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Retraining maximum likelihood classifiers using low-rank model.ppt
 

Retraining maximum likelihood classifiers using low-rank model.ppt

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    Retraining maximum likelihood classifiers using low-rank model.ppt Retraining maximum likelihood classifiers using low-rank model.ppt Presentation Transcript

    • Retraining maximum likelihood classifiers using a low-rank model Arnt-Børre Salberg Norwegian Computing Center Oslo, Norway IGARSS July 25, 2011
    • 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
    • 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
    • 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 .
    • 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
    • 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
    • Parameter estimation
      • Procedure for estimating  and  
        • Select N random samples { y 1, y 2,… y N } from the test image
    • 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
    • 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
    • Experiment 1: Cloud detection in optical images
      • Model
        •  i is the eigenvector corresponding to the largest eigenvalue  i of the matrix
      average Test eigenvector
    • Experiment 1: Cloud detection in optical images
      • Parameter estimation. At iteration l +1 :
      • where
    • Results: Cloud detection in optical images Without retraining With retraining
    • Results: Cloud detection in optical images
    • Results: Cloud detection in optical images
    • 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)
    • 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
    • Experiment 2: Tree cover mapping of tropical forest
      • Parameter estimation: At iteration l + 1
      • where
    • Results: Tree cover mapping of tropical forest
      • *
      Without retraining With retraining February 2010 July 2009
    • 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