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 http://www.cs.unr.edu/CVL

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).

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.

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

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

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

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

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

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

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.

Models

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

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

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

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.

Real Images

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. 132-146, 2002. G. Bebis et al., “Indexing Based on Algebraic Functions of Views”, Computer Vision and Image Understanding (CVIU), vol. 72, no. 3, pp. 360-378, 1998. G. Bebis et al., “Learning Affine Transformations”, Pattern Recognition, vol. 32, pp. 1783-1799, 1999. G. Bebis et al., “Algebraic Functions of Views for Model-Based Object Recognition”, International Conference on Computer Vision (ICCV), pp. 634-639, 1998. http://www.cs.unr.edu/CVL