When comparing against a database of objects many interpretations are plausible. We developed a general framework to deal with this ambiguity based on maximum likelihood. We define view likelihood, the probability that a certain view of a given object is observed and view stability, how little the image changes as the viewpoint is moved. We plug in our metric for image similarity into an algorithm that evaluates these new robust measures for recognition. Finally we can use use this likelihood framework to increase the robustness of our object recognition systems.

In order to accomplish the theory of view stability and likelihood, and detect the canonical views of an object (which are its most stable and likely views), a similarity measure between images is desired. We define few similarity measures for silhouettes of curved objects, where shape is the only available information in the image (color and texture clues are missing). Recently, a new similarity measure has been defined, based on partial curve matching. We show how this measure can be used in order to learn representative views from shape examples.

Ronen Basri and Daphna Weinshall.
*
Distance Metric between 3D Models and 2D Images for Recognition
and Classification*
T-PAMI 18(4) 1996

Michael Werman and Daphna Weinshall.
*
Similarity and Affine Invariant Distance Between Point Sets*
T-PAMI 17(8) August 1995.

Daphna Weinshall and Michael Werman.
*
On View Likelihood and Stability*.
To appear in T-PAMI.

Daphna Weinshall, Michael Werman
*
A computational theory of canonical views*
ARPA Image Understanding Workshop, February 1996.

Yoram Gdalyahu, Daphna Weinshall
*
Measures for Silhouettes Resemblance and Representative Silhouettes of Curved Objects*
ECCV-96, Cambridge, April 1996

Given a sequence of images of a set of points in 3D using unknown cameras, there are two fundamental questions that need be solved:

What is the structure of the set of points in 3D?

What are the positions of the cameras relative to the points?

For a projective camera we show that these problems are dual. The imaging of a set of points in space by multiple cameras can be captured by constraint equations involving: space points, camera centers and image points were the space point and camera centers are symmetrical to one another. This formalism in which points and projections are interchangeable, allow both seemingly different problems to be solved with the same algorithms. The dual algebraic formalization for the case of camera centers are the fundamental matrix, trilinear tensor and quadlinear tensor. We can use this approach for algorithms that reconstruct shape and algorithms that learn invariant relations for indexing into an object database.

D. Weinshall, M. Werman, and A. Shashua
*
Shape Tensors for Efficient and Learnable Indexing*
IEEE Workshop on Visual Scene Representation, Boston, June 1995.

Daphna Weinshall
*
Model-based invariants for 3-D vision*
IJCV 10(1),1993

Stefan Carlsson and Daphna Weinshall.
*
Dual Computation of Projective Shape and Camera Positions
from Multiple Images*
HU TR 96-6, 1996.

We study different possible invariant functions such as the shape tensor for this method. And study different efficient methods to find and represent these manifolds. So that given an image measurement we can know which are the possible object it represents by searching which manifolds does this point exist on.

D. Weinshall, M. Werman, and A. Shashua
*
Shape Tensors for Efficient and Learnable Indexing*
IEEE Workshop on Visual Scene Representation, Boston, June 1995.

Michael Werman, Daphna Weinshall
*
Complexity of Indexing: Efficient and Learnable Large Database Indexing
*
ECCV-96, Cambridge, April 1996