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Optimal Centroid Position and Distance Functions in Binary Vector Quantization

This paper discusses the variable metric for binary vector quantization, focusing on optimal centroid positioning and distance and distortion functions. It defines the distance function in relation to binary data and introduces the internal distortion metric, which accounts for zeroes and ones in data grouping. The proposed algorithm illustrates how to determine the optimal position of centroids based on various metrics. The effectiveness of blockwise quantization is demonstrated with test images, including results for different parameter combinations across varied datasets, such as images of bridges and camera captures.

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Optimal Centroid Position and Distance Functions in Binary Vector Quantization

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  1. Variable Metric For Binary Vector Quantization Ismo Kärkkäinen and Pasi Fränti UNIVERSITY OF JOENSUU DEPARTMENT OF COMPUTER SCIENCE JOENSUU, FINLAND

  2. Distance and distortion functions Distance function: Distortion function:

  3. Distortion for binary data Internal distortion for one variable: qjk = the number of zeroes rjk = the number of ones Cjk = the current centroid value for variable k of group j.

  4. Optimal centroid position Optimal centroid position depends on the metric. Given: The optimal position is:

  5. Proposed algorithm

  6. Example of centroid location

  7. Second example

  8. Test images Blockwise quantization of pixels into two levels according to the mean value of the 4x4 blocks. 44 pixel blocks.

  9. Results for Bridge

  10. Results for Camera

  11. Results for CCITT-5

  12. Results for DNA

  13. Different parameter combinations (Bridge)

  14. Different parameter combinations (DNA)

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