Analysis of Hyperspectral Image Using Minimum Volume Transform (MVT) Ziv Waxman & Chen Vanunu Instructor: Mr. Oleg Kuybeda
Dec 22, 2015
Analysis of Hyperspectral Image Using
Minimum Volume Transform (MVT)
Ziv Waxman & Chen VanunuInstructor: Mr. Oleg Kuybeda
Objectives:
• Testing the MVT algorithm as a tool of analyzing hyperspectral image.
• Obtain end-members (pure spectral signatures) present in hyperspectral image as output.
Analysis Steps
• Pre-processing: rank and end-members estimation (MOCA algorithm).
• Data Depletion (select data upon convex hull).
• Run MVT (apply linear programming) and concurrently perform constraints depletion.
• Get end-members and compare with
MOCA end-members.
Pre-processing
Data depletion
MVT
MVT end-members
MOCA end-members
compare
Assumptions
• LMM – Linear Mixture Model.
Every pixel is a linear
combination of pure spectral
signatures (end members).
• End members are linearly
independent.
• Pixels-scatter-diagram is
convex. Located in the first
octant (for 3D).
MVT Variants
• Dark Point Fixed (DPFT)
- dark point reliably known.
- better when no bias.
• Fixed Point Free (FPFT)
- dark point not known.
- better when constant bias applied to data.
Pixels-Scatter-Diagram for 3-Bands Dist.• Generally looks like a “tear drop”.
• Pi represent the end members. Define facets of a minimum volume
circumscribing simplex.
O
P3
P2
P1
dark point
This facet is x+y+z=1
data
MVT Algorithm – DPFT
DFPT selected – due to random bias applied by scanner. Create simplex without moving actual data.
Project data onto uTx=1
Data Depletion Create start simplex
Get constraints and deplete them
Rotate k’th facet (linear programming –
simplex method)
k=k+1
k=1
End members
If k=n+1 then k=1
Data Depletion
• Only data points upon the convex hull define a simplex.
• Choose these points by applying variant of Gram-Schmidt orthogonalization process.
• should leave 10% of total data.
Constraints Depletion
• Applied when data depletion process leaves too many points.
• Remove redundant constraints, which do not contribute to creation of feasible region (linear programming).
Feasible region
Feasible region
Synthetic data results
• Blue circled – MOCA end-members• Red points – after data depletion• Azure – MVT end-members
Arial view:
- White noise applied
-Constant bias applied