1. 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

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

3. 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)

4. 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

5. 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.

6. 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

7. 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)

8. 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)

9. 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

10. Construction of complementary cone
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11. 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
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12. 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