Application of Fractal and Wavelets in Microcalcification Detection

Breast cancer has been recognized as one or the most frequent, malignant tumors in women, clustered microcalcifications in mammogram images has been widely recognized as an early sign of breast cancer. This work is devote to review the application of Fractal and Wavelets in microcalcifications detection

Texture descriptor combining fractal dimension and artificial crawlers

Texture is an important visual attribute used to describe images. There are many methods available for texture analysis. However, they do not capture the details richness of the image surface. In this paper, we propose a new method to describe textures using the artificial crawler model. This model assumes that each agent can interact with the environment and each other. Since this swarm system alone does not achieve a good discrimination, we developed a new method to increase the discriminatory power of artificial crawlers, together with the fractal dimension theory. Here, we estimated the fractal dimension by the Bouligand-Minkowski method due to its precision in quantifying structural properties of images. We validate our method on two texture datasets and the experimental results reveal that our method leads to highly discriminative textural features. The results indicate that our method can be used in different texture applications.Comment: 12 pages 9 figures. Paper in press: Physica A: Statistical Mechanics and its Application

Three-dimensional multifractal analysis of trabecular bone under clinical computed tomography

Purpose: An adequate understanding of bone structural properties is critical for predicting fragility conditions caused by diseases such as osteoporosis, and in gauging the success of fracture prevention treatments. In this work we aim to develop multiresolution image analysis techniques to extrapolate high-resolution images predictive power to images taken in clinical conditions. Methods: We performed multifractal analysis (MFA) on a set of 17 ex vivo human vertebrae clinical CT scans. The vertebræ failure loads (FFailure) were experimentally measured. We combined bone mineral density (BMD) with different multifractal dimensions, and BMD with multiresolution statistics (e.g., skewness, kurtosis) of MFA curves, to obtain linear models to predict FFailure. Furthermore we obtained short- and long-term precisions from simulated in vivo scans, using a clinical CT scanner. Ground-truth data - high-resolution images - were obtained with a High-Resolution Peripheral Quantitative Computed Tomography (HRpQCT) scanner. Results: At the same level of detail, BMD combined with traditional multifractal descriptors (Lipschitz-Hölder exponents), and BMD with monofractal features showed similar prediction powers in predicting FFailure (87%, adj. R2). However, at different levels of details, the prediction power of BMD with multifractal features raises to 92% (adj. R2) of FFailure. Our main finding is that a simpler but slightly less accurate model, combining BMD and the skewness of the resulting multifractal curves, predicts 90% (adj. R2) of FFailure. Conclusions: Compared to monofractal and standard bone measures, multifractal analysis captured key insights in the conditions leading to FFailure. Instead of raw multifractal descriptors, the statistics of multifractal curves can be used in several other contexts, facilitating further research.Fil: Baravalle, Rodrigo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Thomsen, Felix Sebastian Leo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur; ArgentinaFil: Delrieux, Claudio Augusto. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lu, Yongtao. Dalian University of Technology; ChinaFil: Gómez, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Stošić, Borko. Universidade Federal Rural Pernambuco; BrasilFil: Stošić, Tatijana. Universidade Federal Rural Pernambuco; Brasi

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 in two steps. In the first, we apply a linear transform in the color space of the image aiming at highlighting spatial structuring relations among the color of pixels. In a second moment, we apply a multiscale approach to the calculus of fractal dimension based on Fourier transform. From this multiscale operation, we extract the descriptors 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.Comment: Chaos, Volume 21, Issue 4, 201

Toward reduction of artifacts in fused images

Most fusion satellite image methodologies at pixel-level introduce false spatial details, i.e.artifacts, in the resulting fusedimages. In many cases, these artifacts appears because image fusion methods do not consider the differences in roughness or textural characteristics between different land covers. They only consider the digital values associated with single pixels. This effect increases as the spatial resolution image increases. To minimize this problem, we propose a new paradigm based on local measurements of the fractal dimension (FD). Fractal dimension maps (FDMs) are generated for each of the source images (panchromatic and each band of the multi-spectral images) with the box-counting algorithm and by applying a windowing process. The average of source image FDMs, previously indexed between 0 and 1, has been used for discrimination of different land covers present in satellite images. This paradigm has been applied through the fusion methodology based on the discrete wavelet transform (DWT), using the à trous algorithm (WAT). Two different scenes registered by optical sensors on board FORMOSAT-2 and IKONOS satellites were used to study the behaviour of the proposed methodology. The implementation of this approach, using the WAT method, allows adapting the fusion process to the roughness and shape of the regions present in the image to be fused. This improves the quality of the fusedimages and their classification results when compared with the original WAT metho