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# Retraining maximum likelihood classifiers using low-rank model.ppt

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### Transcript

• 1. Retraining maximum likelihood classifiers using a low-rank model Arnt-Børre Salberg Norwegian Computing Center Oslo, Norway IGARSS July 25, 2011
• 2. Introduction
• Challenge: Dataset shift problem:
• Training data match the test data poorly due to atmospherical, geographical, botanical and phenological variations in the image data
• -> reduced classification performance
• Class-dependent data distribution varies
• between training images
• between test and training images
• Goal: Develop a method that re-estimates the parameters such that classifier possess a good fit to the test data
• 3. Introduction
• Many surface reflectance algorithms often requires data from external sources
• LEDAPS (Landsat):
• ozone and water vapor measurements
• Phenological, botanical and geographical variation in addition to atmospherical makes the calibration problem even harder
• 4. An existing method…
• Models the test image as a mixture distribution and estimates all parameters using the EM-algorithm, with estimated parameters from training data as initial values
• To many degrees of freedom. Statistic fit is excellent, but class labels get mixed .
• 5. Low-rank parameter modeling
• Training image k :
• Class mean vector and covariance matrix (class i )
• Class mean vector and covariance matrix model for the test image
•  and  are unknown parameter vectors to be estimated from the data
• 6. Low-rank data modeling
• The proposed method for modeling the test data is a low-rank approach since the number of parameters in  is L<D.
• This is much less than estimating all C·D parameters i  i , i=1,…,C
• By using a low-rank estimation of the class mean vectors of the test data, the spectral differences between the classes is in larger degree maintained
• 7. Parameter estimation
• Procedure for estimating  and  
• Select N random samples { y 1, y 2,… y N } from the test image
• 8. Parameter estimation
• Procedure for estimating  and  
• Select N random samples { y 1, y 2,… y N } from the test image
• Model them using a Gaussian mixture distribution
• Estimate the parameters by solving the likelihood
• 9. Experiment 1: Cloud detection in optical images
• 15 different QuickBird and WorldView-2 images covering 7 different scenes in Norway
• Features
• Band 2 (green)
• Band 3 (red)
• Classes
• clouds, cloud shadows, vegetation, concrete/asphalt/etc., haze and water
• Resolution down-sampled to 19.2 m (16.0 m)
• 4 different training (sub)images
• 10. Experiment 1: Cloud detection in optical images
• Model
•  i is the eigenvector corresponding to the largest eigenvalue  i of the matrix
average Test eigenvector
• 11. Experiment 1: Cloud detection in optical images
• Parameter estimation. At iteration l +1 :
• where
• 12. Results: Cloud detection in optical images Without retraining With retraining
• 13. Results: Cloud detection in optical images
• 14. Results: Cloud detection in optical images
• 15. Experiment 2: Tree cover mapping of tropical forest
• 13 different Landsat TM images covering an area nearby Amani, Tanzania (path/row 166/063)
• Features
• Band 1-5 and 7
• Classes
• Forest, spares forest, grass and soil
• Two training images (1986-10-06 and 2010-02-10)
• 16. Experiment 2: Tree cover mapping of tropical forest
• Model
•  constrained to contain only positive elements
• Solution found using non-negative least-squares in combination with iterative maximum-likelihood estimation
• 17. Experiment 2: Tree cover mapping of tropical forest
• Parameter estimation: At iteration l + 1
• where
• 18. Results: Tree cover mapping of tropical forest
• *
Without retraining With retraining February 2010 July 2009
• 19. Summary and conclusion
• Proposed a simple method for handling the dataset shift between training and test data
• Cloud detection: Evaluated successfully on a many different Quickbird and WorldView-2 images.
• Haze versus clouds
• Confuses snow and clouds
• Guidelines on how to select the low-rank modeling functions is needed
• EM-algorithm and local minima problem
• More testing and evalidation of the method is necessary