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In this paper we present a novel model of the primary visual cortex (V1) based on orientation, frequency and phase selective behavior of the V1 simple cells. We start from the first level mechanisms of visual perception: receptive profiles.…
In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit…
We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches embedding the sub-Riemannian heat kernel…
Image completion techniques have made significant progress in filling missing regions (i.e., holes) in images. However, large-hole completion remains challenging due to limited structural information. In this paper, we address this problem…
In Fourier ptychography, multiple low resolution images are captured and subsequently combined computationally into a high-resolution, large-field of view micrograph. A theoretical image-formation model based on the assumption of plane-wave…
We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…
Multi-domain data are widely leveraged in vision applications taking advantage of complementary information from different modalities, e.g., brain tumor segmentation from multi-parametric magnetic resonance imaging (MRI). However, due to…
Humans are excellent at perceiving illusory outlines. We are readily able to complete contours, shapes, scenes, and even unseen objects when provided with images that contain broken fragments of a connected appearance. In vision science,…
We introduce a new diffusion-based approach for shape completion on 3D range scans. Compared with prior deterministic and probabilistic methods, we strike a balance between realism, multi-modality, and high fidelity. We propose DiffComplete…
In this paper we propose a deep learning approach for segmenting sub-cortical structures of the human brain in Magnetic Resonance (MR) image data. We draw inspiration from a state-of-the-art Fully-Convolutional Neural Network (F-CNN)…
The adoption of "human-in-the-loop" paradigms in computer vision and machine learning is leading to various applications where the actual data acquisition (e.g., human supervision) and the underlying inference algorithms are closely…
Multimodal medical images play a crucial role in the precise and comprehensive clinical diagnosis. Diffusion model is a powerful strategy to synthesize the required medical images. However, existing approaches still suffer from the problem…
Visual reconstruction algorithms are an interpretive tool that map brain activity to pixels. Past reconstruction algorithms employed brute-force search through a massive library to select candidate images that, when passed through an…
We propose a data-driven method for recovering miss-ing parts of 3D shapes. Our method is based on a new deep learning architecture consisting of two sub-networks: a global structure inference network and a local geometry refinement…
Equipping the rototranslation group $SE(2)$ with a sub-Riemannian structure inspired by the visual cortex V1, we propose algorithms for image inpainting and enhancement based on hypoelliptic diffusion. We innovate on previous…
Recent advances in diffusion models have demonstrated their remarkable ability to capture complex image distributions, but the geometric properties of the learned data manifold remain poorly understood. We address this gap by introducing a…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
Purpose: To introduce a novel deep learning based approach for fast and high-quality dynamic multi-coil MR reconstruction by learning a complementary time-frequency domain network that exploits spatio-temporal correlations simultaneously…
Image completion with large-scale free-form missing regions is one of the most challenging tasks for the computer vision community. While researchers pursue better solutions, drawbacks such as pattern unawareness, blurry textures, and…
Image completion is a task that aims to fill in the missing region of a masked image with plausible contents. However, existing image completion methods tend to fill in the missing region with the surrounding texture instead of…