Fast Detection of Curved Edges at Low SNR

Detecting edges is a fundamental problem in computer vision with many applications, some involving very noisy images. While most edge detection methods are fast, they perform well only on relatively clean images. Indeed, edges in such images can be reliably detected using only local filters. Detecting faint edges under high levels of noise cannot be done locally at the individual pixel level, and requires more sophisticated global processing. Unfortunately, existing methods that achieve this goal are quite slow. In this paper we develop a novel multiscale method to detect curved edges in noisy images. While our algorithm searches for edges over a huge set of candidate curves, it does so in a practical runtime, nearly linear in the total number of image pixels. As we demonstrate experimentally, our algorithm is orders of magnitude faster than previous methods designed to deal with high noise levels. Nevertheless, it obtains comparable, if not better, edge detection quality on a variety of challenging noisy images.Comment: 9 pages, 11 figure

Left-invariant evolutions of wavelet transforms on the Similitude Group

Enhancement of multiple-scale elongated structures in noisy image data is relevant for many biomedical applications but commonly used PDE-based enhancement techniques often fail at crossings in an image. To get an overview of how an image is composed of local multiple-scale elongated structures we construct a multiple scale orientation score, which is a continuous wavelet transform on the similitude group, SIM(2). Our unitary transform maps the space of images onto a reproducing kernel space defined on SIM(2), allowing us to robustly relate Euclidean (and scaling) invariant operators on images to left-invariant operators on the corresponding continuous wavelet transform. Rather than often used wavelet (soft-)thresholding techniques, we employ the group structure in the wavelet domain to arrive at left-invariant evolutions and flows (diffusion), for contextual crossing preserving enhancement of multiple scale elongated structures in noisy images. We present experiments that display benefits of our work compared to recent PDE techniques acting directly on the images and to our previous work on left-invariant diffusions on orientation scores defined on Euclidean motion group.Comment: 40 page

Study on the Mechanical Properties of Carbon Nanotube Coated‒Fiber Multi-Scale (CCFM) Hybrid Composites

L'abstract è presente nell'allegato / the abstract is in the attachmen

Mumford-Shah and Potts Regularization for Manifold-Valued Data with Applications to DTI and Q-Ball Imaging

Mumford-Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and non-convex, they are computationally challenging even for scalar data. For manifold-valued data, the problem becomes even more involved since typical features of vector spaces are not available. In this paper, we propose algorithms for Mumford-Shah and for Potts regularization of manifold-valued signals and images. For the univariate problems, we derive solvers based on dynamic programming combined with (convex) optimization techniques for manifold-valued data. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging), we show that our algorithms compute global minimizers for any starting point. For the multivariate Mumford-Shah and Potts problems (for image regularization) we propose a splitting into suitable subproblems which we can solve exactly using the techniques developed for the corresponding univariate problems. Our method does not require any a priori restrictions on the edge set and we do not have to discretize the data space. We apply our method to diffusion tensor imaging (DTI) as well as Q-ball imaging. Using the DTI model, we obtain a segmentation of the corpus callosum

STRUCTURE DETECTION WITH SECOND ORDER RIESZ TRANSFORMS

A frequently applied indicator of tubular structures is based on the eigenvalues of the Hessian matrix of the original image convolved with a Gaussian, whose standard derivation depends on the size of the tubes. Hence the tube size must either be known in advance or a whole scale of standard deviations has to be tested resulting in higher computational costs – a serious obstacle for data with varying tube thickness. In this paper, we propose to modify the structure indicator by replacing the derivatives of the Gaussian smoothed function by the Riesz transform. We show by various numerical examples that the resulting structure indicator is scale independent. Smoothing with a Gaussian is just necessary to cope with the noise in the image, but is not related to the size of the tubular structures. We apply the novel structure indicator for the fiber orientation analysis of fibrous materials and for the segmentation of leather. The latter one was a special challenging application since all scales are present in the microstructure of leather

Visual Quality Enhancement in Optoacoustic Tomography using Active Contour Segmentation Priors

Segmentation of biomedical images is essential for studying and characterizing anatomical structures, detection and evaluation of pathological tissues. Segmentation has been further shown to enhance the reconstruction performance in many tomographic imaging modalities by accounting for heterogeneities of the excitation field and tissue properties in the imaged region. This is particularly relevant in optoacoustic tomography, where discontinuities in the optical and acoustic tissue properties, if not properly accounted for, may result in deterioration of the imaging performance. Efficient segmentation of optoacoustic images is often hampered by the relatively low intrinsic contrast of large anatomical structures, which is further impaired by the limited angular coverage of some commonly employed tomographic imaging configurations. Herein, we analyze the performance of active contour models for boundary segmentation in cross-sectional optoacoustic tomography. The segmented mask is employed to construct a two compartment model for the acoustic and optical parameters of the imaged tissues, which is subsequently used to improve accuracy of the image reconstruction routines. The performance of the suggested segmentation and modeling approach are showcased in tissue-mimicking phantoms and small animal imaging experiments.Comment: Accepted for publication in IEEE Transactions on Medical Imagin

Doctor of Philosophy

dissertationAtrial fibrillation (AF) is the leading cause of ischemic stroke and is the most commonly observed arrhythmia in clinical cardiology. Catheter ablation of AF, in which specific regions of cardiac anatomy associated with AF are intenionally injured to create scar tissue, has been honed over the last 15 years to become a relatively common and safe treatment option. However, the success of these anatomically driven ablation strategies, particularly in hearts that have been exposed to AF for extended periods, remains poor. AF induces changes in the electrical and structural properties of the cardiac tissue that further promotes the permanence of AF. In a process known as electroanatomical (EAM) mapping, clinicians record time signals known as electrograms (EGMs) from the heart and the locations of the recording sites to create geometric representations, or maps, of the electrophysiological properties of the heart. Analysis of the maps and the individual EGM morphologies can indicate regions of abnormal tissue, or substrates that facilitate arrhythmogenesis and AF perpetuation. Despite this progress, limitations in the control of devices currently used for EAM acquisition and reliance on suboptimal metrics of tissue viability appear to be hindering the potential of treatment guided by substrate mapping. In this research, we used computational models of cardiac excitation to evaluate param- eters of EAM that affect the performance of substrate mapping. These models, which have been validated with experimental and clinical studies, have yielded new insights into the limitations of current mapping systems, but more importantly, they guided us to develop new systems and metrics for robust substrate mapping. We report here on the progress in these simulation studies and on novel measurement approaches that have the potential to improve the robustness and precision of EAM in patients with arrhythmias. Appropriate detection of proarrhythmic substrates promises to improve ablation of AF beyond rudimentary destruction of anatomical targets to directed targeting of complicit tissues. Targeted treatment of AF sustaining tissues, based on the substrate mapping approaches described in this dissertation, has the potential to improve upon the efficacy of current AF treatment options

Improved micro-contact resistance model that considers material deformation, electron transport and thin film characteristics

This paper reports on an improved analytic model forpredicting micro-contact resistance needed for designing microelectro-mechanical systems (MEMS) switches. The originalmodel had two primary considerations: 1) contact materialdeformation (i.e. elastic, plastic, or elastic-plastic) and 2) effectivecontact area radius. The model also assumed that individual aspotswere close together and that their interactions weredependent on each other which led to using the single effective aspotcontact area model. This single effective area model wasused to determine specific electron transport regions (i.e. ballistic,quasi-ballistic, or diffusive) by comparing the effective radius andthe mean free path of an electron. Using this model required thatmicro-switch contact materials be deposited, during devicefabrication, with processes ensuring low surface roughness values(i.e. sputtered films). Sputtered thin film electric contacts,however, do not behave like bulk materials and the effects of thinfilm contacts and spreading resistance must be considered. Theimproved micro-contact resistance model accounts for the twoprimary considerations above, as well as, using thin film,sputtered, electric contact