An Example of an
Approximate Technique

A surface/face based representation has several advantages over contour representations, involving less elements and therefore smaller aspect graphs. The applicability depends on context; a surface based representation is more appropriate for surface based matching against a viewpoint model or for surface inspection. One method which has some justification would be to define as separate aspects each unique subset of visible surfaces. For the case of convex polyhedra this would be equivalent to the line based aspect graph. However, in other cases it would differ.

In this example, we describe the use of cluster analysis to compute VCRs as subsets of surfaces for matching to segmented scene descriptions. This is based not only on unique subsets, but also additional heuristics to limit the number of views present in the final representation. Then we illustrate the automatic generation of VCRs for simulated sensor planning and feature-based inspection of 3D objects. Each is generated from a source CAD model.

We define four attributes of views, which, although not involving direct comparisons between objects, can capture salient object properties. A visibility table is created by raytracing the CAD model from 20, 80, 320 or 1280 viewpoints. From the original model and the visibility table, four continuous measures are derived for each primitive and each viewpoint.

where Ap is the area of a surface primitive, Avp is the area of a primitive visible in a given view, Ao is the total surface area of the object, N(Cp) is the number of adjacent surface pairs in the model, N(Cvp) is the number of adjacent primitives visible in a given view, V is the total number of ray-traced views and Nvp) is the number of views in which a primitive is visible.

Hence, to define the VCR, views are characterised by the partial or complete visibility of primitives, the relative size of primitives, and the proportion of the viewsphere in which the primitive is visible. Covisibility acknowledges the significance of primitive groups (or in this restricted case pairs) in object recognition or location. Here we have adopted heuristics which represent not only the probability of occurrence of features in views, but also measures of how useful these are for object location. For example, pairs of features are necessary to define pose, and segmentation parameters are more accurate in larger patches.


[ Viewer Centred Representations: Contents | Deriving a VCR using cluster analysis ]

Comments to: Sarah Price at ICBL.