LINE SIMPLIFICATION

• Given a polyline L=(p₁,...,p_n), find a simplified line L' with fewer vertices.
  - typically, L is simple, and we want L' to be simple.
• Simplest form of model simplification
  - GIS applications (e.g. <a href=been>TIGER file format</a>)
• Decimation approach: find a subsequence (p_i_1,..., p_i_m, (m<n) of (p₁,..., p_n).
• MEASURES OF DISTORTION:
  - Hausdorff: the min-size approximation may be non-simple.
  - SHOW EXAMPLE.
• E1-measure of Imai and Iri:
  - (i,j) is eps-admissible iff Hausdorff distance between [p_i, p_j] and (p_i,...,p_j) is at most eps.
  - Path is admissible iff each edge is admissible.
  - CONVERTS TO A SHORTEST PATH PROBLEM
  - Graph G(L,eps) comprising all admissible edges.
• COMPLEXITY:
  - O(n³), naive
  - O(n²logn) [Melkman, O'Rourke]
  - O(n²) [Chan-Chin]
  - Extend to 3-D [Barequet, et al]