Related papers: A neuro-mathematical model for geometrical optical…
Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds.…
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
How do different brains create unique visual experiences from identical sensory input? While neural representations vary across individuals, the fundamental architecture underlying these differences remains poorly understood. Here, we…
We consider a differential model describing neuro-physiological contrast perception phenomena induced by surrounding orientations. The mathematical formulation relies on a cortical-inspired modelling [10] largely used over the last years to…
Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…
The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper…
In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are…
State-of-the-art object pose estimation methods are prone to generating geometrically infeasible pose hypotheses. This problem is prevalent in dexterous manipulation, where estimated poses often intersect with the robotic hand or are not…
Making inferences from partial information constitutes a critical aspect of cognition. During visual perception, pattern completion enables recognition of poorly visible or occluded objects. We combined psychophysics, physiology and…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
Computational modeling helps neuroscientists to integrate and explain experimental data obtained through neurophysiological and anatomical studies, thus providing a mechanism by which we can better understand and predict the principles of…
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…
The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts…
Decomposing geometry, materials and lighting from a set of images, namely inverse rendering, has been a long-standing problem in computer vision and graphics. Recent advances in neural rendering enable photo-realistic and plausible inverse…
Color constancy and color illusion perception are two phenomena occurring in the human visual system, which can help us reveal unknown mechanisms of human perception. For decades computer vision scientists have developed numerous color…
Visual illusions in humans arise when interpreting out-of-distribution stimuli: if the observer is adapted to certain statistics, perception of outliers deviates from reality. Recent studies have shown that artificial neural networks (ANNs)…
Human figures have been animated using a variety of geometric models including stick figures, polygonal models, and NURBS-based models with muscles, flexible skin, or clothing. This paper reports on experimental results indicating that a…
Humans possess a remarkable capacity to recognize and manipulate abstract structure, which is especially apparent in the domain of geometry. Recent research in cognitive science suggests neural networks do not share this capacity,…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…