1. Automatic Target Recognition Using Algebraic Functions of Views (AFoVs)
George Bebis and Wenjing Li
Computer Vision Laboratory
Department of Computer Science
University of Nevada, Reno

2. Main Goal
The main goal of this project is to improve the performance of Automatic Target Recognition (ATR) by developing a more powerful ATR frame work which can handle changes in the appearance of a target more efficiently and robustly. The new framework will be built around a hybrid model of appearance by integrating (1) Algebraic Functions of Views (AFoVs), a powerful mathematical model of geometric appearance, with (2) eigenspace representations, a well known empirical model of appearance which has demonstrated significant capabilities in recognizing complex objects under no occlusion. This project is sponsored by The office of Naval Research (ONR).

3. Problem
We address the problem of 3D object recognition from 2D images assuming that:
viewpoint is arbitrary
3D structure information is not available
Given some knowledge of how certain objects may appear and an image of a scene possibly containing those objects, report which objects are present in the scene and where.

4. Objectives
Couple AFoVs with eigenspace representation for enhanced hypothesis generation and verification
Integrate AFoVs with grouping for robust feature extraction and efficient hypothesis generation
Integrate AFoVs with indexing to bypass the correspondence problem and enable efficient searching
Integrate AFoVs with probabilistic hypothesis generation
Integrate AFoVs with incremental learning
Design a methodology for choosing a sparse set of reference views
Extend AFoVs to other types of imagery

5. Framework Training stage Recognition stage Index Structure Images from
various viewpoints
New image
Convex grouping
Convex grouping
Model groups
Image groups
Coarse k-d tree
Access
Compute index
Selection of reference
views
compute probabilities using Gaussian mixtures
Index
Structure
Using SVD & IA
Retrieve
Estimate the range of
parameter values of AFoVs
Establish Hypotheses
Rank them by probability
Sample space of appearances
Estimate AFoVs parameters
Using constraints
Realistic appearances
Predict appearance
Compute index
Verify predictions

6. Experimental Results 3 models 2 views/model group size: 5
16 groups/object
3300 sampled views/object
(on average)

7. Experimental Results (cont’d)
novel view
novel view
reference views
reference views

8. Experimental Results (cont’d)
novel view
novel view
reference views
reference views

9. Experimental Results (cont’d)
novel view
novel view
reference views

10. Work in Progress
Employ a scheme for selecting “good” groups of features.
Devise a method for selecting the reference views.
Reject unrealistic appearances from index table.
Employ improved indexing schemes (e.g., K-d trees).
Represent object appearance more compactly.
Reduces space requirements considerably.
Develop a probabilistic hypothesis generation scheme.
Use probabilistic models to represent geometric model appearance.
Combine geometric and empirical models of appearance.
Can improve hypothesis generation and verification.

11. Models

12. Verification Results
Group 1, MSE=8.0339e-5
Group 2, MSE=4.3283e-5

13. Verification Results Group 2, MSE=5.3829e-5 Group 1, MSE=2.5977e-5

14. Verification Results Group 1, MSE=3.9283e-5
Group 1 (Shift 4), MSE=3.3383e-5

15. Combine Geometric and Empirical Models of Appearance
Current AFoVs framework predicts geometric appearance.
Extend AFoVs framework to predict empirical appearance.
Integrate geometric with empirical appearance.
Improve both hypothesis generation and verification.

16. Real Images

17. Related Publications http://www.cs.unr.edu/CVL
G. Bebis et al., “Genetic Object Recognition Using Combinations of Views”, IEEE Transactions on Evolutionary Computing, vol. 6, no. 2, pp , 2002.
G. Bebis et al., “Indexing Based on Algebraic Functions of Views”, Computer Vision and Image Understanding (CVIU), vol. 72, no. 3, pp , 1998.
G. Bebis et al., “Learning Affine Transformations”, Pattern Recognition, vol. 32, pp , 1999.
G. Bebis et al., “Algebraic Functions of Views for Model-Based Object Recognition”, International Conference on Computer Vision (ICCV), pp , 1998.