2.5D View models of nonconvex polyhedron on view sphere with perspective M. Frydler : Institute of Mathematical Machines W.S. Mokrzycki : Institute of Computer Science

Abstract Introduction (models, depth maps, identification) Objects representation – View models Creation of view models New algorithm Summary

Solution subject 3D polyhedron objects Present solutions are designed for convex polyhedron and have z(n) = o(n^4) complexity Presented routine designed for nonconvex polyhedrons has been tested on convex polyhedron. It complexity equals z(n) = o(n^2)

Fundamentals: View models, depth maps, identification View models apply in object identification (automatics & robotics) Method of identification : matching database of view models to acquired data (depth maps) How to obtain depth map ? – stereo picture or beam scanning

Objects representation Boundary model, absolute but also the most overflow View models, shows strongest connection with identification task. View model itself seems to be solution.

Adopted view model: set of views obtained from view sphere with central projection Construction : Center of view sphere lies in geometric center of object Radius fit tight to object size and camera parameters Observer is moving over view sphere

Present solutions : Views Models – „One View area” (only for convex polyhedron) View sphere divided in to one view areas „One view” : Movement of observer inside this area do not cause appearance or disappearance of any feature set Complexity z(n) = o(n^4)

Old & New Utilized achievements New ideas Model of View Space (view sphere with central projection) View cone, complementary cone, normal vectors of faces attached to center of view sphere. New ideas 3D space scanning : Rotation of complementary cone in space of view sphere around all faces normals and obtaining new views Elimination of already generated views(Optimal solution)

View models as set of sets of vectors View Model it’s set of separated subsets of normal vectors of polyhedron faces View subset A View subset B

Construction of complementary cone Poprawic,tzn. Przesunąć stozek dopelniający i usunąc 2 i 3 od góry

Algorithm Create empty set A For each vector contained in vector representation of object, scan space around this vector with complementary cone by rotating it around vector. If during scanning visual event will occur, that's mean at last one vector leave or enter cone, then mark all vectors in cone as new View. If it doesn't already belong to set A than add it to this set. Set A contains all Views Tutaj powinien byc film

Summary Algorithm is designed for nonconvex polyhedron It has been tested on convex polyhedron It has lower numerical complexity than others well known algorithms ( for convex polyhedron) Farther works : Modification of algorithm ( nonconvex polyhedron) Tests on new solution Comparing of complexity