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Generation of 3D views of polyhedra using view sphere with perspective and complementary cone

Kowalczyk M., Mokrzycki W. S.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2003

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Nr 969

1-24

EN

The paper concerns construction of a complete view representation of 3D exact models of convex polyhedron for a model-based identification system. The system uses 3D views and depth map of the scene. In particular, a new method of view generating is described. The views are of the 3D type, exact, and are made in perspective projection. The method is based on a new concept of a view sphere with perspective and a complementary cone. The object model is generated in a loop: generating feature-dependent views ›determining single-view areas › finding gaps in the view sphere covering › generating missing views (gap views) for filling the gaps › determining single-view areas for the views › return to finding the gaps. The loop terminates when the whole view sphere is covered by the single-view areas. A method of determining single-view areas for convex polyhedra exploring the complementary cone concept is also presented.

PL

Praca niniejsza dotyczy konstruowania kompletnej reprezentacji widokowej trójwymiarowych dokładnych modeli wielościanów wypukłych dla systemu identyfikacyjnego opartego na bazie modeli. Zakłada się, że system taki dostaje jako dane wejściowe widoki 3W i mapę głębi sceny. W pracy opisana jest nowa metoda generowania widoków trójwymiarowych, dokładnych, w rzutowaniu perspektywicznym. Metoda ta wykorzystuje oryginalne koncepcje sfery widokowej z rzutowaniem perspektywicznym oraz stożka dopełniającego.

2

Methods for generating 3D exact views of convex polyhedra for visual identification. Part 2, Non-interative methods, implementation and test results

Kowalczyk M., Mokrzycki W.

Machine Graphics and Vision

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2003

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Vol. 12, No. 4

435-452

EN

This paper is the second part of our study describing methods for obtaining a 3D multiview exact and complete model of convex polyhedra used for visual identification. Non-iterative methods, like the iterative ones, explore the concept of the view sphere with perspective projection and the view sphere covering as a mechanism for representation completeness. The non-iterative methods consist in calculating a view, determining the corresponding single-view area (the so-called seedling single-view area) and then searching for the neighbouring single-view areas (generating the views at the same time) in a spiral way until the whole view sphere is covered by the latter. Having a complete set of the single-view areas (complete view sphere covering), we get a complete set of views as well. Test results and computational complexity estimation are also included.

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Methods for generating 3D exact views of convex polyhedra for visual identification. Part 1, View sphere with perspective projection and interative methods

Kowalczyk M., Mokrzycki W.

Machine Graphics and Vision

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2003

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Vol. 12, No. 4

409-433

EN

The paper studies the methods of generating 3D exact multiview models of convex polyhedra for visual identification systems. In particular, an original view space concept (a view sphere with perspective projection) and the representation completeness controlling concept (a view sphere covering by single-view areas) as well as two groups of methods: iterative (part I of the paper) and non-iterative ones (part II) are characterized. A set of views generated by each method forms a complete view representation which is verified by controlling the view sphere covering by the so called single-view areas). The perspective projection used for calculating the views, the complete, tight covering of the view sphere by the single-view areas and 3-dimensionality of the views ensure unambiguous and proper identification of polyhedral objects. Part I of our study presents the view sphere with perspective projection concept, the view sphere covering by the single-view areas mechanism, and the iterative methods generating feature-dependent views and reaching a complete view set through an iterative process of views generation.