Related papers: A neuro-mathematical model for geometrical optical…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…

Visual illusions allow researchers to devise and test new models of visual perception. Here we show that artificial neural networks trained for basic visual tasks in natural images are deceived by brightness and color illusions, having a…

Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of…

Linear subspace representations of appearance variation are pervasive in computer vision. This paper addresses the problem of robustly matching such subspaces (computing the similarity between them) when they are used to describe the scope…

Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape…

In fine art, especially painting, humans have mastered the skill to create unique visual experiences through composing a complex interplay between the content and style of an image. Thus far the algorithmic basis of this process is unknown…

Recognition of objects from partial information presents a significant challenge for theories of vision because it requires spatial integration and extrapolation from prior knowledge. We combined neurophysiological recordings in human…

Vast literature on the experiments and mathematical formulations on the geometric phases signifies the importance of this subject. Physical mechanism for the origin of the geometric phases in optics was suggested in 1992 by the author in…

This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

Learning geometry, motion, and appearance priors of object classes is important for the solution of a large variety of computer vision problems. While the majority of approaches has focused on static objects, dynamic objects, especially…

Vision-Language Models (VLMs) are trained on vast amounts of data captured by humans emulating our understanding of the world. However, known as visual illusions, human's perception of reality isn't always faithful to the physical world.…

We present another explanation for the moon illusion, the phenomenon in which the moon looks larger near the horizon than near the zenith. In our model of the moon illusion, the sky is considered a spatially-contiguous and…

Humans have the capacity to question what we see and to recognize when our vision is unreliable (e.g., when we realize that we are experiencing a visual illusion). Inspired by this capacity, we present MetaCOG: a hierarchical probabilistic…

The distinction of chiral and mirror symmetric objects is straightforward from a geometrical point of view. Since the biological as well as the optical activity of molecules strongly depend on their handedness, chirality has recently…

Creating virtual models of real spaces and objects is cumbersome and time consuming. This paper focuses on the problem of geometric reconstruction from sparse data obtained from certain image-based modeling approaches. A number of elegant…

This paper presents an approach for inferring geometric constraints in human demonstrations. In our method, geometric constraint models are built to create representations of kinematic constraints such as fixed point, axial rotation,…

Concave mirrors are fundamental optical elements, yet some easily observed behaviors are rarely addressed in standard textbooks, such as the formation of multiple reflected images. Here we investigate self-imaging -- where the observer is…

Heterogeneous object design is an active research area in recent years. The conventional CAD modeling approaches only provide geometry and topology of the object, but do not contain any information with regard to the materials of the object…