Sparse reconstruction from a limited projection number of the coronary artery tree in X-ray rotational imaging

International audienceThis paper deals with the 3D reconstruction of sparse data in X-ray rotational imaging. Due to the cardiac motion, the number of available projections for this reconstruction is equal to four, which leads to a strongly undersampled reconstruction problem. We address thus this illness problem through a regularized iterative method. The whole algorithm is divided into two steps. Firstly, a minimal path segmentation step extracts artery tree boundaries. Secondly, a MAP reconstruction comparing L0-norm and L1-norm priors is applied on this extracted coronary tree. The reconstruction optimization process relies on a separable paraboloidal (SPS) algorithm. Some preliminary results are provided on simulated rotational angiograms

Ensemble Estimation of Information Divergence

Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the parametric rate when the densities are sufficiently smooth. Guidelines for the tuning parameter selection and the asymptotic distribution of this estimator are provided. Based on the theory, an empirical estimator of Rényi-α divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions. The estimator is shown to be robust to the choice of tuning parameters. We show extensive simulation results that verify the theoretical results of our paper. Finally, we apply the proposed estimator to estimate the bounds on the Bayes error rate of a cell classification problem

Connected Attribute Filtering Based on Contour Smoothness

A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform

Nonparametric Estimation of Distributional Functionals and Applications.

Distributional functionals are integrals of functionals of probability densities and include functionals such as information divergence, mutual information, and entropy. Distributional functionals have many applications in the fields of information theory, statistics, signal processing, and machine learning. Many existing nonparametric distributional functional estimators have either unknown convergence rates or are difficult to implement. In this thesis, we consider the problem of nonparametrically estimating functionals of distributions when only a finite population of independent and identically distributed samples are available from each of the unknown, smooth, d-dimensional distributions. We derive mean squared error (MSE) convergence rates for leave-one-out kernel density plug-in estimators and k-nearest neighbor estimators of these functionals. We then extend the theory of optimally weighted ensemble estimation to obtain estimators that achieve the parametric MSE convergence rate when the densities are sufficiently smooth. These estimators are simple to implement and do not require knowledge of the densities’ support set, in contrast with many competing estimators. The asymptotic distribution of these estimators is also derived. The utility of these estimators is demonstrated through their application to sunspot image data and neural data measured from epilepsy patients. Sunspot images are clustered by estimating the divergence between the underlying probability distributions of image pixel patches. The problem of overfitting is also addressed in both applications by performing dimensionality reduction via intrinsic dimension estimation and by benchmarking classification via Bayes error estimationPhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133394/1/krmoon_1.pd

Non-local active contours

This thesis deals with image segmentation problems that arise in various computer vision related fields such as medical imaging, satellite imaging, video surveillance, recognition and robotic vision. More specifically, this thesis deals with a special class of image segmentation technique called Snakes or Active Contour Models. In active contour models, image segmentation is posed as an energy minimization problem, where an objective energy function (based on certain image related features) is defined on the segmenting curve (contour). Typically, a gradient descent energy minimization approach is used to drive the initial contour towards a minimum for the defined energy. The drawback associated with this approach is that the contour has a tendency to get stuck at undesired local minima caused by subtle and undesired image features/edges. Thus, active contour based curve evolution approaches are very sensitive to initialization and noise. The central theme of this thesis is to develop techniques that can make active contour models robust against certain classes of local minima by incorporating global information in energy minimization. These techniques lead to energy minimization with global considerations; we call these models -- 'Non-local active contours'. In this thesis, we consider three widely used active contour models: 1) Edge- and region-based segmentation model, 2) Prior shape knowledge based segmentation model, and 3) Motion segmentation model. We analyze the traditional techniques used for these models and establish the need for robust models that avoid local minima. We address the local minima problem for each model by adding global image considerations.PhDCommittee Chair: Dr. Yezzi, Anthony; Committee Member: Dr. Barnes, Chris; Committee Member: Dr. Narasimha, Rajesh; Committee Member: Dr. Oshinski, John; Committee Member: Dr. Tannenbaum, Allen; Committee Member: Dr. Vela, Patrici