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We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…
We introduce a new machine learning approach for image segmentation that uses a neural network to model the conditional energy of a segmentation given an image. Our approach, combinatorial energy learning for image segmentation (CELIS)…
Random field and random cluster theory are used to describe certain mathematical results concerning the probability distribution of image pixel intensities characterized as generic $2D$ integer arrays. The size of the smallest bounded…
We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to a robust…
We consider the task of feature selection for reconstruction which consists in choosing a small subset of features from which whole data instances can be reconstructed. This is of particular importance in several contexts involving for…
Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion…
Energy-based models (EBMs) offer a flexible framework for parameterizing probability distributions using neural networks. However, learning EBMs by exact maximum likelihood estimation (MLE) is generally intractable, due to the need to…
The volume estimation of brain regions from MRI data is a key problem in many clinical applications, where the acquisition of data at high spatial resolution is desirable. While parallel MRI and constrained image reconstruction algorithms…
We present a novel approach for reconstructing the projected mass distribution of clusters of galaxies from sparse and noisy weak gravitational lensing shear data. The reconstructions are regularised using knowledge gained from numerical…
A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…
Image segmentation techniques are predominately based on parameter-laden optimization. The objective function typically involves weights for balancing competing image fidelity and segmentation regularization cost terms. Setting these…
The best way to combine the results of deep learning with standard 3D reconstruction pipelines remains an open problem. While systems that pass the output of traditional multi-view stereo approaches to a network for regularisation or…
Galaxy clusters are one of the most powerful probes to study extensions of General Relativity and the Standard Cosmological Model. Upcoming surveys like the Vera Rubin Observatory's Legacy Survey of Space and Time are expected to…
In many applications of X-ray computed tomography, an unsupervised segmentation of the reconstructed 3D volumes forms an important step in the image processing chain for further investigation of the digitized object. Therefore, the goal is…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
The main focus of this work is a novel framework for the joint reconstruction and segmentation of parallel MRI (PMRI) brain data. We introduce an image domain deep network for calibrationless recovery of undersampled PMRI data. The proposed…
We investigate the expected cosmological constraints from a combination of weak lensing and large-scale galaxy clustering using realistic redshift distributions. Introducing a systematic bias in the weak lensing redshift distributions (of…
Dense semantic 3D reconstruction is typically formulated as a discrete or continuous problem over label assignments in a voxel grid, combining semantic and depth likelihoods in a Markov Random Field framework. The depth and semantic…
We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different…