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Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function \sigma =d^{2}/2. One suggests a new general method of the…
Can we learn the physics of matter in motion directly from images and video--and trust it? Answering this question requires integrating experiments, physics-based simulation, and data across traditionally separate disciplines. Much of this…
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…
Many surface cues support three-dimensional shape perception, but people can sometimes still see shape when these features are missing -- in extreme cases, even when an object is completely occluded, as when covered with a draped cloth. We…
Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…
Understanding geometry relies heavily on vision. In this work, we evaluate whether state-of-the-art vision language models (VLMs) can understand simple geometric concepts. We use a paradigm from cognitive science that isolates visual…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
Visual perception, the brain's construction of a stable world from sensory data, faces several long-standing, fundamental challenges. While often studied separately, these problems have resisted a single, unifying computational framework.…
The geometric shapes of the outside world objects hide an undisclosed emotional, psychological, artistic, aesthetic and shape-generating potential; they may attract or cause fear as well as a variety of other emotions. This suggests that…
Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…
In this paper we develop a geometrical model of functional architecture for the processing of spatio-temporal visual stimuli. The model arises from the properties of the receptive field linear dynamics of orientation and speed-selective…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…
This paper defines the spacetime geometry attached with observor as vacuum geometry (it defines the idea physical measurement geometry) and the spacetime geometry attached with matter as spacetime geometry. The initial spacetime geometry…
Both a good understanding of geometrical concepts and a broad familiarity with objects lead to our excellent perception of moving objects. The human ability to detect and segment moving objects works in the presence of multiple objects,…