1. Non-linear fully-constrained spectral
unmixing.
Rob Heylen, Dẑevdet Burazerović, Paul Scheunders
IBBT-Visionlab, University of Antwerp, Belgium
IGARSS 2011
July 25-29, Vancouver, Canada
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2. Outline
• Introduction: Spectral unmixing
• Non-linear endmember extraction
• Distance-based unmixing algorithm
• Results
• Conclusions and future work
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3. Spectral unmixing
The linear mixing model
Non-linear mixing models are far more generic
One does not always know the function F:
• Model-based unmixing
• Data-driven manifold techniques
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4. Non-linear unmixing
A data driven, fully-constrained non-linear
unmixing method:
• Endmember extraction by combining graph-
based manifold learning with N-findR.
• Unmixing via a distance-geometry based fully-
constrained unmixing algorithm, applied to the
geodesic distances.
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5. Distance geometry
All properties are expressed as (Euclidean)
distances between the constituents.
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6. Endmember extraction
• Rewrite N-findR to work with mutual distances.
e.g.:
• Use approximate geodesic distances on the
data manifold: Shortest-path distances in
nearest-neighbor graph
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7. Endmember extraction
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8. Non-linear unmixing
Next step: Unmix the data to find abundances of
each pixel.
Aim: Use geodesic distance matrix as input of
the unmixing algorithm.
The DSPU algorithm is fit for this task.
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9. The minimization problem
Linear spectral unmixing can be viewed as a
minimization problem
Simplex projection is equivalent problem:
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10. Simplex projection unmixing
Recursive simplex projection unmixing (SPU)
algorithm:
1. Project the point orthogonally onto the
simplex plane.
2. If the point lies inside the simplex, finish.
3. Else, find which abundance has to be zero.
4. Remove the endmember from the set of
endmembers and go to step 1.
Can be expressed in distance geometry: DSPU
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11. Results: Cuprite data set
• Cuprite data set
• Linear unmixing via N-findR and FCLSU/DSPU
• Non-linear unmixing via the proposed method
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12. Cuprite: Linear unmixing
Typical situation: 99.7% of abundances differ by
less than 10-7 . E.g. for the alunite endmember:
FCLSU DSPU
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13. Cuprite: Non-linear EEA
Kaolinite 0.056, Montmorrilonite 0.048, Alunite 0.043
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14. Cuprite: Non-linear unmixing
Alunite endmember:
N-findR + FCLSU Non-lin. EEA + DSPU
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15. Conclusions and future work
• A data-driven non-linear unmixing algorithm.
• Promising results on artificial data.
• Significant deviations from linear unmixing
results. Hard to quantify on Cuprite data set.
• Assess method on non-linearly mixed data with
ground truth.
• Lots of testing
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