Light Field Mapping:

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Light Field Mapping

• Hardware-Accelerated Visualization of Surface
  Light Fields

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What is a Surface Light Field?

• 4-D Function f (r, s, T, F)
• Defines radiance of every point on surface of an
  object in every viewing direction
• (r,s) Describe surface location
• (T, F) Describe viewing location
• In practice, almost always discrete

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Proposed Approach

• f (r, s, T, F) ? gk(r,s) hk(T, F) (eq 1)

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Surface Light Field Approximation

• Approximation algorithms assume data given as 4-D
  grid
• f (rp, sp, Tq, Fq)
• p 1, , M discrete values of surface location
• q 1, , N discrete values of viewing angles

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Surface Light Field Approximation

• f (rp, sp, Tq, Fq) ? gk(rp,sp) hk(Tq, Fq) (eq
  2)
• Only practical if of terms is small
• Difficult to find good approximation to complete
  SLF using few summation terms

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Surface Light Field Approximation

• Instead, surface of object partitioned into
  smaller units
• By decomposing SLF of each unit, close
  approximation of original data obtained
• Allows for efficient storage and fast rendering

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Using Singular Value Decomposition

• Use SVD to factor SLF
• This method more robust, optimal
• To apply, 4D SLF must be rearranged into matrix

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Approximation Through SVD

• F P USVT
• U square matrix (uk)
• V square matrix (vk)
• S diagonal matrix (sk)
• USVT ?skukvkT (eq 4)

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Triangle-Centered Approximation

• Partition light field function into individual
  triangles
• f (r, s, T, F) ? ??i (r,s) f (r, s, T, F) (eq
  5)
• T azimuth angle
• F elevation angle
• This is the triangle light field
• When rendered, produces visible discontinuities
  at triangle edges

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Vertex-Centered Approximation

• To eliminate discontinuities, partition SLF
  around every vertex
• f (r, s, T, F) ? ?vj (r,s) f (r, s, T, F) (eq
  8)
• In this method, each triangle shares light field
  maps with neighboring triangles

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Representation of Light Field Maps

• 2D texture representation of surface map as Gk
  (s,t)
• 2D texture representation of view map as Hk (x,y)
• Texture coordinate computation
• X(dx 1) /2 (eq 13)
• Y(dy 1) /2

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Rendering Algorithm

• Triangle-centered vertex centered approaches
  differ only in how each individual approximation
  term is evaluated
• Surface map coordinates for both do not need to
  be recomputed
• View map coordinates recomputed every time view
  changes

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Rendering Algorithm

• Now evaluate kth approximation term
• Triangle-centered multiply pixel-by-pixel image
  projections of 2 texture fragments
• Vertex-centered multiply pixel-by-pixel 3 pairs
  of light field maps from each vertex and add
  together

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Hardware Accelerated Implementation

• Pixel-by-pixel approach (modulation)
  multiplication of surface map fragment by view
  map fragment
• Multitexturing hardware support allows for
  effective modulation of two texture fragments in
  one rendering pass
• K-term approximation
• K rendering passes for triangle-centered
• 3K rendering passes for vertex-centered

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Data Acquisition

• First images are captured under fixed lighting
  conditions (200-400 images)
• Object geometry is computed through structured
  lighting system consisting of projector and
  camera(10-20 scans)
• Scans are registered together in same reference
  frame used for image registration
• Resulting points fed into mesh editing software
• Finally, mesh is projected onto camera image

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