Texture Synthesis on Surfaces

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Texture Synthesis on Surfaces

• Paper by Greg Turk
• Presentation by Jon Super

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Texture Synthesis on Surfaces

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Goals of texture placement

• Take a 2D texture and wrap it onto a surface
• Avoid noticeable seams between patches
• Minimize stretching and distortion
• Produce a natural-looking result

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The next best thing

• Lapped Textures Praun et al. SIGGRAPH00
• Uses many overlapped texture patches
• Aligns patches with underlying vector field
• Generally minimizes distortion

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The next best thing

• Lapped textures shortcomings
• Low-frequency components
• Boundary mismatch
• Direction field singularities

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Texture synthesis to the rescue!
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Process

• Create a mesh hierarchy over the model
• Set up a vector field over the mesh
• Calculate sweep distance for each vertex
• Assign colors based on neighbors

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Process

• Create a mesh hierarchy over the model
• Set up a vector field over the mesh
• Calculate sweep distance for each vertex
• Assign colors based on neighbors

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Mesh Hierarchy

• Equivalent of a Gaussian pyramid to a surface
• Multiple layers of different resolutions
• Each layer has 4 times the number of vertices of
  the layer above it
• Each layer contains every vertex of the layer
  above it

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Point placement

• n points randomly placed on the surface
• Repulsion between the points spaces them evenly
• These points are now fixed in place, representing
  level m of an m-level mesh
• Repeated for each layer, adding 3 times more
  points each time (3n, 12n, etc)

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Connectivity

• Connectivity between vertices of each layer
• Delaunay triangulation applied
• Mesh is connected in a web of triangles

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Mesh hierarchy operations

• Interpolation
• Low-pass filtering
• Downsampling
• Upsampling

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Process

• Create a mesh hierarchy over the model
• Set up a vector field over the mesh
• Calculate sweep distance for each vertex
• Assign colors based on neighbors

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Vector field

• Provides order to the placement of the texture on
  the model
• Each mesh vertex is given a vector
• User initiates the process by defining a few key
  vectors (12)

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Vector field creation

• All vertices not user-defined set to 0
• User-defined vectors are downsampled to the
  coarsest mesh
• Low-pass filtering to fill out top mesh
• Upsample for each layer to fill to bottom

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Process

• Create a mesh hierarchy over the model
• Set up a vector field over the mesh
• Calculate sweep distance for each vertex
• Assign colors based on neighbors

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Surface sweeping

• Uses the directional flow of the vector field to
  assign ordering to the vertices
• Ordering will allow a sort of raster scan over
  the 3D model
• The color in the image
• cycles as the sweep
• distance increases

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Sweep distance calculation

• Select an anchor point to base the distance
• Each vertex takes the value that is the weighted
  sum of what its neighbors think
• Distance along the flow direction added to the
  neighbors sweep distance
• Sweep distances will propagate out from the
  anchor until every vertex has one

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Process

• Create a mesh hierarchy over the model
• Set up a vector field over the mesh
• Calculate sweep distance for each vertex
• Assign colors based on neighbors

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Pixel Neighborhoods

• Similar technique to 2D texture synthesis
• Examine nearby colors and look for a similar
  pattern in the texture image
• Different kinds of pixel neighborhoods

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Mesh coordinate space

• Pixel neighborhoods dont translate directly to
  the unorganized vertices in a mesh
• Vertex vector is down
• Rotate 90 degrees CCW for right

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Multi-level synthesis

• Start at top, work down
• Initialize the vertices of mesh layer k with
  color values from Gaussian pyramid layer k
• Make a pass with the half square
• Top layer should have a crude representation of
  the texture

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Multi-level synthesis

• Extrapolate and refine each lower level
• Extrapolate initializes the colors using a large
  full square neighborhood of the level above
• Refine improves on that by combining a large full
  square on the current level with a small full
  square on the level above

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Algorithm
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Results
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Results
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Results
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Results
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Results
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Results