João Batista Florindo

A comparative study on multiscale fractal dimension descriptors

Fractal theory presents a large number of applications to image and signal analysis. Although the fractal dimension can be used as an image object descriptor, a multiscale approach, such as multiscale fractal dimension (MFD), increases the amount of information extracted from an object. MFD provides a curve which describes object complexity along the scale. However, this curve presents much redundant information, which could be discarded without loss in performance. Thus, it is necessary the use of a descriptor technique to analyze this curve and also to reduce the dimensionality of these data by selecting its meaningful descriptors. This paper shows a comparative study among different techniques for MFD descriptors generation. It compares the use of well-known and state-of-the-art descriptors, such as Fourier, Wavelet, Polynomial Approximation (PA), Functional Data Analysis (FDA), Principal Component Analysis (PCA), Symbolic Aggregate Approximation (SAX), kernel PCA, Independent Component Analysis (ICA), geometrical and statistical features. The descriptors are evaluated in a classification experiment using Linear Discriminant Analysis over the descriptors computed from MFD curves from two data sets: generic shapes and rotated fish contours. Results indicate that PCA, FDA, PA and Wavelet Approximation provide the best MFD descriptors for recognition and classification tasks.

Gabor wavelets combined with volumetric fractal dimension applied to texture analysis

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.

Texture analysis by multi-resolution fractal descriptors

This work proposes a novel texture descriptor based on fractal theory. The method is based on the Bouligand-Minkowski descriptors. We decompose the original image recursively into four 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 concatenating such measures. The method is tested in a classification experiment under well known datasets, that is, Brodatz and Vistex. The results demonstrate that the novel technique achieves better results than classical and state-of-the-art texture descriptors, such as Local Binary Patterns, Gabor-wavelets and co-occurrence matrix.

Characterization of nanostructured material images using fractal descriptors

This work presents a methodology to the morphology analysis and characterization of nanostructured material images acquired from FEG-SEM (Field Emission Gun-Scanning Electron Microscopy) technique. The metrics were extracted from the image texture (mathematical surface) by the volumetric fractal descriptors, a methodology based on the Bouligand–Minkowski fractal dimension, which considers the properties of the Minkowski dilation of the surface points. An experiment with galvanostatic anodic titanium oxide samples prepared in oxalyc acid solution using different conditions of applied current, oxalyc acid concentration and solution temperature was performed. The results demonstrate that the approach is capable of characterizing complex morphology characteristics such as those present in the anodic titanium oxide.

ENHANCING MULTISCALE FRACTAL DESCRIPTORS USING FUNCTIONAL DATA ANALYSIS

This work presents a novel approach in order to increase the recognition power of Multiscale Fractal Dimension (MFD) techniques, when applied to image classification. The proposal uses Functional Data Analysis (FDA) with the aim of enhancing the MFD technique precision achieving a more representative descriptors vector, capable of recognizing and characterizing more precisely objects in an image. FDA is applied to signatures extracted by using the Bouligand–Minkowsky MFD technique in the generation of a descriptors vector from them. For the evaluation of the obtained improvement, an experiment using two datasets of objects was carried out. A dataset was used of characters shapes (26 characters of the Latin alphabet) carrying different levels of controlled noise and a dataset of fish images contours. A comparison with the use of the well-known methods of Fourier and wavelets descriptors was performed with the aim of verifying the performance of FDA method. The descriptor vectors were submitted to Linear Discriminant Analysis (LDA) classification method and we compared the correctness rate in the classification process among the descriptors methods. The results demonstrate that FDA overcomes the literature methods (Fourier and wavelets) in the processing of information extracted from the MFD signature. In this way, the proposed method can be considered as an interesting choice for pattern recognition and image classification using fractal analysis.

Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors

The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification.

Brachiaria species identification using imaging techniques based on fractal descriptors

Abstract The use of a rapid and accurate method in diagnosis and classification of species and/or cultivars of forage has practical relevance, scientific and trade in various areas of study, since it has broad representation in grazing from tropical regions. Nowadays it occupies about 90% of the grazing area along Brazil and, besides the grazing areas to feed ruminants, Brachiaria also corresponds to about 80% of seeds being traded in all the world, bringing a large amount of money to Brazil. To identify species and/or cultivars of this genus is of fundamental importance in the fields that produce seeds, to ensure varietal purity and the effectiveness of improvement programs. Thus, leaf samples of fodder plant species Brachiaria were previously identified, collected and scanned to be treated by means of artificial vision to make the database and be used in subsequent classifications. Forage crops used were: Brachiaria decumbens cv. IPEAN; Brachiaria ruziziensis Germain & Evrard; Brachiaria brizantha (Hochst. ex. A. Rich.) Stapf; Brachiaria arrecta (Hack.) Stent. and Brachiaria spp. The images were analyzed by the fractal descriptors method, where a set of measures are obtained from the values of the fractal dimension at different scales. Therefore such values are used as inputs for a state-of-the-art classifier, the Support Vector Machine, which finally discriminates the images according to the respective species. The proposed method outperforms other state-of-the-art image analysis methods and makes possible the correct prediction of species in more than 93% of the samples. Such remarkable result is consequence of the better suitability of representing complex structures like those arising in the plant leaves by measures of complexity from fractal geometry. Finally, this high correctness rate suggests that the fractal method is an important tool to help the botanist.

Fractal descriptors in the Fourier domain applied to color texture analysis.

The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists of two steps. First, we apply a linear transform in the color space of the image aiming at highlighting spatial structuring relations among the color of pixels. Second, we apply a multiscale approach to the calculus of fractal dimension based on Fourier transform. From this multiscale operation, we extract the descriptors that are used to discriminate the texture represented in digital images. The accuracy of the method is verified in the classification of two color texture datasets, by comparing the performance of the proposed technique to other classical and state-of-the-art methods for color texture analysis. The results showed an advantage of almost 3% of the proposed technique over the second best approach.

Texture analysis using fractal descriptors estimated by the mutual interference of color channels

Fractal descriptors are used to describe color textures.Spatial structure and color distribution are analyzed without separating the image into channels.The volumes of the dilated structure express the level of details at each scale based on the intensity/color distribution.The descriptors combine the efficiency of fractals in describing complex structures with the richness of color analysis.The method outperformed other approaches whose effectiveness is widely attested in studies on texture analysis methods. This work presents a method for color texture analysis based on fractal geometry. The method is based on its predecessor 4 and consists of mapping each color channel onto a surface and dilating such surface by spheres with a variable radius. The descriptors are obtained from the relation between the volumes of the dilated surfaces and the dilation radii. The dilation process creates a mutual interference among the color channels. The proposed descriptors measure the degree of such interference as well as the complexity of pixel intensity arrangements. This combination provides a robust and precise texture description. The efficiency of the method is assessed in a classification task of well-known texture data sets and the results demonstrate that it outperforms the best approaches described in the literature.

Closed contour fractal dimension estimation by the Fourier transform

Abstract This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand–Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.