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One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulation problem, which seeks to reconstruct…
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
For the problem of 3D object recognition, researchers using deep learning methods have developed several very different input representations, including "multi-view" snapshots taken from discrete viewpoints around an object, as well as…
"Wireframe" is a line segment based representation designed to well capture large-scale visual properties of regular, structural shaped man-made scenes surrounding us. Unlike the wireframes, conventional edges or line segments focus on all…
The capacity of automatically modeling photographic composition is valuable for many real-world machine vision applications such as digital photography, image retrieval, image understanding, and image aesthetics assessment. The triangle…
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…
Accurate and consistent 3D tracking from multiple cameras is a key component in a vision-based autonomous driving system. It involves modeling 3D dynamic objects in complex scenes across multiple cameras. This problem is inherently…
This paper introduces a novel paradigm for the analysis and verification of concurrent programs -- the Singularity Theory. We model the execution space of a concurrent program as a branched topological space, where program states are points…
In this paper, we propose a learning-based approach to the task of automatically extracting a "wireframe" representation for images of cluttered man-made environments. The wireframe (see Fig. 1) contains all salient straight lines and their…
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a…
We propose an approach for estimating the relative pose between calibrated image pairs by jointly exploiting points, lines, and their coincidences in a hybrid manner. We investigate all possible configurations where these data modalities…
Camera localization in 3D LiDAR maps has gained increasing attention due to its promising ability to handle complex scenarios, surpassing the limitations of visual-only localization methods. However, existing methods mostly focus on…
Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…
Thin structures, such as wire-frame sculptures, fences, cables, power lines, and tree branches, are common in the real world. It is extremely challenging to acquire their 3D digital models using traditional image-based or depth-based…
Modern computer vision has moved beyond the domain of internet photo collections and into the physical world, guiding camera-equipped robots and autonomous cars through unstructured environments. To enable these embodied agents to interact…
Wide-angle cameras are widely used in photogrammetry and autonomous systems which rely on the accurate metric measurements derived from images. To find the geometric relationship between incoming rays and image pixels, geometric camera…
Estimating metric relative camera pose from a pair of images is of great importance for 3D reconstruction and localisation. However, conventional two-view pose estimation methods are not metric, with camera translation known only up to a…