1. Robust supervised image classifiers by spatial AdaBoost based on robust loss functions Ryuei Nishii and Shinto Eguchi Proc. Of SPIE Vol. 5982 59820D-2

2. terminology Supervised image classification A prior knowledge of your image area is required. Loss function A function that maps an event onto a real number representing the cost or regret associated with the event. Contextual Related to neighborhoods of the pixel Markov Random Fields(MRF)

3. Real Adaboost with multiclass Adaboost combines week classifiers into a weighted voting machine. possible categories. category label Let be a training region with n pixels. Let be m-dimensional feature vector. is its true label.

4. Loss function : classification function of feature vector a label in the label set Exponential loss function

5. Empirical risks The average of the loss functions evaluated by the training data set Exponential risk AdaBoost aim to minimize the exponential risk.

6. Real AdaBoost procedure 1. A weak classifier and coefficient which minimize the empirical risk,says and. 2. Consider. Then find the optimal class and the coefficient which minimize the empirical risk, says and. 3. This is repeated T-times. Final classifier

7. Neighborhoods and contextual classifiers We add contextual classifiers to the set of noncontextual classifiers. Define a subset of. First-order neighbor Second-order neighbor

8. Neighborhoods and contextual classifiers

9. Contextual classifiers Average of posteriors probabilities in the subset Noncontextual classification The importance of the posteriors

10. Improvement The classifier give a poor result for some data when exponential loss puts too big penalty for misclassified data. Logit loss function gives a linear penalty for misclassified data approximately.

11. Example: two-category case(1) For the two-category (g=2), put the label set {1,-1} True label If, then is classified into the label 1,otherwise into -1. If, the vector is misclassified.

12. Example: two-category case(2) Loss function

13. Conclusion To substitute the exponential loss function to more robust loss function, e.g., the logit loss function.