1. www.nr.no earthobs.nr.no Retraining maximum likelihood classifiers using a low-rank model Arnt-Børre Salberg Norwegian Computing Center Oslo, Norway IGARSS July 25, 2011

2. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no Parameter estimation ► Procedure for estimating  and  ▪Select N random samples {y 1, y 2,… y N } from the test image

8. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no Experiment 1: Cloud detection in optical images ► Parameter estimation. At iteration l +1: where

12. www.nr.no earthobs.nr.no Results: Cloud detection in optical images Without retrainingWith retraining

13. www.nr.no earthobs.nr.no Results: Cloud detection in optical images

14. www.nr.no earthobs.nr.no Results: Cloud detection in optical images

15. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no 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. www.nr.no earthobs.nr.no Experiment 2: Tree cover mapping of tropical forest ► Parameter estimation: At iteration l + 1 where

18. www.nr.no earthobs.nr.no Results: Tree cover mapping of tropical forest ►* ►* Without retrainingWith retraining February 2010 July 2009

19. www.nr.no earthobs.nr.no 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