Related papers: A Computer Vision Problem in Flatland
It is proved that a straight projective-metric space has an open set of centers, if and only if it is either the hyperbolic or a Minkowskian geometry. It is also shown that if a straight projective-metric space has some finitely many…
To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…
The cross-depiction problem is that of recognising visual objects regardless of whether they are photographed, painted, drawn, etc. It is a potentially significant yet under-researched problem. Emulating the remarkable human ability to…
Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane.…
The human visual system processes images with varied degrees of resolution, with the fovea, a small portion of the retina, capturing the highest acuity region, which gradually declines toward the field of view's periphery. However, the…
Place recognition is one of the hot research fields in automation technology and is still an open issue, Camera and Lidar are two mainstream sensors used in this task, Camera-based methods are easily affected by illumination and season…
Every lens space has a locally flat embedding in a connected sum of 8 copies of the complex projective plane and a smooth embedding in n copies of the complex projective plane for some positive integer n. We show that there is no n such…
We examine the problem of projecting subsets of a commutative, positively ordered monoid into an $o$-ideal. We prove that to this end one may restrict to a sufficient subset, for whose cardinality we provide an explicit upper bound. Several…
Common object counting in a natural scene is a challenging problem in computer vision with numerous real-world applications. Existing image-level supervised common object counting approaches only predict the global object count and rely on…
Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…
We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many…
Single-shot diffraction imaging of isolated nanosized particles has seen remarkable success in recent years, yielding in-situ measurements with ultra-high spatial and temporal resolution. The progress of high-repetition-rate sources for…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
We present a new method for efficient high-quality image segmentation of objects and scenes. By analogizing classical computer graphics methods for efficient rendering with over- and undersampling challenges faced in pixel labeling tasks,…
Spatial relationships between objects represent key scene information for humans to understand and interact with the world. To study the capability of current computer vision systems to recognize physically grounded spatial relations, we…
A de facto standard in solving computer vision problems is to use a common high-resolution camera and choose its placement on an agent (i.e., position and orientation) based on human intuition. On the other hand, extremely simple and…
Image registration is a classical problem in machine vision which seeks methods to align discrete images of the same scene to subpixel accuracy in general situations. As with all estimation problems, the underlying difficulty is the partial…
Robots coexisting with humans in their environment and performing services for them need the ability to interact with them. One particular requirement for such robots is that they are able to understand spatial relations and can place…
We prove that an equivalent condition for a uniform space to be coverable is that the images of the natural projections in the fundamental inverse system are uniformly open in a certain sense. As corollaries we (1) obtain a concrete way to…
We discuss homogeneity and universality issues in the theory of abstract linear spaces, namely, structures with points and lines satisfying natural axioms, as in Euclidean or projective geometry. We show that the two smallest projective…