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In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision. The subject has given new insights in multiple view geometry and its application…
Multi-Angled Parallelism (MAP) is a method to recognize lines in binary images. It is suitable to be implemented in parallel processing and image processing hardware. The binary image is transformed into directional planes, upon which,…
We study three-dimensional microlensing where two lenses are located at different distances along the line of sight. We formulate the lens equation in complex notations and recover several previous results. There are in total either 4 or 6…
Multi-perspective cameras with potentially non-overlapping fields of view have become an important exteroceptive sensing modality in a number of applications such as intelligent vehicles, drones, and mixed reality headsets. In this work, we…
We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the…
Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…
Multi-view image generation attracts particular attention these days due to its promising 3D-related applications, e.g., image viewpoint editing. Most existing methods follow a paradigm where a 3D representation is first synthesized, and…
Vision-based metric distance and area measurement remains challenging in large-scale outdoor environments due to long-range sensing, camera zoom, and unstable imaging conditions. This work studies planar metric measurement in a real-world…
Computing the epipolar geometry from feature points between cameras with very different viewpoints is often error prone, as an object's appearance can vary greatly between images. For such cases, it has been shown that using motion…
We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an…
In this paper, we will study the following pattern recognition problem: Every pattern is a 3-dimensional graph, its surface can be split up into some regions, every region is composed of the pixels with the approximately same colour value…
We study the joint image of lines incident to points, meaning the set of image tuples obtained from fixed cameras observing a varying 3D point-line incidence. We prove a formula for the number of complex critical points of the triangulation…
Structure and continuous motion estimation from point correspondences is a fundamental problem in computer vision that has been powered by well-known algorithms such as the familiar 5-point or 8-point algorithm. However, despite their…
We introduce a network that directly predicts the 3D layout of lanes in a road scene from a single image. This work marks a first attempt to address this task with on-board sensing without assuming a known constant lane width or relying on…
Estimating a depth map from multiple views of a scene is a fundamental task in computer vision. As soon as more than two viewpoints are available, one faces the very basic question how to measure similarity across >2 image patches.…
Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the…
New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar,…
Time-of-flight cameras provide depth information, which is complementary to the photometric appearance of the scene in ordinary images. It is desirable to merge the depth and colour information, in order to obtain a coherent scene…
Most previous works of outdoor instance segmentation for images only use color information. We explore a novel direction of sensor fusion to exploit stereo cameras. Geometric information from disparities helps separate overlapping objects…
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…