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Operationally Optimal VERTEX-BASED SHAPE CODING

Operationally Optimal VERTEX-BASED SHAPE CODING. Guido M. Schuster, Gerry Melnikov, and Aggelos K. Katesaggelos. Outline. Introduction Rate and Distortion Directed Acyclic Graph Formulation Experimental Results and Comparisons Conclusions. Introduction.

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Operationally Optimal VERTEX-BASED SHAPE CODING

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  1. Operationally Optimal VERTEX-BASED SHAPE CODING Guido M. Schuster, Gerry Melnikov, and Aggelos K. Katesaggelos

  2. Outline • Introduction • Rate and Distortion • Directed Acyclic Graph Formulation • Experimental Results and Comparisons • Conclusions

  3. Introduction • The lossy polygon approximation was developed to allow proper representation of objects in low-bit-rate application. • Starting points : • Using those two contour points with the maximum distance between them. • Additional points are added until the shape approximation error is less then one threshold. • Splines are defined using the polygon points. • Vertex coordinates and the curve type are arithmetically encoded.

  4. Introduction

  5. Introduction • Optimal in the rate-distortion sense? • The contour approximation can be done using a polygon, B-splines, or higher order curves. • The problem reduces to finding the shortest path in a directed acyclic graph (DAG).

  6. B-splines • A 2-D curve segment Qu with control points (pu-1, pu, pu+1) is defined as follows : • The entire curve Q, consisting of Np curve segments

  7. B-splines

  8. pk-1 pk Distortion measure • B = {b0, …, bNB-1} (the connected boundary) • P = {p0, …, pNP-1} (the approximated polygon) • Segment distortion measure : d(pk-1, pk)

  9. Distortion measure • Maximum operator • Summation operator

  10. Rate • The required bit rate for the differential encoding of vertex pk given vertex pk-1 by r(pk-1, pk)

  11. Optimization problem Distortion measure : summation operator

  12. The algorithm • The Lagrangian cost function • Minimize the function where

  13. The algorithm Find the shortest path between the first and the last vertex of the graph. => Dijkstra’s algorithm

  14. The graph becomes a DAG, and we can use the DAG shortest path algorithm, which has a lower computation complexity the Dijkstra’s algorithm.

  15. Vertex Encoding • Eight-connect chain code + • Run-length encoding scheme

  16. Comparisons • MMR • CAE • Baseline - Block-based Contour-based

  17. Comparison of RD curves

  18. Comparison of RD curves

  19. Comparison of RD curves

  20. Comparison of RD curves

  21. Comparison of RD curves

  22. Comparison of RD curves

  23. Conclusions

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