Fractal Topological Analysis for 2D Binary Digital Images

Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological model of them, called Homological Spanning Forest (HSF, for short). Defined at interpixel level, this set of two trees allows to topologically describe the (black and white) connected component distribution within the image with regards to the relationship “to be surrounded by”. This distribution is condensed into a rooted tree, such that its nodes are connected components determined by some special sub-trees of the previous HSF and the levels of the tree specify the degree of nesting of each connected component. We ask for topological auto-similarity by comparing this topological description of the whole image with a regular rooted tree pattern. Such an analysis can be used to directly quantify some characteristics of biomedical images (e.g. cells samples or clinical images) that are not so noticeable when using geometrical approaches.Ministerio de Economía y Competitividad TEC2016-77785-PMinisterio de Economía y Competitividad MTM2016-81030-

Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.JCM: Higher Education Funding Council for England and the UK National Institute for Health Research, University College London, Biomedical Research Centre; GC: NIHR BRC University College London. DAB: Intramural research program, National Institutes of Health

Closed Contour Fractal Dimension Estimation by the Fourier Transform

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, it is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e. g., Bouligand-Minkowski, box-couting 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

Fractal descriptors based on the probability dimension: a texture analysis and classification approach

In this work, we propose a novel technique for obtaining descriptors of gray-level texture images. The descriptors are provided by applying a multiscale transform to the fractal dimension of the image estimated through the probability (Voss) method. The effectiveness of the descriptors is verified in a classification task using benchmark over texture datasets. The results obtained demonstrate the efficiency of the proposed method as a tool for the description and discrimination of texture images.Comment: 7 pages, 6 figures. arXiv admin note: text overlap with arXiv:1205.282

Characterising the tumour morphological response to therapeutic intervention:an ex vivo model

In cancer, morphological assessment of histological tissue samples is a fundamental part of both diagnosis and prognosis. Image analysis offers opportunities to support that assessment through quantitative metrics of morphology. Generally, morphometric analysis is carried out on two dimensional tissue section data and so only represents a small fraction of any tumour. We present a novel application of three-dimensional (3D) morphometrics for 3D imaging data obtained from tumours grown in a culture model. Minkowski functionals, a set of measures that characterise geometry and topology in n-dimensional space, are used to quantify tumour topology in the absence of and in response to therapeutic intervention. These measures are used to stratify the morphological response of tumours to therapeutic intervention. Breast tumours are characterised by estrogen receptor (ER) status, human epidermal growth factor receptor (HER)2 status and tumour grade. Previously, we have shown that ER status is associated with tumour volume in response to tamoxifen treatment ex vivo. Here, HER2 status is found to predict the changes in morphology other than volume as a result of tamoxifen treatment ex vivo. Finally, we show the extent to which Minkowski functionals might be used to predict tumour grade.Minkowski functionals are generalisable to any 3D data set, including in vivo and cellular systems. This quantitative topological analysis can provide a valuable link among biomarkers, drug intervention and tumour morphology that is complementary to existing, non-morphological measures of tumour response to intervention and could ultimately inform patient treatment

Deep Cellular Recurrent Neural Architecture for Efficient Multidimensional Time-Series Data Processing

Efficient processing of time series data is a fundamental yet challenging problem in pattern recognition. Though recent developments in machine learning and deep learning have enabled remarkable improvements in processing large scale datasets in many application domains, most are designed and regulated to handle inputs that are static in time. Many real-world data, such as in biomedical, surveillance and security, financial, manufacturing and engineering applications, are rarely static in time, and demand models able to recognize patterns in both space and time. Current machine learning (ML) and deep learning (DL) models adapted for time series processing tend to grow in complexity and size to accommodate the additional dimensionality of time. Specifically, the biologically inspired learning based models known as artificial neural networks that have shown extraordinary success in pattern recognition, tend to grow prohibitively large and cumbersome in the presence of large scale multi-dimensional time series biomedical data such as EEG. Consequently, this work aims to develop representative ML and DL models for robust and efficient large scale time series processing. First, we design a novel ML pipeline with efficient feature engineering to process a large scale multi-channel scalp EEG dataset for automated detection of epileptic seizures. With the use of a sophisticated yet computationally efficient time-frequency analysis technique known as harmonic wavelet packet transform and an efficient self-similarity computation based on fractal dimension, we achieve state-of-the-art performance for automated seizure detection in EEG data. Subsequently, we investigate the development of a novel efficient deep recurrent learning model for large scale time series processing. For this, we first study the functionality and training of a biologically inspired neural network architecture known as cellular simultaneous recurrent neural network (CSRN). We obtain a generalization of this network for multiple topological image processing tasks and investigate the learning efficacy of the complex cellular architecture using several state-of-the-art training methods. Finally, we develop a novel deep cellular recurrent neural network (CDRNN) architecture based on the biologically inspired distributed processing used in CSRN for processing time series data. The proposed DCRNN leverages the cellular recurrent architecture to promote extensive weight sharing and efficient, individualized, synchronous processing of multi-source time series data. Experiments on a large scale multi-channel scalp EEG, and a machine fault detection dataset show that the proposed DCRNN offers state-of-the-art recognition performance while using substantially fewer trainable recurrent units

In vivo morphometric and mechanical characterization of trabecular bone from high resolution magnetic resonance imaging

La osteoporosis es una enfermedad ósea que se manifiesta con una menor densidad ósea y el deterioro de la arquitectura del hueso esponjoso. Ambos factores aumentan la fragilidad ósea y el riesgo de sufrir fracturas óseas, especialmente en mujeres, donde existe una alta prevalencia. El diagnóstico actual de la osteoporosis se basa en la cuantificación de la densidad mineral ósea (DMO) mediante la técnica de absorciometría dual de rayos X (DXA). Sin embargo, la DMO no puede considerarse de manera aislada para la evaluación del riesgo de fractura o los efectos terapéuticos. Existen otros factores, tales como la disposición microestructural de las trabéculas y sus características que es necesario tener en cuenta para determinar la calidad del hueso y evaluar de manera más directa el riesgo de fractura. Los avances técnicos de las modalidades de imagen médica, como la tomografía computarizada multidetector (MDCT), la tomografía computarizada periférica cuantitativa (HR-pQCT) y la resonancia magnética (RM) han permitido la adquisición in vivo con resoluciones espaciales elevadas. La estructura del hueso trabecular puede observarse con un buen detalle empleando estas técnicas. En particular, el uso de los equipos de RM de 3 Teslas (T) ha permitido la adquisición con resoluciones espaciales muy altas. Además, el buen contraste entre hueso y médula que proporcionan las imágenes de RM, así como la utilización de radiaciones no ionizantes sitúan a la RM como una técnica muy adecuada para la caracterización in vivo de hueso trabecular en la enfermedad de la osteoporosis. En la presente tesis se proponen nuevos desarrollos metodológicos para la caracterización morfométrica y mecánica del hueso trabecular en tres dimensiones (3D) y se aplican a adquisiciones de RM de 3T con alta resolución espacial. El análisis morfométrico está compuesto por diferentes algoritmos diseñados para cuantificar la morfología, la complejidad, la topología y los parámetros de anisotropía del tejido trabecular. En cuanto a la caracterización mecánica, se desarrollaron nuevos métodos que permiten la simulación automatizada de la estructura del hueso trabecular en condiciones de compresión y el cálculo del módulo de elasticidad. La metodología desarrollada se ha aplicado a una población de sujetos sanos con el fin de obtener los valores de normalidad del hueso esponjoso. Los algoritmos se han aplicado también a una población de pacientes con osteoporosis con el fin de cuantificar las variaciones de los parámetros en la enfermedad y evaluar las diferencias con los resultados obtenidos en un grupo de sujetos sanos con edad similar.Los desarrollos metodológicos propuestos y las aplicaciones clínicas proporcionan resultados satisfactorios, presentando los parámetros una alta sensibilidad a variaciones de la estructura trabecular principalmente influenciadas por el sexo y el estado de enfermedad. Por otra parte, los métodos presentan elevada reproducibilidad y precisión en la cuantificación de los valores morfométricos y mecánicos. Estos resultados refuerzan el uso de los parámetros presentados como posibles biomarcadores de imagen en la enfermedad de la osteoporosis.Alberich Bayarri, Á. (2010). In vivo morphometric and mechanical characterization of trabecular bone from high resolution magnetic resonance imaging [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8981Palanci

Application of Fractal Dimension in Industry Practice

Today, industrial production lines commonly use off-line and automatic on-line quality monitoring and control. Monitoring and control units analyse data from a production process, and analysis should be able to obtain reliable information that correspond with the character of the data obtained. The character of the data set obtained from production processes or from products can be highly structured in all industrial areas. Structured surface, complex time series (topologically one dimensional signals), difficulty to describe dividing curves are much more common than it can be expected. For this kind of data set, a powerful tool for analysis of complexity —fractal geometry (especially a fractal dimension) should be used. The fractal dimension with a combination of statistical tools is an interesting and powerful tool for complex data quantification, for tracing the source of poor quality, production optimization and investigating the source of instability of production process subsystems in industrial applications. The methodology for evaluation of complex and irregular data was developed and applied in industrial practice. This methodology searches appropriated parameters for a complex evaluation of data. Only the chosen parameters are used for a complete analysis of the data in order to reduce processing time

Enhanced Parallel Generation of Tree Structures for the Recognition of 3D Images

Segmentations of a digital object based on a connectivity criterion at n-xel or sub-n-xel level are useful tools in image topological analysis and recognition. Working with cell complex analogous of digital objects, an example of this kind of segmentation is that obtained from the combinatorial representation so called Homological Spanning Forest (HSF, for short) which, informally, classifies the cells of the complex as belonging to regions containing the maximal number of cells sharing the same homological (algebraic homology with coefficient in a field) information. We design here a parallel method for computing a HSF (using homology with coefficients in Z/2Z) of a 3D digital object. If this object is included in a 3D image of m1 × m2 × m3 voxels, its theoretical time complexity order is near O(log(m1 + m2 + m3)), under the assumption that a processing element is available for each voxel. A prototype implementation validating our results has been written and several synthetic, random and medical tridimensional images have been used for testing. The experiments allow us to assert that the number of iterations in which the homological information is found varies only to a small extent from the theoretical computational time.Ministerio de Economía y Competitividad MTM2016-81030-