Analysis of Hyperspectral Image Using Minimum Volume Transform (MVT)

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Analysis of Hyperspectral Image Using Minimum
Volume Transform (MVT)

• Ziv Waxman Chen Vanunu
• Instructor Mr. Oleg Kuybeda

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Objectives

• Testing the MVT algorithm as a tool of analyzing
  hyperspectral image.
• Obtain end-members (pure spectral signatures)
  present in hyperspectral image as output.

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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
MOCA end-members
Data depletion
MVT
compare
MVT end-members
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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).

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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.

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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.

P2
This facet is xyz1
P1
dark point
data
P3
O
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MVT Algorithm DPFT
DFPT selected due to random bias applied by
scanner. Create simplex without moving actual
data.
Project data onto uTx1
Data Depletion
Create start simplex
k1
Rotate kth facet (linear programming simplex
method)
Get constraints and deplete them
End members
kk1
If kn1 then k1
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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.

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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
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Synthetic data results
Arial view - White noise applied - Constant bias
applied

• Blue circled MOCA end-members
• Red points after data depletion
• Azure MVT end-members

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Real image results

• random bias
• Three images represent
  each end member

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Discussion

• Creates a minimum volume simplex for a given
  data.
• Extremely efficient when bias is constant.
• Preserves rare-vectors MOCA and MVT do not
  ignore abnormalities in an image.
• MVT is very sensitive to random bias.
• Sensitive to noise.