General%20Tensor%20Discriminant%20Analysis%20and%20Gabor%20Features%20for%20Gait%20Recognition

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General Tensor Discriminant Analysis and Gabor
Features for Gait Recognition by D. Tao, X. Li,
and J. Maybank, TPAMI 2007 Presented by Iulian
Pruteanu Duke University Machine Learning Group
Friday, June 8th, 2007
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Outline

1. Introduction
2. Gabor representation
3. Linear discriminant analysis
4. General tensor discriminant analysis
5. Results (from the paper)
6. ISA vs. Gabor features
7. Results on video analysis
8. Conclusions

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1. Introduction

1. The under sample problem (USP) the
   dimensionality of the feature space is much
   higher than the number of training samples.
2. General tensor discriminant analysis as a
   preprocessing step for LDA has some benefits
   compared with PCA or simple LDA the USP is
   reduced and the discriminative information in the
   training tensors is preserved.
3. Gabor functions are used as a preprocessing step
   for feature extraction in image representation.
4. The LDA is used for classification combined with
   a dissimilarity measure the distance between the
   gallery sequence and the probe sequence.

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2. Gabor representation

• A Gabor function is the product of an elliptical
  Gaussian envelope and a complex plane wave
• where is the variable in a
  spatial domain and is the frequency vector
  which determines the scale and direction of Gabor
  functions

The real part of Gabor functions (5 scales, 8
directions)
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2. Gabor representation (contd.)
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• given a number of training samples
  in known classes, where
  is the class number, and is
  the sample ID in the class with
  , the aim of LDA is to find a projection
  of the , which is optimal for separating the
  different classes in a low dimensional space.
• we define two scatter matrices
• between-class
• within-class
• the projection
  is chosen such as

3. Linear discriminant analysis
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• if , LDA reduces to the Fisher linear
  discriminant and the solution corresponds to the
  largest eigenvalue of the following equation
  

3. Linear discriminant analysis (contd.)
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• the general tensor discriminant analysis allows
  us to chose the optimal reduction in the feature
  space. The projection matrix has a number of
  columns calculated in order to get the best
  performance.
• if we want to extract features, we estimate
  as , where are
  the largest eigenvalues of
  .

4. General tensor discriminant analysis
tuning parameter
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Alternating projection optimization procedure
for GTDA Step 1 Step 2 Convergence where
is the number of classes (in our case
) and is the current step indicates
the feature dimension which is minimized. The
tuning parameter and the dimension of the
output tensors are determined automatically.
4. General tensor discriminant analysis (contd.)
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The experiments are carried out upon the USF
HumanID outdoor gait (1,870 sequences from 122
subjects). For algorithm training, the database
provides a gallery that has all the 122 subjects,
collected at a separate moment in time. For
testing they use the dissimilarity measure the
distance between the gallery sequence and the
probe sequence.
5. Results (from the paper)
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6. ISA vs. Gabor features

• Gabor functions
• we use Gabor functions with five different
  scales and eight different orientations, making a
  total of forty Gabor functions.

GTDA Gabor features The original Gabor
features dim 80 x 60 x 5 x 8. The GaborSD
features dim 80 x 60. The GTDA GaborSD
features dim 10 x 6. GTDA ISA
features The original ISA features dim
40. The GTDA ISA features dim 32.
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ISA features (dim 40)
GTDA Gabor features (dim 60)
GTDA ISA features (dim 32)
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ISA features
GTDA Gabor features
GTDA ISA features
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Conclusion

1. Gabor functions and general tensor discriminant
   analysis have been introduced for visual
   information processing and recognition.
2. Tensor gait is also introduced to represent the
   Gabor features.
3. To further take the feature selection into
   account, the size of tensor gait is reduced by
   the GTDA
4. Gabor features and ISA are compared in abnormal
   event detection.

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