On Invariance, Equivariance, Correlation and Convolution of Spherical Harmonic Representations for Scalar and Vectorial Data

The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation and practical implementation of SH representations, summarizing works on rotation invariant and equivariant features, as well as convolutions and exact correlations of signals on spheres. In extension, these methods are then generalized from scalar SH representations to Vectorial Harmonics (VH), providing the same capabilities for 3d vector fields on spheresComment: 106 pages, tech repor

Variable illumination and invariant features for detecting and classifying varnish defects

This work presents a method to detect and classify varnish defects on wood surfaces. Since these defects are only partially visible under certain illumination directions, one image doesn\u27t provide enough information for a recognition task. A classification requires inspecting the surface under different illumination directions, which results in image series. The information is distributed along this series and can be extracted by merging the knowledge about the defect shape and light direction

Generalizable automated pixel-level structural segmentation of medical and biological data

Over the years, the rapid expansion in imaging techniques and equipments has driven the demand for more automation in handling large medical and biological data sets. A wealth of approaches have been suggested as optimal solutions for their respective imaging types. These solutions span various image resolutions, modalities and contrast (staining) mechanisms. Few approaches generalise well across multiple image types, contrasts or resolution. This thesis proposes an automated pixel-level framework that addresses 2D, 2D+t and 3D structural segmentation in a more generalizable manner, yet has enough adaptability to address a number of specific image modalities, spanning retinal funduscopy, sequential fluorescein angiography and two-photon microscopy. The pixel-level segmentation scheme involves: i ) constructing a phase-invariant orientation field of the local spatial neighbourhood; ii ) combining local feature maps with intensity-based measures in a structural patch context; iii ) using a complex supervised learning process to interpret the combination of all the elements in the patch in order to reach a classification decision. This has the advantage of transferability from retinal blood vessels in 2D to neural structures in 3D. To process the temporal components in non-standard 2D+t retinal angiography sequences, we first introduce a co-registration procedure: at the pairwise level, we combine projective RANSAC with a quadratic homography transformation to map the coordinate systems between any two frames. At the joint level, we construct a hierarchical approach in order for each individual frame to be registered to the global reference intra- and inter- sequence(s). We then take a non-training approach that searches in both the spatial neighbourhood of each pixel and the filter output across varying scales to locate and link microvascular centrelines to (sub-) pixel accuracy. In essence, this \link while extract" piece-wise segmentation approach combines the local phase-invariant orientation field information with additional local phase estimates to obtain a soft classification of the centreline (sub-) pixel locations. Unlike retinal segmentation problems where vasculature is the main focus, 3D neural segmentation requires additional exibility, allowing a variety of structures of anatomical importance yet with different geometric properties to be differentiated both from the background and against other structures. Notably, cellular structures, such as Purkinje cells, neural dendrites and interneurons, all display certain elongation along their medial axes, yet each class has a characteristic shape captured by an orientation field that distinguishes it from other structures. To take this into consideration, we introduce a 5D orientation mapping to capture these orientation properties. This mapping is incorporated into the local feature map description prior to a learning machine. Extensive performance evaluations and validation of each of the techniques presented in this thesis is carried out. For retinal fundus images, we compute Receiver Operating Characteristic (ROC) curves on existing public databases (DRIVE & STARE) to assess and compare our algorithms with other benchmark methods. For 2D+t retinal angiography sequences, we compute the error metrics ("Centreline Error") of our scheme with other benchmark methods. For microscopic cortical data stacks, we present segmentation results on both surrogate data with known ground-truth and experimental rat cerebellar cortex two-photon microscopic tissue stacks.Open Acces

Deep Learning in Medical Image Analysis

The accelerating power of deep learning in diagnosing diseases will empower physicians and speed up decision making in clinical environments. Applications of modern medical instruments and digitalization of medical care have generated enormous amounts of medical images in recent years. In this big data arena, new deep learning methods and computational models for efficient data processing, analysis, and modeling of the generated data are crucially important for clinical applications and understanding the underlying biological process. This book presents and highlights novel algorithms, architectures, techniques, and applications of deep learning for medical image analysis

Object Recognition

Vision-based object recognition tasks are very familiar in our everyday activities, such as driving our car in the correct lane. We do these tasks effortlessly in real-time. In the last decades, with the advancement of computer technology, researchers and application developers are trying to mimic the human's capability of visually recognising. Such capability will allow machine to free human from boring or dangerous jobs

A machine learning approach to the unsupervised segmentation of mitochondria in subcellular electron microscopy data

Recent advances in cellular and subcellular microscopy demonstrated its potential towards unravelling the mechanisms of various diseases at the molecular level. The biggest challenge in both human- and computer-based visual analysis of micrographs is the variety of nanostructures and mitochondrial morphologies. The state-of-the-art is, however, dominated by supervised manual data annotation and early attempts to automate the segmentation process were based on supervised machine learning techniques which require large datasets for training. Given a minimal number of training sequences or none at all, unsupervised machine learning formulations, such as spectral dimensionality reduction, are known to be superior in detecting salient image structures. This thesis presents three major contributions developed around the spectral clustering framework which is proven to capture perceptual organization features. Firstly, we approach the problem of mitochondria localization. We propose a novel grouping method for the extracted line segments which describes the normal mitochondrial morphology. Experimental findings show that the clusters obtained successfully model the inner mitochondrial membrane folding and therefore can be used as markers for the subsequent segmentation approaches. Secondly, we developed an unsupervised mitochondria segmentation framework. This method follows the evolutional ability of human vision to extrapolate salient membrane structures in a micrograph. Furthermore, we designed robust non-parametric similarity models according to Gestaltic laws of visual segregation. Experiments demonstrate that such models automatically adapt to the statistical structure of the biological domain and return optimal performance in pixel classification tasks under the wide variety of distributional assumptions. The last major contribution addresses the computational complexity of spectral clustering. Here, we introduced a new anticorrelation-based spectral clustering formulation with the objective to improve both: speed and quality of segmentation. The experimental findings showed the applicability of our dimensionality reduction algorithm to very large scale problems as well as asymmetric, dense and non-Euclidean datasets

Lattice deformations and spin-orbit effects in two dimensional materials

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física de la Materia Condensada. Fecha de lectura: 18-09-2014This thesis deals with the interplay between structural and electronic properties of two-dimensional materials such as graphene, and the novel and very interesting phenomena, both from the point of view of fundamental Physics and potential applications, which emerge when lattice distortions such as strains or superlattice modulations are combined with the dynamics of the electrons confined in two spatial dimensions. The main microscopic ingredient which is behind all these phenomena is the spin-orbit interaction. On the one hand, we analyze in detail how the spin-orbit interaction modifies the electronic structure of these materials, and on the other, how structural changes affect the spin-orbit interaction suffered by the electrons of the solid, then modifying its electronic response in a very peculiar manner due to the entanglement of the spin and orbital degrees of freedom. The contents of the thesis are divided in three blocks. The first part is devoted to study the effect of out-of-plane (flexural) vibration modes on the electronic properties of graphene. We examine in detail the influence of the electron-phonon coupling on the mobilities of suspended graphene samples, and we compare our findings with transport experiments, revealing that scattering by these phonon modes constitute the main intrinsic limitation to electron mobilities. Then, we study how flexural phonons contribute to enhance the spin-orbit coupling in graphene, which is in principle very weak due to the lightness of carbon. In the second part we analyze in detail different spin relaxation mechanisms mediated by the spin-orbit interaction. We focus on the standard Elliot-Yafet and D’yakonov- Perel’ mechanisms, and how such conventional theories are modified when spatially varying spin-orbit fields are considered due to the presence of impurities or curvature. In the last part we propose novel platforms for engineering topological states of matter based on the interplay between strain and superlattice perturbations in combination with the spin-orbit interaction. Our first proposal relies on the application of shear strain in monolayers of transition metal dichalcogenides in order to cretae spin-polarized pseudo-Landau levels. The resulting system resembles a time reversal invariant version of the quantum Hall effect. We also study a system consisting on graphene grown on iridium with some monolayers of lead intercalated between them. The experiments show that the local density of states develops a sequence of regularly spaced sharp resonances due to the presence of the lead. These resonances are attributed to the confinement due to spatially modulated spin-orbit fields created by lead, which mimic the effect of a magnetic field.Esta tesis trata de la interacción entre las propiedades estructurales y electrónicas de materiales bidimensionales como el grafeno, y los fenómenos que emergen cuando deformaciones de la red como las tensiones elásticas o las modulaciones producidas por super-redes se combinan con la dinámica de los electrones confinados en dos dimensiones espaciales, muy interesantes tanto desde el punto de vista de la Física fundamental como del de las aplicaciones. El ingrediente microscópico esencial que está detrás de esta fenomenología es la interacción espín-órbita. Por un lado, analizamos en detalle cómo la interacción espín-órbita modifica la estructura electrónica de estos materiales, y por otro, cómo los cambios estructurales afectan a la interacción espín-órbita experimentada por los electrones del sólido, modificando su respuesta electrónica de una manera muy peculiar debido al entrelazamiento de los grados de libertad orbitales y de espín. Los contenidos de esta tesis están divididos en tres bloques. El primero está dedicado al estudio del efecto de las vibraciones fuera del plano (flexurales) en las propiedas electrónicas del grafeno. Examinamos en detalle la influencia del acoplo electrónfonón en las movilidades de las muestras de grafeno suspendido, y comparamos nuestros hallazgos con experimentos de transporte que revelan que la dispersión debida a estos modos de fonones constituye la principal limitación intrínseca de las movilidades electrónicas. Estudiamos entonces cómo estos modos de fonones flexurales conribuyen al aumento del acoplo espín-órbita en grafeno, que es en principio muy débil debido al bajo número atómico del carbono. En la segunda parte analizamos en detalle diferentes mecanismos de relajación de espín mediados por la interacción espín-órbita. Nos centramos en los mecanismos convencionales de Elliot-Yafet y D’yakonov-Perel’, y cómo éstos se modifican cuando se incluye el efecto de campos espín-órbita que varían en el espacio debido a la presencia de impurezas o curvatura. En la última parte proponemos nuevas plataformas para el diseño de estados topológicos de la materia basados en la combinación de tensiones y perturbaciones debido a super-redes con la interacción espín-órbita. Nuestra primera propuesta se basa en la aplicación de tensiones de cizalladura en monocapas de dicalcogenuros de metales de transición con el objeto de crear pseudo-niveles de Landau polarizados en espín. El sistema resultante recuerda a una versión invariante bajo inversión temporal del efecto Hall cuántico. También estudiamos el sistema formado por grafeno crecido sobre iridio con algunas monocapas de plomo intercaladas entre ambos. Los experimentos muestran que la densidad local de estados desarrolla una secuencia de resonancias muy nítidas y regularmente espaciadas debidas a la presencia del plomo. Estas resonancias se atribuyen al confinamiento debido a la modulación espacial de campos espín-órbita creados por el plomo que imitan el efecto de un campo magnético