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Template matching is a basic method in image analysis to extract useful information from images. In this paper, we suggest a new method for pattern matching. Our method transform the template image from two dimensional image into one…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Estimating camera geometry typically involves solving minimal problems formulated as systems of multivariate polynomial equations, which often pose computational challenges when using existing Gr\"obner-basis or resultant-based methods due…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
In today's information systems, the availability of massive amounts of data necessitates the development of fast and accurate algorithms to summarize these data and represent them in a succinct format. One crucial problem in big data…
The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…
Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e., solving minimal…
The estimation of parameters from data is a common problem in many areas of the physical sciences, and frequently used algorithms rely on sets of simulated data which are fit to data. In this article, an analytic solution for…
Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being…
We study the problem of selecting a subset of k random variables from a large set, in order to obtain the best linear prediction of another variable of interest. This problem can be viewed in the context of both feature selection and sparse…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
One of the major challenges of model-free visual tracking problem has been the difficulty originating from the unpredictable and drastic changes in the appearance of objects we target to track. Existing methods tackle this problem by…
6D pose estimation is a central problem in robot vision. Compared with pose estimation based on point correspondences or its robust versions, correspondence-free methods are often more flexible. However, existing correspondence-free methods…
We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
Active learning is increasingly adopted for expensive multi-objective combinatorial optimization problems, but it involves a challenging subset selection problem, optimizing the batch acquisition score that quantifies the goodness of a…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…
Lensless cameras provide a framework to build thin imaging systems by replacing the lens in a conventional camera with an amplitude or phase mask near the sensor. Existing methods for lensless imaging can recover the depth and intensity of…
Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used…