For a subgroup Γ of the linear group of IR d , we describe the Γ-orbit closures of points of IR d... more For a subgroup Γ of the linear group of IR d , we describe the Γ-orbit closures of points of IR d in terms of the limit set of Γ in the projective space IP d−1 , under proximality and irreducibility conditions. In particular, we show the minimality of the action of Γ on the corresponding asymptotic set in the linear space when Γ is a Schottky group.
A rapid and automatic iterative corner extraction and matching for 2D mosaic construction is pres... more A rapid and automatic iterative corner extraction and matching for 2D mosaic construction is presented. This new system progressively estimates the geometric transformation parameters between two misaligned images. It combines corner extraction, matching, and transformation parameters estimation into an iterative scheme. By aligning the images in successive iterations, accuracy improves significantly. The accurately aligned images are used to re-extract new features, which are subsequently matched to select correspondences used to estimate a transformation with n-degrees of freedom. The false correspondences are suppressed progressively to achieve an accurate transformation estimate. The system is used to construct a mosaic from two misaligned images. The performance of the system is demonstrated experimentally using various images of differing complexity.
We describe necessary and sufficient conditions for orbits of linear transformations onR n ,n≥1, ... more We describe necessary and sufficient conditions for orbits of linear transformations onR n ,n≥1, and sets arising as sums of elements from orbits, to be harmonious subsets. This is done via a generalization of the notion of Pisot-Vijayaraghavan and Salem numbers.
For a subgroup Γ of the linear group of IR d , we describe the Γ-orbit closures of points of IR d... more For a subgroup Γ of the linear group of IR d , we describe the Γ-orbit closures of points of IR d in terms of the limit set of Γ in the projective space IP d−1 , under proximality and irreducibility conditions. In particular, we show the minimality of the action of Γ on the corresponding asymptotic set in the linear space when Γ is a Schottky group.
A rapid and automatic iterative corner extraction and matching for 2D mosaic construction is pres... more A rapid and automatic iterative corner extraction and matching for 2D mosaic construction is presented. This new system progressively estimates the geometric transformation parameters between two misaligned images. It combines corner extraction, matching, and transformation parameters estimation into an iterative scheme. By aligning the images in successive iterations, accuracy improves significantly. The accurately aligned images are used to re-extract new features, which are subsequently matched to select correspondences used to estimate a transformation with n-degrees of freedom. The false correspondences are suppressed progressively to achieve an accurate transformation estimate. The system is used to construct a mosaic from two misaligned images. The performance of the system is demonstrated experimentally using various images of differing complexity.
We describe necessary and sufficient conditions for orbits of linear transformations onR n ,n≥1, ... more We describe necessary and sufficient conditions for orbits of linear transformations onR n ,n≥1, and sets arising as sums of elements from orbits, to be harmonious subsets. This is done via a generalization of the notion of Pisot-Vijayaraghavan and Salem numbers.
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Papers by Dani Salem