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Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…
The Halpern algorithm is a powerful fixed point approximation method for finding the closest point in the fixed point set of a nonexpansive mapping to the initial point. However, in practice, it is not necessarily true that this algorithm…
This study addresses the challenge of performing visual localization in demanding conditions such as night-time scenarios, adverse weather, and seasonal changes. While many prior studies have focused on improving image-matching performance…
We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the…
In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the…
We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances…
We propose a new algorithm for the optimization of convex functions over a polyhedral set in Rn. The algorithm extends the spectral projected-gradient method with limited-memory BFGS iterates restricted to the present face whenever…
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
It has been shown numerically that the performance of the Levenberg-Marquardt algorithm can be improved by including a second order correction known as the geodesic acceleration. In this paper we give the method a more sound theoretical…
Consider a mobile robot tasked with localizing targets at unknown locations by obtaining relative measurements. The observations can be bearing or range measurements. How should the robot move so as to localize the targets and minimize the…
This paper proposes a geodesic-distance-based feature that encodes global information for improved video segmentation algorithms. The feature is a joint histogram of intensity and geodesic distances, where the geodesic distances are…
Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific…
Direct SLAM methods have shown exceptional performance on odometry tasks. However, they are susceptible to dynamic lighting and weather changes while also suffering from a bad initialization on large baselines. To overcome this, we propose…
*The following abbreviates the abstract. Please refer to the thesis for the full abstract.* After a disaster, locating and extracting victims quickly is critical because mortality rises rapidly after the first two days. To assist search and…
We present a novel, data driven approach for solving the problem of registration of two point cloud scans. Our approach is direct in the sense that a single pair of corresponding local patches already provides the necessary transformation…
It has been shown that global scene understanding tasks like layout estimation can benefit from wider field of views, and specifically spherical panoramas. While much progress has been made recently, all previous approaches rely on…
Few-shot detection-based counters estimate the number of instances in the image specified only by a few test-time exemplars. A common approach to localize objects across multiple sizes is to merge backbone features of different resolutions.…
In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which…
We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set $S$ of point sites in a static simple polygon $P$. Our data structure allows us to insert a new site in $S$, delete a site from $S$,…
Accurate information about the location and orientation of a camera in mobile devices is central to the utilization of location-based services (LBS). Most of such mobile devices rely on GPS data but this data is subject to inaccuracy due to…