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What does it mean for a machine to recognize beauty? While beauty remains a culturally and experientially compelling but philosophically elusive concept, deep learning systems increasingly appear capable of modeling aesthetic judgment. In…
Despite remarkable progress in computer vision, modern recognition systems remain fundamentally limited by their dependence on rich, redundant visual inputs. In contrast, humans can effortlessly understand sparse, minimal representations…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
For humans, visual understanding is inherently generative: given a 3D shape, we can postulate how it would look in the world; given a 2D image, we can infer the 3D structure that likely gave rise to it. We can thus translate between the 2D…
Animals build Bayesian 3D models of their surroundings, to control their movements. There is strong selection pressure to make these models as precise as possible, given their sense data. A previous paper has described how a precise 3D…
Selecting the dimensionality reduction technique that faithfully represents the structure is essential for reliable visual communication and analytics. In reality, however, practitioners favor projections for other attractions, such as…
The authors present a visual instrument developed as part of the creation of the artwork Learning to See. The artwork explores bias in artificial neural networks and provides mechanisms for the manipulation of specifically trained for…
The motivation for using qualitative shape descriptions is as follows: qualitative shape descriptions can implicitly act as a schema for measuring the similarity of shapes, which has the potential to be cognitively adequate. Then, shapes…
By comparing biological and artificial perception through the lens of illusions, we highlight critical differences in how each system constructs visual reality. Understanding these divergences can inform the development of more robust,…
The power of neural networks lies in their ability to generalize to unseen data, yet the underlying reasons for this phenomenon remain elusive. Numerous rigorous attempts have been made to explain generalization, but available bounds are…
Physical representations of data offer physical and spatial ways of looking at, navigating, and interacting with data. While digital fabrication has facilitated the creation of objects with data-driven geometry, rendering data as a…
A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
Both humans and deep learning models can recognize objects from 3D shapes depicted with sparse visual information, such as a set of points randomly sampled from the surfaces of 3D objects (termed a point cloud). Although deep learning…
In this paper we provide a first analysis of the research questions that arise when dealing with the problem of communicating pieces of formal argumentation through natural language interfaces. It is a generally held opinion that formal…
Linear Geometry studies geometric properties which can be expressed via the notion of a line. All information about lines is encoded in a ternary relation called a line relation. A set endowed with a line relation is called a liner. So,…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
Visual illusions teach us that what we see is not always what it is represented in the physical world. Its special nature make them a fascinating tool to test and validate any new vision model proposed. In general, current vision models are…
Large vision language models (LVLM) are the leading A.I approach for achieving a general visual understanding of the world. Models such as GPT, Claude, Gemini, and LLama can use images to understand and analyze complex visual scenes. 3D…
Our understanding of how visual systems detect, analyze and interpret visual stimuli has advanced greatly. However, the visual systems of all animals do much more; they enable visual behaviours. How well the visual system performs while…