A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves

We develop a novel remote sensing technique for the observation of waves on the ocean surface. Our method infers the 3-D waveform and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are given by minimizers of a composite energy functional that combines a photometric matching term along with regularization terms involving the smoothness of the unknowns. The desired ocean surface shape and radiance are the solution of a system of coupled partial differential equations derived from the optimality conditions of the energy functional. The proposed method is naturally extended to study the spatiotemporal dynamics of ocean waves and applied to three sets of stereo video data. Statistical and spectral analysis are carried out. Our results provide evidence that the observed omnidirectional wavenumber spectrum S(k) decays as k-2.5 is in agreement with Zakharov's theory (1999). Furthermore, the 3-D spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents

Lamin A/C sustains PcG protein architecture, maintaining transcriptional repression at target genes

Beyond its role in providing structure to the nuclear envelope, lamin A/C is involved in transcriptional regulation. However, its cross talk with epigenetic factors--and how this cross talk influences physiological processes--is still unexplored. Key epigenetic regulators of development and differentiation are the Polycomb group (PcG) of proteins, organized in the nucleus as microscopically visible foci. Here, we show that lamin A/C is evolutionarily required for correct PcG protein nuclear compartmentalization. Confocal microscopy supported by new algorithms for image analysis reveals that lamin A/C knock-down leads to PcG protein foci disassembly and PcG protein dispersion. This causes detachment from chromatin and defects in PcG protein-mediated higher-order structures, thereby leading to impaired PcG protein repressive functions. Using myogenic differentiation as a model, we found that reduced levels of lamin A/C at the onset of differentiation led to an anticipation of the myogenic program because of an alteration of PcG protein-mediated transcriptional repression. Collectively, our results indicate that lamin A/C can modulate transcription through the regulation of PcG protein epigenetic factors

Mathematical Methods Applied to Digital Image Processing

Introduction: Digital image processing (DIP) is an important research area since it spans a variety of applications. Although over the past few decades there has been a rapid rise in this field, there still remain issues to address. Examples include image coding, image restoration, 3D image processing, feature extraction and analysis, moving object detection, and face recognition. To deal with these issues, the use of sophisticated and robust mathematical algorithms plays a crucial role. The aim of this special issue is to provide an opportunity for researchers to publish their latest theoretical and technological achievements in mathematical methods and their various applications related to DIP. This special issue covers topics related to the development of mathematical methods and their applications. It has a total of twenty-four high-quality papers covering various important topics in DIP, including image preprocessing, image encoding/decoding, stereo image reconstruction, dimensionality and data size reduction, and applications

Comprehensive analysis of Hox gene expression in the amphipod crustacean Parhyale hawaiensis.

Hox genes play crucial roles in establishing regional identity along the anterior-posterior axis in bilaterian animals, and have been implicated in generating morphological diversity throughout evolution. Here we report the identification, expression, and initial genomic characterization of the complete set of Hox genes from the amphipod crustacean Parhyale hawaiensis. Parhyale is an emerging model system that is amenable to experimental manipulations and evolutionary comparisons among the arthropods. Our analyses indicate that the Parhyale genome contains a single copy of each canonical Hox gene with the exception of fushi tarazu, and preliminary mapping suggests that at least some of these genes are clustered together in the genome. With few exceptions, Parhyale Hox genes exhibit both temporal and spatial colinearity, and expression boundaries correlate with morphological differences between segments and their associated appendages. This work represents the most comprehensive analysis of Hox gene expression in a crustacean to date, and provides a foundation for functional studies aimed at elucidating the role of Hox genes in arthropod development and evolution

Artificial Intelligence, Mathematical Modeling and Magnetic Resonance Imaging for Precision Medicine in Neurology and Neuroradiology

La tesi affronta la possibilità di utilizzare metodi matematici, tecniche di simulazione, teorie fisiche riadattate e algoritmi di intelligenza artificiale per soddisfare le esigenze cliniche in neuroradiologia e neurologia al fine di descrivere e prevedere i patterns e l’evoluzione temporale di una malattia, nonché di supportare il processo decisionale clinico. La tesi è suddivisa in tre parti. La prima parte riguarda lo sviluppo di un workflow radiomico combinato con algoritmi di Machine Learning al fine di prevedere parametri che favoriscono la descrizione quantitativa dei cambiamenti anatomici e del coinvolgimento muscolare nei disordini neuromuscolari, con particolare attenzione alla distrofia facioscapolo-omerale. Il workflow proposto si basa su sequenze di risonanza magnetica convenzionali disponibili nella maggior parte dei centri neuromuscolari e, dunque, può essere utilizzato come strumento non invasivo per monitorare anche i più piccoli cambiamenti nei disturbi neuromuscolari oltre che per la valutazione della progressione della malattia nel tempo. La seconda parte riguarda l’utilizzo di un modello cinetico per descrivere la crescita tumorale basato sugli strumenti della meccanica statistica per sistemi multi-agente e che tiene in considerazione gli effetti delle incertezze cliniche legate alla variabilità della progressione tumorale nei diversi pazienti. L'azione dei protocolli terapeutici è modellata come controllo che agisce a livello microscopico modificando la natura della distribuzione risultante. Viene mostrato come lo scenario controllato permetta di smorzare le incertezze associate alla variabilità della dinamica tumorale. Inoltre, sono stati introdotti metodi di simulazione numerica basati sulla formulazione stochastic Galerkin del modello cinetico sviluppato. La terza parte si riferisce ad un progetto ancora in corso che tenta di descrivere una porzione di cervello attraverso la teoria quantistica dei campi e di simularne il comportamento attraverso l'implementazione di una rete neurale con una funzione di attivazione costruita ad hoc e che simula la funzione di risposta del modello biologico neuronale. E’ stato ottenuto che, nelle condizioni studiate, l'attività della porzione di cervello può essere descritta fino a O(6), i.e, considerando l’interazione fino a sei campi, come un processo gaussiano. Il framework quantistico definito può essere esteso anche al caso di un processo non gaussiano, ovvero al caso di una teoria di campo quantistico interagente utilizzando l’approccio della teoria wilsoniana di campo efficace.The thesis addresses the possibility of using mathematical methods, simulation techniques, repurposed physical theories and artificial intelligence algorithms to fulfill clinical needs in neuroradiology and neurology. The aim is to describe and to predict disease patterns and its evolution over time as well as to support clinical decision-making processes. The thesis is divided into three parts. Part 1 is related to the development of a Radiomic workflow combined with Machine Learning algorithms in order to predict parameters that quantify muscular anatomical involvement in neuromuscular diseases, with special focus on Facioscapulohumeral dystrophy. The proposed workflow relies on conventional Magnetic Resonance Imaging sequences available in most neuromuscular centers and it can be used as a non-invasive tool to monitor even fine change in neuromuscular disorders and to evaluate longitudinal diseases’ progression over time. Part 2 is about the description of a kinetic model for tumor growth by means of classical tools of statistical mechanics for many-agent systems also taking into account the effects of clinical uncertainties related to patients’ variability in tumor progression. The action of therapeutic protocols is modeled as feedback control at the microscopic level. The controlled scenario allows the dumping of uncertainties associated with the variability in tumors’ dynamics. Suitable numerical methods, based on Stochastic Galerkin formulation of the derived kinetic model, are introduced. Part 3 refers to a still-on going project that attempts to describe a brain portion through a quantum field theory and to simulate its behavior through the implementation of a neural network with an ad-hoc activation function mimicking the biological neuron model response function. Under considered conditions, the brain portion activity can be expressed up to O(6), i.e., up to six fields interaction, as a Gaussian Process. The defined quantum field framework may also be extended to the case of a Non-Gaussian Process behavior, or rather to an interacting quantum field theory in a Wilsonian Effective Field theory approach

SEGMENTATION, RECOGNITION, AND ALIGNMENT OF COLLABORATIVE GROUP MOTION

Modeling and recognition of human motion in videos has broad applications in behavioral biometrics, content-based visual data analysis, security and surveillance, as well as designing interactive environments. Significant progress has been made in the past two decades by way of new models, methods, and implementations. In this dissertation, we focus our attention on a relatively less investigated sub-area called collaborative group motion analysis. Collaborative group motions are those that typically involve multiple objects, wherein the motion patterns of individual objects may vary significantly in both space and time, but the collective motion pattern of the ensemble allows characterization in terms of geometry and statistics. Therefore, the motions or activities of an individual object constitute local information. A framework to synthesize all local information into a holistic view, and to explicitly characterize interactions among objects, involves large scale global reasoning, and is of significant complexity. In this dissertation, we first review relevant previous contributions on human motion/activity modeling and recognition, and then propose several approaches to answer a sequence of traditional vision questions including 1) which of the motion elements among all are the ones relevant to a group motion pattern of interest (Segmentation); 2) what is the underlying motion pattern (Recognition); and 3) how two motion ensembles are similar and how we can 'optimally' transform one to match the other (Alignment). Our primary practical scenario is American football play, where the corresponding problems are 1) who are offensive players; 2) what are the offensive strategy they are using; and 3) whether two plays are using the same strategy and how we can remove the spatio-temporal misalignment between them due to internal or external factors. The proposed approaches discard traditional modeling paradigm but explore either concise descriptors, hierarchies, stochastic mechanism, or compact generative model to achieve both effectiveness and efficiency. In particular, the intrinsic geometry of the spaces of the involved features/descriptors/quantities is exploited and statistical tools are established on these nonlinear manifolds. These initial attempts have identified new challenging problems in complex motion analysis, as well as in more general tasks in video dynamics. The insights gained from nonlinear geometric modeling and analysis in this dissertation may hopefully be useful toward a broader class of computer vision applications

A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction

Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning models for high-fidelity data reconstruction require low-fidelity data for model training. Such requirement restrains the application performance of these models, since their data reconstruction accuracy would drop significantly if the low-fidelity input data used in model test has a large deviation from the training data. To overcome this restraint, we propose a diffusion model which only uses high-fidelity data at training. With different configurations, our model is able to reconstruct high-fidelity data from either a regular low-fidelity sample or a sparsely measured sample, and is also able to gain an accuracy increase by using physics-informed conditioning information from a known partial differential equation when that is available. Experimental results demonstrate that our model can produce accurate reconstruction results for 2d turbulent flows based on different input sources without retraining

Foetal echocardiographic segmentation

Congenital heart disease affects just under one percentage of all live births [1]. Those defects that manifest themselves as changes to the cardiac chamber volumes are the motivation for the research presented in this thesis. Blood volume measurements in vivo require delineation of the cardiac chambers and manual tracing of foetal cardiac chambers is very time consuming and operator dependent. This thesis presents a multi region based level set snake deformable model applied in both 2D and 3D which can automatically adapt to some extent towards ultrasound noise such as attenuation, speckle and partial occlusion artefacts. The algorithm presented is named Mumford Shah Sarti Collision Detection (MSSCD). The level set methods presented in this thesis have an optional shape prior term for constraining the segmentation by a template registered to the image in the presence of shadowing and heavy noise. When applied to real data in the absence of the template the MSSCD algorithm is initialised from seed primitives placed at the centre of each cardiac chamber. The voxel statistics inside the chamber is determined before evolution. The MSSCD stops at open boundaries between two chambers as the two approaching level set fronts meet. This has significance when determining volumes for all cardiac compartments since cardiac indices assume that each chamber is treated in isolation. Comparison of the segmentation results from the implemented snakes including a previous level set method in the foetal cardiac literature show that in both 2D and 3D on both real and synthetic data, the MSSCD formulation is better suited to these types of data. All the algorithms tested in this thesis are within 2mm error to manually traced segmentation of the foetal cardiac datasets. This corresponds to less than 10% of the length of a foetal heart. In addition to comparison with manual tracings all the amorphous deformable model segmentations in this thesis are validated using a physical phantom. The volume estimation of the phantom by the MSSCD segmentation is to within 13% of the physically determined volume