Title: General%20Tensor%20Discriminant%20Analysis%20and%20Gabor%20Features%20for%20Gait%20Recognition
1General 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
2Outline
- Introduction
- Gabor representation
- Linear discriminant analysis
- General tensor discriminant analysis
- Results (from the paper)
- ISA vs. Gabor features
- Results on video analysis
- Conclusions
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31. Introduction
- The under sample problem (USP) the
dimensionality of the feature space is much
higher than the number of training samples. - 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. - Gabor functions are used as a preprocessing step
for feature extraction in image representation. - 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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42. 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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52. Gabor representation (contd.)
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6- 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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7- 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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8-
-
- 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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9 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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10 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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116. 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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12ISA features (dim 40)
GTDA Gabor features (dim 60)
GTDA ISA features (dim 32)
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13ISA features
GTDA Gabor features
GTDA ISA features
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14Conclusion
- Gabor functions and general tensor discriminant
analysis have been introduced for visual
information processing and recognition. - Tensor gait is also introduced to represent the
Gabor features. - To further take the feature selection into
account, the size of tensor gait is reduced by
the GTDA - Gabor features and ISA are compared in abnormal
event detection.
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