Slides (PPT) - University of Oxford

Multi-Attribute Spaces: Calibration for Attribute
Fusion and Similarity Search
Walter Scheirer, Neeraj Kumar, Peter N. Belhumeur, Terrance E. Boult,
CVPR 2012
University of Oxford
5th December 2012
Attributes based image description
Ionic columns
Slide Courtesy: Neeraj Kumar
Attribute Classifiers
Attribute and Simile Classifiers for Face Verification
N. Kumar, A. C. Berg, P. N. Belhumeur, and S. K. Nayar
ICCV 2009
FaceTracer: A Search Engine for Large Collections of Images with Faces
N. Kumar, P. N. Belhumeur, and S. K. Nayar
ICCV 2009
Attributes Fusion
FaceTracer: “smiling asian men with glasses”
Slide Courtesy: Neeraj Kumar
Score Normalization: Problem
• Necessary to prevent high confidence for one attribute
from dominating the results.
• Ideal normalization technique should,
1) Normalize scores to a uniform range say, [0,1]
2) Assign perceptual quality to the scores.
• Positive and negative distributions of different classifiers do
not necessarily follow same distribution.
• Fitting a Gaussian or any other distribution to scores
satisfies condition 1 but doesn’t satisfy condition 2.
Negative Scores Distributions
Positive Scores Distributions
Score Normalization: Solution
• Model distance between positive scores and the negative
scores .
• If we knew distribution of negative scores, we could do a
hypothesis test for each positive score using that distribution.
• Unfortunately, we don’t know anything about overall negative
But, we know something about tail of the negative score
Extreme Value Theory
• Central Limit Theorem:
• The “mean” of a sufficiently large iid random
variables will be distributed according to Normal
• Extreme Value Theory:
• The maximum of a sufficiently large iid random
variable will be distributed according to Gumbell,
Frechet or Weibull distribution.
• If the values are bounded from above and below, the
the values are distributed according to “Weibull”
Weibull Distribution
• Weibull Distribution
k and λ are shape and location parameters respectively.
Extreme Value Theory: Application
Overall Negative Score Distribution
Maximum values of random variables
• Tail of negative scores can be seen as a collection of maxima of some random
• Hence it follows Weibull distribution according to Extreme Value Theory.
W-score normalization: Procedure
For any classifier,
• Fix the decision boundary on the scores
(Ideally this should be at score = 0 )
• Select maximum N (tail size) samples from
negative side of the boundary.
• Fit a Weibull Distribution to these tail scores.
• Renormalize scores using Cumulative Density Function
(CDF) of this Weibull distribution.
Results: Dataset
• “Labeled Faces In The Wild” dataset.
• About 13,000 images of 5000 celebrities.
• 75 different attribute classification scores available from
“Attribute and Simile Classifiers for Face Verification”. Kumar et al. ICCV 09.
Labeled Faces in the Wild: A Database for Studying Face Recognition in Unconstrained
Multi Attribute Fusion:
• Joint score can be computed as multiplication of individual
attribute probabilities.
• Attributes may not be independent.
• Low probability due to:
• bad classifier
• absence of images belonging to an attribute.
• Instead of product, authors propose use l1 norm of
probabilities as a fusion score.
Similarity Search:
• Given an image and a set of attributes, find nearest images.
• Perceived difference between images in different ranges
might be similar.
• Distances between query attribute and its nearest neighbor
needs to be normalized.
• Normalize query attribute scores on query image.
• Get nearest neighbor distances.
• Fit Weibull distribution to distances.
• Provides way of normalizing scores intuitively.
• Provides way for combining attributes.
• Relies on finding the right threshold and tail size. Requires
fair bit of tuning.

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