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Multi -Attribute Spaces: Calibration for Attribute Fusion and Similarity Search

This work presents a method for calibrating multi-attribute classifiers to improve image similarity search and attribute fusion techniques. It discusses score normalization to prevent one attribute from dominating results, and introduces statistical approaches such as Weibull distribution for better handling of negative score distributions. With applications to the "Labeled Faces In The Wild" dataset, the study provides insights into joint score computation using attributes and proposes normalization strategies to refine distance measurements for image retrieval.

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Multi -Attribute Spaces: Calibration for Attribute Fusion and Similarity Search

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  1. Multi-Attribute Spaces: Calibration for Attribute Fusion and Similarity Search Walter Scheirer, Neeraj Kumar, Peter N. Belhumeur, Terrance E. Boult, CVPR 2012 5th December 2012 University of Oxford

  2. Attributes based image description 4-Legged White Male Orange Symmetric Asian Striped Ionic columns Beard Furry Classical Smiling Slide Courtesy: Neeraj Kumar

  3. 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

  4. Attributes Fusion FaceTracer: “smiling asian men with glasses” Slide Courtesy: Neeraj Kumar

  5. Score Normalization: Problem • Necessary to prevent high confidence for one attribute from dominating the results. • Ideal normalization technique should, • Normalize scores to a uniform range say, [0,1] • 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

  6. 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 distribution. But, we know something about tail of the negative score distribution.

  7. Extreme Value Theory • Central Limit Theorem: • The “mean” of a sufficiently large iid random variables will be distributedaccording to Normal distribution • 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” distribution.

  8. Weibull Distribution • Weibull Distribution • PDF • CDF • k and λ are shape and location parameters respectively. PDF CDF

  9. Extreme Value Theory: Application Overall Negative Score Distribution Maximum values of random variables Tail • Tail of negative scores can be seen as a collection of maxima of some random • variables. • Hence it follows Weibull distribution according to Extreme Value Theory.

  10. 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.

  11. 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 StudyingFace Recognition in Unconstrained Environments.

  12. Results

  13. 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.

  14. Results

  15. 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.

  16. Summary • 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.

  17. Questions?

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