Application

Construction

Demos

References

** Aspect** is the topological appearance of an object. Appearance to the eye, esp, when seen from a specific view.

** Viewpoint Space Partition** is a partition of viewpoint space into maximal regions of constant aspect.

** Event** is a change in topological appearance. Represent boundaries of viewpoint space partition.

** Aspect Graph** is a graph with a node for every aspect and edges connecting adjacent aspects. The

Aspect graphs can be made for:

Prev | NextAn early application of aspect graphs:

How will an L-shaped object look from different regions of a cube?

Perspective Model | | | Orthographic Model |

More Freedom Viewpoint can be anywhere! | Aspect Graph is easier! Viewpoint can be thought of as being restricted to a certain type of surface.What kind of surface??? |

Images can be compared in **parallel**.

What is Visible?

At what point might you need to include a new image?

Prev | Next

Compute the VSP in 3-space for the object to be recognized. Since each region of the VSP has constant aspect, make a characteristic view for each region. Use these characteristic views to compare against the input image.

Images can be compared in **parallel**.

4-sided polygon

5-sided polygon

Maximum size of the VSP ----------------------- Convex Non-convex Polyhedra Polyhedra ------------------------------------------ Orthographic O(n^2) O(n^6) Perspective O(n^3) O(n^9) Construction time of the VSP & aspect graph ------------------------------------------- Convex Non-convex Polyhedra Polyhedra -------------------------------------------- Orthographic O(n^2) O(n^6 log n) Perspective O(n^3) O(n^9 log n)

Precompuation: - Compute the aspect graph. Catalog all VE events found Runtime: --let A be the aspect graph containing B boundaries --let S be the set of visible polygons --let B be the set of polygons added or deleted by crossing boundary 1. Find region containing viewpoint. 2. S = {visible polygons from that region} 3. while(!done) (wait for mouse input) forall B in A if (viewpoint crossed region boundary) S = S + B (eg. S = S + p1 + p2 - p3 -p4) render S 4. end

References

[2] Ziv Gigus and Jitendra Malik. Computing the Aspect Graph for Line Drawings of Polyhedral Objects. *IEEE Transactions on Pattern Analysis and Machine Intelligence*, Vol. 12, No. 2, February 1990.

[3] Ziv Gigus and John Canny. Efficiently Computing and Representing Aspect Graphs of Polyhedral Objects. *IEEE Transactions on Pattern Analysis and Machine Intelligence*, Vol. 13, No. 6, June 1991.

[4] Harry Plantinga and Charles Dyer. Visibility, Occlusion, and the Aspect Graph. *Int. J. of Computer Vision*, 5:2, 137-1609 (1990).