Related papers: Convexity Helps Iterated Search in 3D
Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…
Inverse design aims to design the input variables of a physical system to optimize a specified objective function, typically formulated as a search or optimization problem. However, in 3D domains, the design space grows exponentially,…
Visual place recognition is an important subproblem of mobile robot localization. Since it is a special case of image retrieval, the basic source of information is the pairwise similarity of image descriptors. However, the embedding of the…
Searching on bipartite graphs is basal and versatile to many real-world Web applications, e.g., online recommendation, database retrieval, and query-document searching. Given a query node, the conventional approaches rely on the similarity…
In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including…
Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time within $\Theta(n\log{n})$ in the…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in $R^3$, (ii) reporting intersections between query lines…
Despite recent advances in feed-forward 3D Gaussian Splatting, generalizable 3D reconstruction remains challenging, particularly in multi-view correspondence modeling. Existing approaches face a fundamental trade-off: explicit methods…
This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
Querying graph data with low latency is an important requirement in application domains such as social networks and knowledge graphs. Graph queries perform multiple hops between vertices. When data is partitioned and stored across multiple…
This work presents a compact, cumulative and coalescible probabilistic voxel mapping method to enhance performance, accuracy and memory efficiency in LiDAR odometry. Probabilistic voxel mapping requires storing past point clouds and…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…
Let G=(V,E) be a finite graph, and f:V->N be any function. The Local Search problem consists in finding a local minimum of the function f on G, that is a vertex v such that f(v) is not larger than the value of f on the neighbors of v in G.…
We propose a novel method for multi-objective motion planning problems by leveraging the paradigm of lexicographic optimization and applying it for the first time to graph search over probabilistic roadmaps. The competing resources of…
We consider the following $q$-analog of the basic combinatorial search problem: let $q$ be a prime power and $\GF(q)$ the finite field of $q$ elements. Let $V$ denote an $n$-dimensional vector space over $\GF(q)$ and let $\mathbf{v}$ be an…
Massive amount of multimedia data that contain times- tamps and geographical information are being generated at an unprecedented scale in many emerging applications such as photo sharing web site and social networks applications. Due to…
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…
Modern convolutional neural networks apply the same operations on every pixel in an image. However, not all image regions are equally important. To address this inefficiency, we propose a method to dynamically apply convolutions conditioned…