Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

Developing a flexible and expressive realtime polyphonic wave terrain synthesis instrument based on a visual and multidimensional methodology

The Jitter extended library for Max/MSP is distributed with a gamut of tools for the generation, processing, storage, and visual display of multidimensional data structures. With additional support for a wide range of media types, and the interaction between these mediums, the environment presents a perfect working ground for Wave Terrain Synthesis. This research details the practical development of a realtime Wave Terrain Synthesis instrument within the Max/MSP programming environment utilizing the Jitter extended library. Various graphical processing routines are explored in relation to their potential use for Wave Terrain Synthesis

New tools for quantitative analysis of nuclear architecture

The cell nucleus houses a wide variety of macromolecular substructures including the cell’s genetic material. The spatial configuration of these substructures is thought to be fundamentally associated with nuclear function, yet the architectural organisation of the cell nucleus is only poorly understood. Advances in microscopy and associated fluorescence techniques have provided a wealth of nuclear image data. Such images offer the opportunity for both visualising nuclear substructures and quantitative investigation of the spatial configuration of these objects. In this thesis, we present new tools to study and explore the subtle principles behind nuclear architecture. We describe a novel method to segment fluorescent microscopy images of nuclear objects. The effectiveness of this segmentation algorithm is demonstrated using extensive simulation. Additionally, we show that the method performs as well as manual-thresholding, which is considered the gold standard. Next, randomisationbased tests from spatial point pattern analysis are employed to inspect spatial interactions of nuclear substructures. The results suggest new and interesting spatial relationships in the nucleus. However, this approach probes only relative nuclear organisation and cannot readily yield a description of absolute spatial preference, which may be a key component of nuclear architecture. To address this problem we have developed methodology based on techniques employed in statistical shape analysis and image registration. The approach proposes that the nuclear boundary can be used to align nuclei from replicate images into a common coordinate system. Each nucleus and its contents can therefore be registered to the sample mean shape using rigid and non-rigid deformations. This aggregated data allows inference regarding global nuclear spatial organisation. For example, the kernel smoothed intensity function is computed to return an estimate of the intensity function of the registered nuclear object. Simulation provides evidence that the registration procedure is sensible and the results accurate. Finally, we have investigated a large database of nuclear substructures using conventional methodology as well as our new tools. We have identified novel spatial relationships between nuclear objects that offer significant clues to their function. We have also examined the absolute spatial configuration of these substructures in registered data. The results reveal dramatic underlying spatial preferences and present new and clear insights into nuclear architecture

Study of space battery accelerated testing techniques. Phase 2 report - Ideal approaches towards accelerated tests and analysis of data

Ideal approaches to accelerated life tests and data analysis applied to space batterie

Singular integrals and maximal operators related to Carleson's theorem and curves in the plane

In this thesis we study several different operators that are related to Carleson's theorem and curves in the plane. An interesting open problem in harmonic analysis is the study of analogues of Carleson's operator that feature integration along curves. In that context it is natural to ask whether the established methods of time-frequency analysis carry over to an anisotropic setting. We answer that question and also provide certain partial bounds for the Carleson operator along monomial curves using entirely different methods. Another line of results in this thesis concerns maximal operators and Hilbert transforms along variable curves in the plane. These are related to Carleson-type operators via a partial Fourier transform in the second variable. A central motivation for studying these operators stems from Zygmund's conjecture on differentiation along Lipschitz vector fields. One of our results can be understood as proving a curved variant of this conjecture

Disruption of Orbitofronto-Striatal Functional Connectivity Underlies Maladaptive Persistent Behaviors in Alcohol-Dependent Patients

OBJECTIVE: Alcohol dependence is characterized by persistent alcohol-seeking despite negative consequences. Previous studies suggest that maladaptive persistent behaviors reflect alcohol-induced brain changes that cause alterations in the cortico-striatal-limbic circuit. METHODS: Twenty one alcohol dependent patients and 24 age-matched healthy controls performed a decision-making task during functional MRI. We defined the medial orbitofrontal cortex (mOFC) as a region-of-interest and performed seed-based functional connectivity analysis. RESULTS: Healthy controls were more flexible in adapting an alternative behavioral strategy, which correlated with stronger mOFC-dorsal striatum functional connectivity. In contrast, alcohol dependent patients persisted to the first established behavioral strategy. The mOFC-dorsal striatum functional connectivity was impaired in the alcohol-dependent patients, but increased in correlation with the duration of abstinence. CONCLUSION: Our findings support that the disruption of the mOFC-striatal circuitry contribute to the maldaptive persistent behaviors in alcohol dependent patients.ope

Medical ultrasonics: adaptive time gain compensation in diagnostic imaging

Large errors can occur with time gain compensation (TGC) which is set up manually since one gain function is unlikely to be appropriate for all scan lines and the operator may not have sufficient time or experience to optimise it. Adaptive TGC offers the benefit of improved images which are less operator dependentThe clinical application of simple adaptive TGC in abdominal and obstetric ultrasound is described.Recent developments in diqital electronics allow powerful methods of gain control to be implemented. A microcomputer controlled system has been built to investigate various methods of adaptive TGC. The microcoputer is interfaced to a real-time scanner from which it can collect echo data. The echo data is processed by programs written in a combination of assembly language and Fortran IV, and the microcomputer can then set up a unique TGC function for each scan line in the image. The design and construction of the microcomputer system are described. Several algorithms for adaptive TGC have been developed. These range from the derivation of a single gain function applied across the whole image to more sophisticated algorithms which apply a unique TGC function to each scan line and are capable of detecting regions of low attenuation.The algorithms were tested using tissue equivalent phantoms, and clinically in routine abdominal and obstetric scanning. The results were compared with those of a skilled operator setting up the TGC by hand. The performance of the algorithms was also investigated using computer simulations. The clinical results show that adaptive TGC is capable of producing consistently better images than a skilled operator setting the TGC manually.Further developments of adaptive TGC are considered - in particular, the implementation of a hard-wired system which would operate in real-time and the development of an interactive gain control system