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Multilevel thresholding by fast PNN based algorithm

Multilevel thresholding by fast PNN based algorithm. Olli Virmajoki and Pasi Fränti. UNIVERSITY OF JOENSUU DEPARTMENT OF COMPUTER SCIENCE FINLAND. Multi-level thresholding. Given image with N input values, threshold the image into M values.

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Multilevel thresholding by fast PNN based algorithm

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  1. Multilevel thresholding by fast PNN based algorithm Olli Virmajoki and Pasi Fränti UNIVERSITY OF JOENSUU DEPARTMENT OF COMPUTER SCIENCE FINLAND

  2. Multi-level thresholding • Given image with N input values, threshold the image into M values. • Considered as algorithmic problem: given a minimization criterion (MSE), find optimal thresholds.

  3. Optimal thresholding • Optimal thresholding by exhaustive search in O(NM-1) time [Otsu 1979]. • Medical images can have 16 bpp. Exhaustive search takes ~6553610. • Sub-optimal methods: Lloyd-Max quantizer with O(N)time.

  4. Pairwise Nearest Neighbor method (PNN) • New multilevel thresholding algorithm based on the pairwise nearest neighbor (PNN). • PNN used in vector quantization (Equitz 1989) but considered slow: • Original method takes O(N3), • Kurita’s method takes O(N2 log N) • Using Nearest neighbor pointers: O(N2). • PNN is lower limited by (N2) • Our contribution: To show that PNN can be implemented in O(N log N) time !!!

  5. PNN algorithm SET m=N (N-1 thresholds) REPEAT • Find threshold to be removed: O(N) • Remove threshold: O(1) • Update the class parameters: O(1) • SET m=m-1 UNTIL m=M

  6. PNN with heap structure

  7. Time complexity

  8. Histograms of test images 8 bpp 12 bpp 16 bpp

  9. Methods in comparison • Uniform quantizer (UQ) • LMQ • PNN • PNN + LMQ • Optimal (Otsu’s method)

  10. MSE comparison (Medical3) 1. MSE values significantly smaller than Uniform Quantizer 3. PNN+LMQ values can be significantly smaller than LMQ alone 2. PNN+LMQ gives near-optimal results (for small M values)

  11. Time Comparison (Medical3) • All sub-optimal methods are fast 2. Optimal thresholding is too slow for larger M values.

  12. Conclusions • Fast PNN-based O(N log N) time algorithm for multilevel non-parametric thresholding. • Considerably faster than optimalthresholding. • Better quality than the Lloyd-Max quantizer alone.

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