Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

Bayesian Estimation of the Multifractality Parameter for Image Texture Using a Whittle Approximation

International audienceTexture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a challenge. This is due in the main to the fact that current estimation procedures consist of performing linear regressions across frequency scales of the 2D dyadic wavelet transform, for which only a few such scales are computable for images. The strongly non-Gaussian nature of multifractal processes, combined with their complicated dependence structure, makes it difficult to develop suitable models for parameter estimation. Here, we propose a Bayesian procedure that addresses the difficulties in the estimation of the multifractality parameter. The originality of the procedure is threefold. The construction of a generic semiparametric statistical model for the logarithm of wavelet leaders; the formulation of Bayesian estimators that are associated with this model and the set of parameter values admitted by multifractal theory; the exploitation of a suitable Whittle approximation within the Bayesian model which enables the otherwise infeasible evaluation of the posterior distribution associated with the model. Performance is assessed numerically for several 2D multifractal processes, for several image sizes and a large range of process parameters. The procedure yields significant benefits over current benchmark estimators in terms of estimation performance and ability to discriminate between the two most commonly used classes of multifractal process models. The gains in performance are particularly pronounced for small image sizes, notably enabling for the first time the analysis of image patches as small as 64 × 64 pixels

Function spaces vs. Scaling functions: Some issues in image classification

Criteria based on the computation of fractal dimensions have been used in order to perform image analysis and classification; we show that such criteria often amount to deter- mine the regularity of the image in some classes of function spaces, and that looking for richer criteria naturally leads to the introduction of new classes of function spaces. We will investigate the properties of some of these classes, and show which type of additional information they yield for the initial image

Computer-aided detection and diagnosis of breast cancer in 2D and 3D medical imaging through multifractal analysis

This Thesis describes the research work performed in the scope of a doctoral research program and presents its conclusions and contributions. The research activities were carried on in the industry with Siemens S.A. Healthcare Sector, in integration with a research team. Siemens S.A. Healthcare Sector is one of the world biggest suppliers of products, services and complete solutions in the medical sector. The company offers a wide selection of diagnostic and therapeutic equipment and information systems. Siemens products for medical imaging and in vivo diagnostics include: ultrasound, computer tomography, mammography, digital breast tomosynthesis, magnetic resonance, equipment to angiography and coronary angiography, nuclear imaging, and many others. Siemens has a vast experience in Healthcare and at the beginning of this project it was strategically interested in solutions to improve the detection of Breast Cancer, to increase its competitiveness in the sector. The company owns several patents related with self-similarity analysis, which formed the background of this Thesis. Furthermore, Siemens intended to explore commercially the computer- aided automatic detection and diagnosis eld for portfolio integration. Therefore, with the high knowledge acquired by University of Beira Interior in this area together with this Thesis, will allow Siemens to apply the most recent scienti c progress in the detection of the breast cancer, and it is foreseeable that together we can develop a new technology with high potential. The project resulted in the submission of two invention disclosures for evaluation in Siemens A.G., two articles published in peer-reviewed journals indexed in ISI Science Citation Index, two other articles submitted in peer-reviewed journals, and several international conference papers. This work on computer-aided-diagnosis in breast led to innovative software and novel processes of research and development, for which the project received the Siemens Innovation Award in 2012. It was very rewarding to carry on such technological and innovative project in a socially sensitive area as Breast Cancer.No cancro da mama a deteção precoce e o diagnóstico correto são de extrema importância na prescrição terapêutica e caz e e ciente, que potencie o aumento da taxa de sobrevivência à doença. A teoria multifractal foi inicialmente introduzida no contexto da análise de sinal e a sua utilidade foi demonstrada na descrição de comportamentos siológicos de bio-sinais e até na deteção e predição de patologias. Nesta Tese, três métodos multifractais foram estendidos para imagens bi-dimensionais (2D) e comparados na deteção de microcalci cações em mamogramas. Um destes métodos foi também adaptado para a classi cação de massas da mama, em cortes transversais 2D obtidos por ressonância magnética (RM) de mama, em grupos de massas provavelmente benignas e com suspeição de malignidade. Um novo método de análise multifractal usando a lacunaridade tri-dimensional (3D) foi proposto para classi cação de massas da mama em imagens volumétricas 3D de RM de mama. A análise multifractal revelou diferenças na complexidade subjacente às localizações das microcalci cações em relação aos tecidos normais, permitindo uma boa exatidão da sua deteção em mamogramas. Adicionalmente, foram extraídas por análise multifractal características dos tecidos que permitiram identi car os casos tipicamente recomendados para biópsia em imagens 2D de RM de mama. A análise multifractal 3D foi e caz na classi cação de lesões mamárias benignas e malignas em imagens 3D de RM de mama. Este método foi mais exato para esta classi cação do que o método 2D ou o método padrão de análise de contraste cinético tumoral. Em conclusão, a análise multifractal fornece informação útil para deteção auxiliada por computador em mamogra a e diagnóstico auxiliado por computador em imagens 2D e 3D de RM de mama, tendo o potencial de complementar a interpretação dos radiologistas

Extending multifractal analysis to negative regularity: p-exponents and p-leaders

International audienceScale invariance is a widely used concept to analyze real-world data from many different applications and multifractal analysis has become the standard corresponding signal processing tool. It characterizes data by describing globally and geometrically the fluctuations of local regularity, usually measured by means of the Hölder exponent. A major limitation of the current procedure is that it applies only to locally bounded functions or signals, i.e., to signals with positive regularity. The present contribution proposes to characterize local regularity with a new quantity, the p-exponent, that permits negative regularity in data, a widely observed property in real-world data. Relations to Hölder exponents are detailed and a corresponding p-leader multifractal formalism is devised and shown at work on synthetic multifractal processes, representative of a class of models often used in applications. We formulate a conjecture regarding the equivalence between Hölder and p-exponents for a subclass of processes. Even when Hölder and p-exponents coincide, the p-leader formalism is shown to achieve better estimation performance

Bread crumb classification using fractal and multifractal features

Adequate image descriptors are fundamental in image classification and object recognition. Main requirements for image features are robustness and low dimensionality which would lead to low classification errors in a variety of situations and with a reasonable computational cost. In this context, the identification of materials poses a significant challenge, since typical (geometric and/or differential) feature extraction methods are not robust enough. Texture features based on Fourier or wavelet transforms, on the other hand, do withstand geometric and illumination variations, but tend to require a high amount of descriptors to perform adequately. Recently, the theory of fractal sets has shown to provide local image features that are both robust and low-dimensional. In this work we apply fractal and multifractal feature extraction techniques for bread crumb classification based on colour scans of slices of different bread types. Preliminary results show that fractal based classification is able to distinguish different bread crumbs with very high accuracy.Fil: Baravalle, Rodrigo Guillermo. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; ArgentinaFil: Delrieux, Claudio Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Investigación en Ingeniería Eléctrica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Electrica y de Computadoras; ArgentinaFil: Gómez, Juan Carlos. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y Sistemas; Argentin

Ultrasonic characterization and multiscale analysis for the evaluation of dental implant stability: a sensitivity study Biomedical Signal Processing and Control 42 (2018) 37-44

International audienceWith the aim of surgical success, the evaluation of dental implant long-term stability is an important task for dentists. About that, the complexity of the newly formed bone and the complex boundary conditions at the bone-implant interface induce the main difficulties. In this context, for the quantitative evaluation of primary and secondary stabilities of dental implants, ultrasound based techniques have already been proven to be effective. The microstructure, the mechanical properties and the geometry of the bone-implant system affect the ultrasonic response. The aim of this work is to extract relevant information about primary stability from the complex ultrasonic signal obtained from a probe screwed to the implant. To do this, signal processing based on multiscale analysis has been used. The comparison between experimental and numerical results has been carried out, and a correlation has been observed between the multifractal signature and the stability. Furthermore, a sensitivity study has shown that the variation of certain parameters (i.e. central frequency and trabecular bone density) does not lead to a change in the response

A survey on prescription of multifractal behavior

International audienceMultifractal behavior has been identified and mathematically established for large classes of functions, stochastic processes and measures. Multifractality has also been observed on many data coming from Geophysics, turbulence, Physics, Biology, to name a few. Developing mathematical models whose scaling and multifractal properties fit those measured on data is thus an important issue. This raises several still unsolved theoretical questions about the prescription of multifractality (i.e. how to build mathematical models with a singularity spectrum known in advance), typical behavior in function spaces, and existence of solutions to PDEs or SPDEs with possible multifractal behavior. In this survey, we gather some of the latest results in this area. Dedicated to Alain Arnéodo, pioneer in the development of wavelet tools for data analysis