorted adjacency matrix is then used as input for feature extraction and machine learning algorithms to classify the networks. The results indicate that the proposed methodology outperforms previous literature results on synthetic and real-world data.

Kallil M. C. Zielinski, Lucas C. Ribas, Jeaneth Machicao et al.

Network modeling has proven to be an efficient tool for many interdisciplinary areas, including social, biological, transport, and many other real world complex systems. In addition, cellular automata (CA) are a formalism that has been studied in the last decades as a model for exploring patterns in the dynamic spatio-temporal behavior of these systems based on local rules. Some studies explore the use of cellular automata to analyze the dynamic behavior of networks, denominating them as network automata (NA). Recently, NA proved to be efficient for network classification, since it uses a time-evolution pattern (TEP) for the feature extraction. However, the TEPs explored by previous studies are composed of binary values, which does not represent detailed information on the network analyzed. Therefore, in this paper, we propose alternate sources of information to use as descriptor for the classification task, which we denominate as density time-evolution pattern (D-TEP) and state density time-evolution pattern (SD-TEP). We explore the density of alive neighbors of each node, which is a continuous value, and compute feature vectors based on histograms of the TEPs. Our results show a significant improvement compared to previous studies at five synthetic network databases and also seven real world databases. Our proposed method demonstrates not only a good approach for pattern recognition in networks, but also shows great potential for other kinds of data, such as images.

Gonzalo Travieso, Joao Merenda, Odemir M. Bruno

Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based on its structure? This classification problem involves extracting relevant features from the network. Existing literature has proposed various methods that combine structural measurements and dynamical processes for feature extraction. In this study, we introduce a novel approach to characterize networks using statistics from random walks, which can be particularly informative about network properties. We present the employed statistical metrics and compare their performance on multiple datasets with other state-of-the-art feature extraction methods. Our results demonstrate that the proposed method is effective in many cases, often outperforming existing approaches, although some limitations are observed across certain datasets.

Leonardo Scabini, Kallil M. Zielinski, Emir Konuk et al.

Texture recognition has recently been dominated by ImageNet-pre-trained deep Convolutional Neural Networks (CNNs), with specialized modifications and feature engineering required to achieve state-of-the-art (SOTA) performance. However, although Vision Transformers (ViTs) were introduced a few years ago, little is known about their texture recognition ability. Therefore, in this work, we introduce VORTEX (ViTs with Orderless and Randomized Token Encodings for Texture Recognition), a novel method that enables the effective use of ViTs for texture analysis. VORTEX extracts multi-depth token embeddings from pre-trained ViT backbones and employs a lightweight module to aggregate hierarchical features and perform orderless encoding, obtaining a better image representation for texture recognition tasks. This approach allows seamless integration with any ViT with the common transformer architecture. Moreover, no fine-tuning of the backbone is performed, since they are used only as frozen feature extractors, and the features are fed to a linear SVM. We evaluate VORTEX on nine diverse texture datasets, demonstrating its ability to achieve or surpass SOTA performance in a variety of texture analysis scenarios. By bridging the gap between texture recognition with CNNs and transformer-based architectures, VORTEX paves the way for adopting emerging transformer foundation models. Furthermore, VORTEX demonstrates robust computational efficiency when coupled with ViT backbones compared to CNNs with similar costs. The method implementation and experimental scripts are publicly available in our online repository.

Leonardo Scabini, Andre Sacilotti, Kallil M. Zielinski et al.

Texture, a significant visual attribute in images, has been extensively investigated across various image recognition applications. Convolutional Neural Networks (CNNs), which have been successful in many computer vision tasks, are currently among the best texture analysis approaches. On the other hand, Vision Transformers (ViTs) have been surpassing the performance of CNNs on tasks such as object recognition, causing a paradigm shift in the field. However, ViTs have so far not been scrutinized for texture recognition, hindering a proper appreciation of their potential in this specific setting. For this reason, this work explores various pre-trained ViT architectures when transferred to tasks that rely on textures. We review 21 different ViT variants and perform an extensive evaluation and comparison with CNNs and hand-engineered models on several tasks, such as assessing robustness to changes in texture rotation, scale, and illumination, and distinguishing color textures, material textures, and texture attributes. The goal is to understand the potential and differences among these models when directly applied to texture recognition, using pre-trained ViTs primarily for feature extraction and employing linear classifiers for evaluation. We also evaluate their efficiency, which is one of the main drawbacks in contrast to other methods. Our results show that ViTs generally outperform both CNNs and hand-engineered models, especially when using stronger pre-training and tasks involving in-the-wild textures (images from the internet). We highlight the following promising models: ViT-B with DINO pre-training, BeiTv2, and the Swin architecture, as well as the EfficientFormer as a low-cost alternative. In terms of efficiency, although having a higher number of GFLOPs and parameters, ViT-B and BeiT(v2) can achieve a lower feature extraction time on GPUs compared to ResNet50.

Kallil M. Zielinski, Leonardo Scabini, Lucas C. Ribas et al.

In recent years, we have seen many advancements in wood species identification. Methods like DNA analysis, Near Infrared (NIR) spectroscopy, and Direct Analysis in Real Time (DART) mass spectrometry complement the long-established wood anatomical assessment of cell and tissue morphology. However, most of these methods have some limitations such as high costs, the need for skilled experts for data interpretation, and the lack of good datasets for professional reference. Therefore, most of these methods, and certainly the wood anatomical assessment, may benefit from tools based on Artificial Intelligence. In this paper, we apply two transfer learning techniques with Convolutional Neural Networks (CNNs) to a multi-view Congolese wood species dataset including sections from different orientations and viewed at different microscopic magnifications. We explore two feature extraction methods in detail, namely Global Average Pooling (GAP) and Random Encoding of Aggregated Deep Activation Maps (RADAM), for efficient and accurate wood species identification. Our results indicate superior accuracy on diverse datasets and anatomical sections, surpassing the results of other methods. Our proposal represents a significant advancement in wood species identification, offering a robust tool to support the conservation of forest ecosystems and promote sustainable forestry practices.

Leonardo F. S. Scabini, Odemir M. Bruno

Understanding the behavior of Artificial Neural Networks is one of the main topics in the field recently, as black-box approaches have become usual since the widespread of deep learning. Such high-dimensional models may manifest instabilities and weird properties that resemble complex systems. Therefore, we propose Complex Network (CN) techniques to analyze the structure and performance of fully connected neural networks. For that, we build a dataset with 4 thousand models and their respective CN properties. They are employed in a supervised classification setup considering four vision benchmarks. Each neural network is approached as a weighted and undirected graph of neurons and synapses, and centrality measures are computed after training. Results show that these measures are highly related to the network classification performance. We also propose the concept of Bag-Of-Neurons (BoN), a CN-based approach for finding topological signatures linking similar neurons. Results suggest that six neuronal types emerge in such networks, independently of the target domain, and are distributed differently according to classification accuracy. We also tackle specific CN properties related to performance, such as higher subgraph centrality on lower-performing models. Our findings suggest that CN properties play a critical role in the performance of fully connected neural networks, with topological patterns emerging independently on a wide range of models.

Lucas C. Ribas, Leonardo F. S. Scabini, Jarbas Joaci de Mesquita Sá Junior et al.

Texture is a visual attribute largely used in many problems of image analysis. Currently, many methods that use learning techniques have been proposed for texture discrimination, achieving improved performance over previous handcrafted methods. In this paper, we present a new approach that combines a learning technique and the Complex Network (CN) theory for texture analysis. This method takes advantage of the representation capacity of CN to model a texture image as a directed network and uses the topological information of vertices to train a randomized neural network. This neural network has a single hidden layer and uses a fast learning algorithm, which is able to learn local CN patterns for texture characterization. Thus, we use the weighs of the trained neural network to compose a feature vector. These feature vectors are evaluated in a classification experiment in four widely used image databases. Experimental results show a high classification performance of the proposed method when compared to other methods, indicating that our approach can be used in many image analysis problems.

Jeaneth Machicao, Odemir M. Bruno, Murilo S. Baptista

In previous work, the $k$-logistic map [Machicao and Bruno, Chaos, vol. 27, 053116 (2017)] was introduced as a transformation operating in the $k$ less significant digits of the Logistic map. It exploited the map's pseudo-randomness character that is present in its less significant digits. In this work, we comprehensively analyze the dynamical and ergodic aspects of this transformation, show its applicability to generic chaotic maps or sets, and its potential impact on enabling the creation of a cryptosystem that is fast, light and reliable.

Leonardo F. S. Scabini, Lucas C. Ribas, Odemir M. Bruno

Texture is one of the most-studied visual attribute for image characterization since the 1960s. However, most hand-crafted descriptors are monochromatic, focusing on the gray scale images and discarding the color information. In this context, this work focus on a new method for color texture analysis considering all color channels in a more intrinsic approach. Our proposal consists of modeling color images as directed complex networks that we named Spatio-Spectral Network (SSN). Its topology includes within-channel edges that cover spatial patterns throughout individual image color channels, while between-channel edges tackle spectral properties of channel pairs in an opponent fashion. Image descriptors are obtained through a concise topological characterization of the modeled network in a multiscale approach with radially symmetric neighborhoods. Experiments with four datasets cover several aspects of color-texture analysis, and results demonstrate that SSN overcomes all the compared literature methods, including known deep convolutional networks, and also has the most stable performance between datasets, achieving $98.5(\pm1.1)$ of average accuracy against $97.1(\pm1.3)$ of MCND and $96.8(\pm3.2)$ of AlexNet. Additionally, an experiment verifies the performance of the methods under different color spaces, where results show that SSN also has higher performance and robustness.

Jeaneth Machicao, Marcela Alves, Murilo S. Baptista et al.

This paper explores the deep-zoom properties of the chaotic k-logistic map, in order to propose an improved chaos-based cryptosystem. This map was shown to enhance the random features of the Logistic map, while at the same time reducing the predictability about its orbits. We incorporate its strengths to security into a previously published cryptosystem to provide an optimal pseudo-random number generator (PRNG) as its core operation. The result is a reliable method that does not have the weaknesses previously reported about the original cryptosystem.

Lucas C. Ribas, Wesley N. Goncalves, Odemir M. Bruno

Dynamic texture is a field of research that has gained considerable interest from computer vision community due to the explosive growth of multimedia databases. In addition, dynamic texture is present in a wide range of videos, which makes it very important in expert systems based on videos such as medical systems, traffic monitoring systems, forest fire detection system, among others. In this paper, a new method for dynamic texture characterization based on diffusion in directed networks is proposed. The dynamic texture is modeled as a directed network. The method consists in the analysis of the dynamic of this network after a series of graph cut transformations based on the edge weights. For each network transformation, the activity for each vertex is estimated. The activity is the relative frequency that one vertex is visited by random walks in balance. Then, texture descriptor is constructed by concatenating the activity histograms. The main contributions of this paper are the use of directed network modeling and diffusion in network to dynamic texture characterization. These tend to provide better performance in dynamic textures classification. Experiments with rotation and interference of the motion pattern were conducted in order to demonstrate the robustness of the method. The proposed approach is compared to other dynamic texture methods on two very well know dynamic texture database and on traffic condition classification, and outperform in most of the cases.

Lucas C. Ribas, Jarbas J. M. Sa Junior, Leonardo F. S. Scabini et al.

This paper presents a high discriminative texture analysis method based on the fusion of complex networks and randomized neural networks. In this approach, the input image is modeled as a complex networks and its topological properties as well as the image pixels are used to train randomized neural networks in order to create a signature that represents the deep characteristics of the texture. The results obtained surpassed the accuracies of many methods available in the literature. This performance demonstrates that our proposed approach opens a promising source of research, which consists of exploring the synergy of neural networks and complex networks in the texture analysis field.

Gisele H. B. Miranda, Jeaneth Machicao, Odemir M. Bruno

The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes with different theoretical approaches. We performed a study on the relationship between the shape architecture and the network topology constructed over the shape boundary. For that, we used a method for network modeling proposed in 2009. Firstly, together with curvature analysis, we evaluated the proposed approach for regular polygons. This way, it was possible to investigate how the network measurements vary according to some specific shape properties. Secondly, we evaluated the performance of the proposed shape descriptor in classification tasks for three datasets, accounting for both real-world and synthetic shapes. We demonstrated that not only degree related measurements are capable of distinguishing classes of objects. Yet, when using measurements that account for distinct properties of the network structure, the construction of the shape descriptor becomes more computationally efficient. Given the fact the network is dynamically constructed, the number of iterations can be reduced. The proposed approach accounts for a more robust set of structural measurements, that improved the discriminant power of the shape descriptors.

Mariane B. Neiva, Patrick Guidotti, Odemir M. Bruno

The main purpose of this paper is to propose a new preprocessing step in order to improve local feature descriptors and texture classification. Preprocessing is implemented by using transformations which help highlight salient features that play a significant role in texture recognition. We evaluate and compare four different competing methods: three different anisotropic diffusion methods including the classical anisotropic Perona-Malik diffusion and two subsequent regularizations of it and the application of a Gaussian kernel, which is the classical multiscale approach in texture analysis. The combination of the transformed images and the original ones are analyzed. The results show that the use of the preprocessing step does lead to improved texture recognition.

Mayra Z. Rodriguez, Cesar H. Comin, Dalcimar Casanova et al.

Many real-world systems can be studied in terms of pattern recognition tasks, so that proper use (and understanding) of machine learning methods in practical applications becomes essential. While a myriad of classification methods have been proposed, there is no consensus on which methods are more suitable for a given dataset. As a consequence, it is important to comprehensively compare methods in many possible scenarios. In this context, we performed a systematic comparison of 7 well-known clustering methods available in the R language. In order to account for the many possible variations of data, we considered artificial datasets with several tunable properties (number of classes, separation between classes, etc). In addition, we also evaluated the sensitivity of the clustering methods with regard to their parameters configuration. The results revealed that, when considering the default configurations of the adopted methods, the spectral approach usually outperformed the other clustering algorithms. We also found that the default configuration of the adopted implementations was not accurate. In these cases, a simple approach based on random selection of parameters values proved to be a good alternative to improve the performance. All in all, the reported approach provides subsidies guiding the choice of clustering algorithms.

João B. Florindo, Odemir M. Bruno

This work presents a novel descriptor for texture images based on fractal geometry and its application to image analysis. The descriptors are provided by estimating the triangular prism fractal dimension under different scales with a weight exponential parameter, followed by dimensionality reduction using Karhunen-Loève transform. The efficiency of the proposed descriptors is tested on two well-known texture data sets, that is, Brodatz and Vistex, both for classification and image retrieval. The novel method is also tested concerning invariances in situations when the textures are rotated or affected by Gaussian noise. The obtained results outperform other classical and state-of-the-art descriptors in the literature and demonstrate the power of the triangular descriptors in these tasks, suggesting their use in practical applications of image analysis based on texture features.

João B. Florindo, Odemir M. Bruno

This work presents a new procedure to extract features of grey-level texture images based on the discrete Schroedinger transform. This is a non-linear transform where the image is mapped as the initial probability distribution of a wave function and such distribution evolves in time following the Schroedinger equation from Quantum Mechanics. The features are provided by statistical moments of the distribution measured at different times. The proposed method is applied to the classification of three databases of textures used for benchmark and compared to other well-known texture descriptors in the literature, such as textons, local binary patterns, multifractals, among others. All of them are outperformed by the proposed method in terms of percentage of images correctly classified. The proposal is also applied to the identification of plant species using scanned images of leaves and again it outperforms other texture methods. A test with images affected by Gaussian and "salt \& pepper" noise is also carried out, also with the best performance achieved by the Schroedinger descriptors.

Jeaneth Machicao, Edilson A. Corrêa, Gisele H. B. Miranda et al.

The authorship attribution is a problem of considerable practical and technical interest. Several methods have been designed to infer the authorship of disputed documents in multiple contexts. While traditional statistical methods based solely on word counts and related measurements have provided a simple, yet effective solution in particular cases; they are prone to manipulation. Recently, texts have been successfully modeled as networks, where words are represented by nodes linked according to textual similarity measurements. Such models are useful to identify informative topological patterns for the authorship recognition task. However, there is no consensus on which measurements should be used. Thus, we proposed a novel method to characterize text networks, by considering both topological and dynamical aspects of networks. Using concepts and methods from cellular automata theory, we devised a strategy to grasp informative spatio-temporal patterns from this model. Our experiments revealed an outperformance over traditional analysis relying only on topological measurements. Remarkably, we have found a dependence of pre-processing steps (such as the lemmatization) on the obtained results, a feature that has mostly been disregarded in related works. The optimized results obtained here pave the way for a better characterization of textual networks.

Jeaneth Machicao, Jan M. Baetens, Anderson G. Marco et al.

Evidence of signatures associated with cryptographic modes of operation is established. Motivated by some analogies between cryptographic and dynamical systems, in particular with chaos theory, we propose an algorithm based on Lyapunov exponents of discrete dynamical systems to estimate the divergence among ciphertexts as the encryption algorithm is applied iteratively. The results allow to distinguish among six modes of operation, namely ECB, CBC, OFB, CFB, CTR and PCBC using DES, IDEA, TEA and XTEA block ciphers of 64 bits, as well as AES, RC6, Twofish, Seed, Serpent and Camellia block ciphers of 128 bits. Furthermore, the proposed methodology enables a classification of modes of operation of cryptographic systems according to their strength.

João B. Florindo, Odemir M. Bruno

This work proposes a texture descriptor based on fractal theory. The method is based on the Bouligand-Minkowski descriptors. We decompose the original image recursively into 4 equal parts. In each recursion step, we estimate the average and the deviation of the Bouligand-Minkowski descriptors computed over each part. Thus, we extract entropy features from both average and deviation. The proposed descriptors are provided by the concatenation of such measures. The method is tested in a classification experiment under well known datasets, that is, Brodatz and Vistex. The results demonstrate that the proposed technique achieves better results than classical and state-of-the-art texture descriptors, such as Gabor-wavelets and co-occurrence matrix.

Álvaro Gomez Z., João B. Florindo, Odemir M. Bruno

Texture analysis and classification remain as one of the biggest challenges for the field of computer vision and pattern recognition. On this matter, Gabor wavelets has proven to be a useful technique to characterize distinctive texture patterns. However, most of the approaches used to extract descriptors of the Gabor magnitude space usually fail in representing adequately the richness of detail present into a unique feature vector. In this paper, we propose a new method to enhance the Gabor wavelets process extracting a fractal signature of the magnitude spaces. Each signature is reduced using a canonical analysis function and concatenated to form the final feature vector. Experiments were conducted on several texture image databases to prove the power and effectiveness of the proposed method. Results obtained shown that this method outperforms other early proposed method, creating a more reliable technique for texture feature extraction.

André R. Backes, Odemir M. Bruno

Texture plays an important role in computer vision. It is one of the most important visual attributes used in image analysis, once it provides information about pixel organization at different regions of the image. This paper presents a novel approach for texture characterization, based on complexity analysis. The proposed approach expands the idea of the Mass-radius fractal dimension, a method originally developed for shape analysis, to a set of coordinates in 3D-space that represents the texture under analysis in a signature able to characterize efficiently different texture classes in terms of complexity. An experiment using images from the Brodatz album illustrates the method performance.

Lucas Assirati, Núbia R. da Silva, Lilian Berton et al.

In image processing, edge detection is a valuable tool to perform the extraction of features from an image. This detection reduces the amount of information to be processed, since the redundant information (considered less relevant) can be unconsidered. The technique of edge detection consists of determining the points of a digital image whose intensity changes sharply. This changes are due to the discontinuities of the orientation on a surface for example. A well known method of edge detection is the Difference of Gaussians (DoG). The method consists of subtracting two Gaussians, where a kernel has a standard deviation smaller than the previous one. The convolution between the subtraction of kernels and the input image results in the edge detection of this image. This paper introduces a method of extracting edges using DoG with kernels based on the q-Gaussian probability distribution, derived from the q-statistic proposed by Constantino Tsallis. To demonstrate the method's potential, we compare the introduced method with the traditional DoG using Gaussians kernels. The results showed that the proposed method can extract edges with more accurate details.

Ricardo Fabbri, Ivan N. Bastos, Francisco D. Moura Neto et al.

Several experimental measurements are expressed in the form of one-dimensional profiles, for which there is a scarcity of methodologies able to classify the pertinence of a given result to a specific group. The polarization curves that evaluate the corrosion kinetics of electrodes in corrosive media are an application where the behavior is chiefly analyzed from profiles. Polarization curves are indeed a classic method to determine the global kinetics of metallic electrodes, but the strong nonlinearity from different metals and alloys can overlap and the discrimination becomes a challenging problem. Moreover, even finding a typical curve from replicated tests requires subjective judgement. In this paper we used the so-called multi-q approach based on the Tsallis statistics in a classification engine to separate multiple polarization curve profiles of two stainless steels. We collected 48 experimental polarization curves in aqueous chloride medium of two stainless steel types, with different resistance against localized corrosion. Multi-q pattern analysis was then carried out on a wide potential range, from cathodic up to anodic regions. An excellent classification rate was obtained, at a success rate of 90%, 80%, and 83% for low (cathodic), high (anodic), and both potential ranges, respectively, using only 2% of the original profile data. These results show the potential of the proposed approach towards efficient, robust, systematic and automatic classification of highly non-linear profile curves.

João B. Florindo, Mariana S. Sikora, Ernesto C. Pereira et al.

This work proposes the application of fractal descriptors to the analysis of nanoscale materials under different experimental conditions. We obtain descriptors for images from the sample applying a multiscale transform to the calculation of fractal dimension of a surface map of such image. Particularly, we have used the}Bouligand-Minkowski fractal dimension. We applied these descriptors to discriminate between two titanium oxide films prepared under different experimental conditions. Results demonstrate the discrimination power of proposed descriptors in such kind of application.

André R. Backes, João B. Florindo, Odemir M. Bruno

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from the shape by applying a multiscale approach to the calculus of the fractal dimension of that shape. The fractal dimension is obtained by the application of the curvature scale-space technique to the original shape. Through the application of a multiscale transform to the dimension calculus, it is obtained a set of numbers (descriptors) capable of describing with a high precision the shape in analysis. The obtained descriptors are validated in a classification process. The results demonstrate that the novel technique provides descriptors highly reliable, confirming the precision of the proposed method.