Automatic Target Recognition Using Algebraic Functions of Views AFoVs

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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
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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).

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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.
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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

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Framework
Training stage
Recognition stage
Images from various viewpoints
New image
Convex grouping
Convex grouping
Image groups
Model groups
Coarse k-d tree
Access
Compute index
Selection of reference views
compute probabilities using Gaussian mixtures
Index Structure
Retrieve
Using SVD IA
Establish Hypotheses Rank them by probability
Estimate the range of parameter values of AFoVs
Sample space of appearances
Estimate AFoVs parameters
Using constraints
Realistic appearances
Predict appearance
Compute index
Verify predictions
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Experimental Results
3 models 2 views/model group size 5 16
groups/object 3300 sampled views/object
(on average)
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Experimental Results (contd)
novel view
novel view
reference views
reference views
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Experimental Results (contd)
novel view
novel view
reference views
reference views
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Experimental Results (contd)
novel view
novel view
reference views
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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.

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Models
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Verification Results
Group 1, MSE8.0339e-5
Group 2, MSE4.3283e-5
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Verification Results
Group 2, MSE5.3829e-5
Group 1, MSE2.5977e-5
Group 3, MSE5.9901e-5
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Verification Results
Group 1, MSE3.9283e-5
Group 1 (Shift 4), MSE3.3383e-5
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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.

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Real Images
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Related Publications

• 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