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Mixture models are well-established learning approaches that, in computer vision, have mostly been applied to inverse or ill-defined problems. However, they are general-purpose divide-and-conquer techniques, splitting the input space into…

The increasing congestion in the near-Earth space environment has amplified the need for robust and efficient conjunction analysis techniques including the computation of the minimum distance between orbital paths in the presence of…

Inter-object relations underpin spatial intelligence, yet existing representations -- linguistic prepositions or object-level scene graphs -- are too coarse to specify which regions actually support, contain, or contact one another, leading…

In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…

Mars exploration requires precise and reliable terrain models to ensure safe rover navigation across its unpredictable and often hazardous landscapes. Stereoscopic vision serves a critical role in the rover's perception, allowing scene…

In recent years, an ever-increasing number of remote satellites are orbiting the Earth which streams vast amount of visual data to support a wide range of civil, public and military applications. One of the key information obtained from…

In this paper, we propose a novel object-level mapping system that can simultaneously segment, track, and reconstruct objects in dynamic scenes. It can further predict and complete their full geometries by conditioning on reconstructions…

For large-scale data fitting, the least-squares progressive iterative approximation is a widely used method in many applied domains because of its intuitive geometric meaning and efficiency. In this work, we present a randomized progressive…

Although modern object detectors rely heavily on a significant amount of training data, humans can easily detect novel objects using a few training examples. The mechanism of the human visual system is to interpret spatial relationships…

Restricting path tracing to a small number of paths per pixel for performance reasons rarely achieves a satisfactory image quality for scenes of interest. However, path space filtering may dramatically improve the visual quality by sharing…

We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…

Non-point spatial objects (e.g., polygons, linestrings, etc.) are ubiquitous. We study the problem of indexing non-point objects in memory for range queries and spatial intersection joins. We propose a secondary partitioning technique for…

The bilateral filter is a non-linear filter that uses a range filter along with a spatial filter to perform edge-preserving smoothing of images. A direct computation of the bilateral filter requires $O(S)$ operations per pixel, where $S$ is…

Set intersection is a fundamental operation in information retrieval and database systems. This paper introduces linear space data structures to represent sets such that their intersection can be computed in a worst-case efficient way. In…

In this paper, we present an improved numerical algorithm for computing the intersection area of multiple circles and a complex polygon efficiently. This geometric problem is fundamental to applications such as wireless sensor networks and…

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…

3D pose estimation from sparse multi-views is a critical task for numerous applications, including action recognition, sports analysis, and human-robot interaction. Optimization-based methods typically follow a two-stage pipeline, first…

The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…

Background: Pose estimation of rigid objects is a practical challenge in optical metrology and computer vision. This paper presents a novel stochastic-geometrical modeling framework for object pose estimation based on observing multiple…

We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…