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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…

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

Human visual perception is a complex, dynamic and fluctuating process. In addition to the incoming visual stimulus, it is affected by many other factors including temporal context, both external and internal to the observer. In this study…

The goal of this work is to characterize the representational impact that foveation operations have for machine vision systems, inspired by the foveated human visual system, which has higher acuity at the center of gaze and texture-like…

Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…

Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…

Foveal vision makes up less than 1% of the visual field. The other 99% is peripheral vision. Precisely what human beings see in the periphery is both obvious and mysterious in that we see it with our own eyes but can't visualize what we…

Many animals and humans process the visual field with a varying spatial resolution (foveated vision) and use peripheral processing to make eye movements and point the fovea to acquire high-resolution information about objects of interest.…

We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual stimulus and its associated percept. They take place in the…

Humans (and many vertebrates) face the problem of fusing together multiple fixations of a scene in order to obtain a representation of the whole, where each fixation uses a high-resolution fovea and decreasing resolution in the periphery.…

Text-to-image diffusion models generate highly detailed textures, yet they often rely on surface appearance and fail to follow strict geometric constraints, particularly when those constraints conflict with the style implied by the text…

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

Illusions are entertaining, but they are also a useful diagnostic tool in cognitive science, philosophy, and neuroscience. A typical illusion shows a gap between how something "really is" and how something "appears to be", and this gap…

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration…

Identifying covariate shift is crucial for making machine learning systems robust in the real world and for detecting training data biases that are not reflected in test data. However, detecting covariate shift is challenging, especially…

This paper presents a theory for how geometric image transformations can be handled by a first layer of linear receptive fields, in terms of true covariance properties, which, in turn, enable geometric invariance properties at higher levels…

Foveated graphics is a promising approach to solving the bandwidth challenges of immersive virtual and augmented reality displays by exploiting the falloff in spatial acuity in the periphery of the visual field. However, the perceptual…

Variational inference approximates Bayesian posterior distributions by projecting onto a tractable family of distributions. While most theoretical analyses evaluate the quality of this approximation using global divergence measures, many…

Face hallucination, which is the task of generating a high-resolution face image from a low-resolution input image, is a well-studied problem that is useful in widespread application areas. Face hallucination is particularly challenging…

Intermediate feature representations represent the backbone for the expressivity and adaptability of deep neural networks. However, their geometric structure remains poorly understood. In this submission, we provide indirect insights into…