Trace Inference, Curvature Consistency, and Curve Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Perceptual Organization of Texture Flow: A Contextual Inference Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Euler Spiral for Shape Completion
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Hue geometry and horizontal connections
Neural Networks - 2004 Special issue Vision and brain
A Cortical Based Model of Perceptual Completion in the Roto-Translation Space
Journal of Mathematical Imaging and Vision
Differentiation of discrete multidimensional signals
IEEE Transactions on Image Processing
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We investigate solutions to the minimal surface problem with Dirichlet boundary conditions in the roto-translation group equipped with a sub-Riemannian metric. By work of G. Citti and A. Sarti, such solutions are completions of occluded visual data when using a model of the first layer of the visual cortex. Using a characterization of smooth non-characteristic minimal surfaces as ruled surfaces, we give a method to compute a minimal spanning surface given fixed boundary data presuming such a surface exists. Moreover, we describe a number of obstructions to existence and uniqueness but also show that under suitable conditions, smooth minimal spanning surfaces with good properties exist. Not only does this provide an explicit realization of the disocclusion process for the neurobiological model, but it also has application to constructing disocclusion algorithms in digital image processing.