A cortical based model of perceptual completion in the roto-translation space
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Publication:851799
DOI10.1007/s10851-005-3630-2zbMath1478.92100OpenAlexW2081720765WikidataQ126281784 ScholiaQ126281784MaRDI QIDQ851799
Giovanna Citti, Alessandro Sarti
Publication date: 22 November 2006
Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)
Full work available at URL: http://amsacta.unibo.it/822/1/corticalpaper4.pdf
Computing methodologies for image processing (68U10) Biomedical imaging and signal processing (92C55) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Methods involving semicontinuity and convergence; relaxation (49J45) Numerical methods for integral transforms (65R10)
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Cites Work
- Long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator
- Balls and metrics defined by vector fields. I: Basic properties
- The visual cortex is a contact bundle
- Subelliptic estimates and function spaces on nilpotent Lie groups
- Lifting vector fields to nilpotent Lie groups
- Hypoelliptic differential operators and nilpotent groups
- Free systems of vector fields
- Approximately differentiable transformations and change of variables on nilpotent groups
- A direct variational approach to a problem arising in image reconstruction
- Segmentation with depth but without detecting junctions
- On the structure of finite perimeter sets in step 2 Carnot groups
- Minimal surfaces in the Heisenberg group
- The geometric Sobolev embedding for vector fields and the isoperimetric inequality
- Hypoelliptic second order differential equations
- AN IMAGE SEGMENTATION VARIATIONAL MODEL WITH FREE DISCONTINUITIES AND CONTOUR CURVATURE
- Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
- On the rothschild-stein lifting theorem
- Filling-in by joint interpolation of vector fields and gray levels
- Subjective surfaces: A method for completing missing boundaries
- Neuronal Oscillations in the Visual Cortex: $\Gamma$-Convergence to the Riemannian Mumford--Shah Functional
- Fundamental solutions for non-divergence form operators on stratified groups
- A notion of rectifiability modeled on Carnot groups
- A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item