Jigsaw Image Mosaics

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Jigsaw Image Mosaics

• Junhwan Kim, Fabio Pellacini
• (Cornell University)
• Siggraph 2002

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What is it?
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What does it do?

• The Jigsaw Image Mosaic (JIM) algorithm takes
  as input an arbitrarily-shaped container image
  and a set of image tiles of arbitrary shape and
  generates a mosaic.
• It then packs the container as compactly as
  possible with tiles of similar color to the
  container taken from the input set while
  optionally deforming them slightly to achieve a
  more visually-pleasing effect.

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Related work (1)

• Photomosaics square tiles on a rectangular
  grid.
• Silvers, Hawley, 1997 Finkelstein, Range 1998

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Related work (2)

• Simulated Decorative Mosaics square tiles with
  varying orientations.
• Hausner 2001

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Related work (3)

• Regular tiling with slight distortions of tile
  shapes. Kaplan, Salesin 2000
• Random positions of tiles, gaps filled with
  samples from original image. Haeberli 1990
• Packing problem (NP-hard) heuristics. Downsland
  1995, Milenkovic 1999

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The problem

• Given an arbitrarily-shaped container image and
  a set of arbitrarily-shaped tiles Ti, find a
  set of shapes Sj such that
• the union over the Sj resembles the container
  image as closely as possible and
• each Sj is a translated and rotated copy of one
  of the Ti, possibly incorporating a small
  deformation.

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Energy minimization framework
(Color, Gap, Overlap, Deformation)
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The algorithm-overview

• Prepare and segment images using active contours.
  Kass 1987
• Place tiles roughly, ignoring deformation
  (packing).
• Refine placement of tiles and deform if
  necessary.
• Assemble the final image.

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The algorithm
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Packing (1)

• Place tiles one by one, ignoring the deformation
  term, such that the energy is minimized, and the
  tile is aligned to the container boundary.

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Packing (2)

• Place tiles until the container is full. If
  there is no suitable tile, backtrack to the last
  minimal energy configuration.

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Refining

• Use active contours whose vertices are subject
  to forces that maintain the initial shape,
  repulse two penetrating contours and attract two
  contours separated by a gap.

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Optimizations (1)

• Packing use centroidal Voronoi diagrams with
  sites the size of the medium tile size, and
  always pick a site with the minimal number of
  neighbors.

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Optimizations (2)

• Branch-and-bound with look-ahead to reduce
  backtracking overhead, penalize tiles that would
  make it harder to fill the container in the next
  iteration favor tiles with a small area and
  short circumference.
• Container cleanup separate fragments shallower
  than the shallowest tile.

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Optimizations (3)

• Geometric hashing create a grid of squares
  representing hash table entries, then for each
  possible position and orientation of a tile,
  record the tile in the hash table.

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Results
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Summary

• General energy-based framework.
• New kind of mosaic.
• Effective algorithm.