Geometry-Aware Neighborhood Search for Learning Local Models for Image Reconstruction

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean distance as a dissimilarity metric. However, the Euclidean distance may not always be a good dissimilarity measure for comparing data samples lying on a manifold. In this paper, we propose two algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we take into account the underlying geometry of the data. The first algorithm, called Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme which can be seen as an out-of-sample extension of the replicator graph clustering method for local model learning. The second method, called Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive alternative for training subset selection. The proposed AGNN and GOC methods are evaluated in image super-resolution, deblurring and denoising applications and shown to outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings.Comment: 15 pages, 10 figures and 5 table

Trends in Mathematical Imaging and Surface Processing

Motivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments

Doctor of Philosophy

dissertationRecent developments in magnetic resonance imaging (MRI) provide an in vivo and noninvasive tool for studying the human brain. In particular, the detection of anisotropic diffusion in biological tissues provides the foundation for diffusion-weighted imaging (DWI), an MRI modality. This modality opens new opportunities for discoveries of the brain's structural connections. Clinically, DWI is often used to analyze white matter tracts to understand neuropsychiatric disorders and the connectivity of the central nervous system. However, due to imaging time required, DWI used in clinical studies has a low angular resolution. In this dissertation, we aim to accurately track and segment the white matter tracts and estimate more representative models from low angular DWI. We first present a novel geodesic approach to segmentation of white matter tracts from diffusion tensor imaging (DTI), estimated from DWI. Geodesic approaches treat the geometry of brain white matter as a manifold, often using the inverse tensor field as a Riemannian metric. The white matter pathways are then inferred from the resulting geodesics. A serious drawback of current geodesic methods is that geodesics tend to deviate from the major eigenvectors in high-curvature areas in order to achieve the shortest path. We propose a method for learning an adaptive Riemannian metric from the DTI data, where the resulting geodesics more closely follow the principal eigenvector of the diffusion tensors even in high-curvature regions. Using the computed geodesics, we develop an automatic way to compute binary segmentations of the white matter tracts. We demonstrate that our method is robust to noise and results in improved geodesics and segmentations. Then, based on binary segmentations, we present a novel Bayesian approach for fractional segmentation of white matter tracts and simultaneous estimation of a multitensor diffusion model. By incorporating a prior that assumes the tensor fields inside each tract are spatially correlated, we are able to reliably estimate multiple tensor compartments in fiber crossing regions, even with low angular diffusion-weighted imaging. This reduces the effects of partial voluming and achieves a more reliable analysis of diffusion measurements

Distortion Robust Biometric Recognition

abstract: Information forensics and security have come a long way in just a few years thanks to the recent advances in biometric recognition. The main challenge remains a proper design of a biometric modality that can be resilient to unconstrained conditions, such as quality distortions. This work presents a solution to face and ear recognition under unconstrained visual variations, with a main focus on recognition in the presence of blur, occlusion and additive noise distortions. First, the dissertation addresses the problem of scene variations in the presence of blur, occlusion and additive noise distortions resulting from capture, processing and transmission. Despite their excellent performance, ’deep’ methods are susceptible to visual distortions, which significantly reduce their performance. Sparse representations, on the other hand, have shown huge potential capabilities in handling problems, such as occlusion and corruption. In this work, an augmented SRC (ASRC) framework is presented to improve the performance of the Spare Representation Classifier (SRC) in the presence of blur, additive noise and block occlusion, while preserving its robustness to scene dependent variations. Different feature types are considered in the performance evaluation including image raw pixels, HoG and deep learning VGG-Face. The proposed ASRC framework is shown to outperform the conventional SRC in terms of recognition accuracy, in addition to other existing sparse-based methods and blur invariant methods at medium to high levels of distortion, when particularly used with discriminative features. In order to assess the quality of features in improving both the sparsity of the representation and the classification accuracy, a feature sparse coding and classification index (FSCCI) is proposed and used for feature ranking and selection within both the SRC and ASRC frameworks. The second part of the dissertation presents a method for unconstrained ear recognition using deep learning features. The unconstrained ear recognition is performed using transfer learning with deep neural networks (DNNs) as a feature extractor followed by a shallow classifier. Data augmentation is used to improve the recognition performance by augmenting the training dataset with image transformations. The recognition performance of the feature extraction models is compared with an ensemble of fine-tuned networks. The results show that, in the case where long training time is not desirable or a large amount of data is not available, the features from pre-trained DNNs can be used with a shallow classifier to give a comparable recognition accuracy to the fine-tuned networks.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201