We introduce and study a two-dimensional model for the reconstruction of a smooth generic three-dimensional scene E, which may handle the self-occlusions and that can be considered as an improvement of the 2.1D sketch of Nitzberg and Mumford. We characterize from the topological viewpoint the apparent contour of E, namely, we characterize those planar graphs G that are apparent contours of some scene E. Moreover, we show that if E and F are two of these scenes, then E and F differ by a global homeomorphism which is strictly increasing on each fiber along the direction of the eye of the observer. These two topological theorems allow to find the domain of the functional F describing the model. Compactness, semicontinuity and relaxation properties of F are then studied, as well as connections of our model with the problem of completion of hidden contours.

Bellettini, G., Beorchia, V., Paolini, M., Topological and variational properties of a model for the reconstruction of three-dimensional transparent images with self-occlusions, <<JOURNAL OF MATHEMATICAL IMAGING AND VISION>>, 2008; (32): 265-291 [http://hdl.handle.net/10807/19383]

Topological and variational properties of a model for the reconstruction of three-dimensional transparent images with self-occlusions

Bellettini, Giovanni;Beorchia, Valentina;Paolini, Maurizio
2008

Abstract

We introduce and study a two-dimensional model for the reconstruction of a smooth generic three-dimensional scene E, which may handle the self-occlusions and that can be considered as an improvement of the 2.1D sketch of Nitzberg and Mumford. We characterize from the topological viewpoint the apparent contour of E, namely, we characterize those planar graphs G that are apparent contours of some scene E. Moreover, we show that if E and F are two of these scenes, then E and F differ by a global homeomorphism which is strictly increasing on each fiber along the direction of the eye of the observer. These two topological theorems allow to find the domain of the functional F describing the model. Compactness, semicontinuity and relaxation properties of F are then studied, as well as connections of our model with the problem of completion of hidden contours.
Inglese
Bellettini, G., Beorchia, V., Paolini, M., Topological and variational properties of a model for the reconstruction of three-dimensional transparent images with self-occlusions, <<JOURNAL OF MATHEMATICAL IMAGING AND VISION>>, 2008; (32): 265-291 [http://hdl.handle.net/10807/19383]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/19383
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