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Learning Globally-Consistent Local Distance Functions for Shape-Based
Image Retrieval and Classification
Computer Vision, 2007. ICCV 2007. IEEE 11th International Conference on
Andrea Frome , EECS, UC BerkeleyYoram Singer, Google, Inc
• Introduction• Training step• Testing step• Experiment & Result• Conclusion
Outline
• Introduction• Training step• Testing step• Experiment & Result• Conclusion
What we do?
• Goal– classify an image to a more appropriate category
• Machine learning• Two steps– Training step– Testing step
Outline
• Introduction
• Training step• Testing step• Experiment & Result• Conclusion
Flow chart: training
Generate features each image from dataset, ex: SIFT or geometric blur
Input distances to SVM for training , evaluate W
Compute distance dji, dki
Flow chart: training
Generate features each image from dataset, ex: SIFT or geometric blur
Input distances to SVM for training , evaluate W
Compute distance dji, dki
Choosing features
• Dataset: Caltech101• Patch-based Features– SIFT• Old school
– Geometric Blur• It’s a notion of blurring• The measure of similarity between image patches• The extension of Gaussian blur
Geometric blur
Flow chart: training
Generate features each image from dataset, ex: SIFT or geometric blur
Input distances to SVM for training , evaluate W
Compute distance dji, dki
Triplet
• dji is the distance from image j to i• It’s not symmetric, ex: dji ≠ dij• dki > dji
dji dki
How to compute distance
• L2 norm
12
3
dji, 1
m features
dji, 1distance vector dji
Image j
Image i
Example
• Given 101 category, 15 images each category101*15
Feature j
101*15
distance vector
distance vector
Image j vs training data
Flow chart: training
Generate features each image from dataset, ex: SIFT or geometric blur
Input distances to SVM for training , evaluate W
Compute distance dji, dki
Machine learning: SVM
• Support Vector Machine• Function: Classify prediction• Supervised learning• Training data are n dimension vector
Example
• Male investigate– Annual income– Free time
• Have girlfriend?
Ex: Training data
spacefree
income
vector
Mathematical expression(1/2)
Mathematical expression(2/2)
Support vector
Model
free
income
But the world is not so ideal.
Real world data
Hyper-dimension
Error cut
SVM standard mathematical expression
Trade-off
In this paper
• Goal: to get the weight vector W
101*15
feature
Image weight wj of W wj, 1
wj
Visualization of the weights
How to choose Triplets?
• Reference Image– Good friend - In the same class– Bad friend - In the different class
• Ex: 101category, 15 images per category– 14 good friends & 15*100(1500) bad friends– 15*101(1515) reference images– total of about 31.8 million triplets
Mathematical expression(1/2)
• Idealistic: • Scaling:• Different:
The length of Weight i
0 0
triplet
Mathematical expression(2/2)
• Empirical loss:
• Vector machine:
Dual problem
•
•
Dual variable
• Iterate the dual variables:
Early stopping
• Satisfy KTT condition– In mathematics, a solution in
nonlinear programming to be optimal.• Threshold– Dual variable update falls below a value