The proposed approach has been demonstrated using real 3D objects shown in Fig. 1. Each object was represented from a particular aspect only using two reference views. Both reference views  have many features in common. The second reference view was obtained by rotating the object about the y-axis by a small angle (10-20 degrees). Knowledge of rotation between the reference views allow us to enforce the rigidity constraints. In these experiments, we used groups containing 6 point features. These groups were formed by two adjacent convex groups of size 4. The groups extracted are highlighted by yellow lines in Fig. 1. To order the points in a group during recognition, we choose the common points as starting points and trace the rest of points counterclockwise. A spare set of 3118 sampled views of the groups were represented in a k-d tree. The manifold of each group was then learned using the EM algorithm. The ratio of sparse to dense views used in this case was 33%.

Figure 1. Five model objects with two reference views per object

Fig. 2 shows some of the test views used in our experiments. Group of point features are extracted from the scene and used to retrieved hypothetical matches from the k-d tree. Each hypothesis is then ranked using the mixture models of the model groups. The verification results can be seen in Fig. 2 where yellow lines correspond to scene groups and the red lines to the predicted models. The MSE error was less than 8 pixels.

Figure 2 Test views & verification results