Optimal Threshold Estimation Using Prototype Selection

  • Uri Lipowezky
  • Victor Shenkar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)


A technique is proposed for choosing the thresholds for a number of object detection tasks, based on a prototype selection technique. The chosen prototype subset has to be correctly classified. The positive and negative objects are introduced in order to provide the optimization via empirical risk minimization. A Boolean function and its derivatives are obtained for each object. A special technique, based on the fastest gradient descent, is proposed for the sum of Boolean functions maximization. The method is applied to the detection task of house edges, using its images in aerial photos. It is shown that proposed method can be expanded to solving of a wide range of tasks, connected to the function optimization, while the function is given in vertices of a 2n single hyper - cube.


Prototype selection Sum of Boolean function optimization Edge detection 


  1. 1.
    Antamoshkin, A. A., Saraev, V. M.: On Definition of Informative Subsystem of Signs in the Pattern Recognition Problem. Computers and Artificial Intell. 4 (1985) 245–252Google Scholar
  2. 2.
    Beveridge J. R., Riserman E. M.: How Easy Matching 2D Line Models Using Local Search? IEEE Trans, on Pattern Anal, and Machine Intell. 6(1997) 564–579CrossRefGoogle Scholar
  3. 3.
    Decaestecker C: Finding Prototypes for Nearest Neighbor Classification by Means of Gradient Descent and Deterministic Annealing. Pattern Recognition 30(1997) 281–288CrossRefGoogle Scholar
  4. 4.
    Demigny D., Kamle T.: A Discrete Expression of Canny’s Criteria for Step Edge Detector Performances Evaluation. IEEE Trans, on Pattern Anal, and Machine Intell. 19(1977) 1199–1211CrossRefGoogle Scholar
  5. 5.
    Dennis J. E. Jr., Schnabel R. B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall Inc., New Jersey (1983)zbMATHGoogle Scholar
  6. 6.
    Devijer P. A., Kittler J.: Pattern Recognition: A Statistical Approach. Prentice-Hall Inc., Englewood Cliffs, N. J. (1982)Google Scholar
  7. 7.
    Foroutan I., Sklansky J.: Feature Selection for Automatic Classification of Non-Gaussian Data. IEEE Trans, on System Man and Cybernetics 17(1987) 187–198CrossRefGoogle Scholar
  8. 8.
    Gates G. W.: The Reduced Nearest Neighbor Rule. Trans, on Inf. Theory 18(1972) 431–433CrossRefGoogle Scholar
  9. 9.
    Hart P. E.: The Condensed Nearest Neighbor Rule. Trans on Inf. Theory 14(1968) 515–516CrossRefGoogle Scholar
  10. 10.
    Jain A., Zongker D.: Feature Selection: Evaluation, Application and Small Sample Performance. IEEE Trans. on Pattern Anal. and Mach. Intell. 19(1997) 153–158CrossRefGoogle Scholar
  11. 11.
    Kim J., Yu J. R., Kim S. H.: Learning of Prototypes and Decision Boundaries for a Verification Problem. Pattern Recognition Lett. 17(1996) 691–697CrossRefGoogle Scholar
  12. 12.
    Kittler J.: Feature Set Search Algorithms. In Chen C. H. (ed.): Pattern Recognition and Signal Processing. Sijthoff and Noordhoff, Alphen van der Rijn, The Nethrlands (1978) 41–60Google Scholar
  13. 13.
    Kuncheva L. I.: Editing For the k-Nearest Neighbors Rule by a Genetic Algorithm. Pattern Recognition Lett. 16(1995) 809–814CrossRefGoogle Scholar
  14. 14.
    Lipowezky U.: Tree-Plantation Decipherment of Panchromatic Aerial Photo Images Using Supervised Template Matching. In Proc. of 9-th. Mediterranean Electromechanical Conf. Melecon’98, vol. 1 Tel-Aviv (1998) 48–52CrossRefGoogle Scholar
  15. 15.
    Lipowezky U.: Selection of the Optimal Prototype Subset for 1-NN Classification. Pattern Recognition Lett. 19(1998) 907–918CrossRefGoogle Scholar
  16. 16.
    Sanchez J. S., Fla F., Ferry F. J.: Prototype Selection for the Nearest Neighbor Rule Through Proximity Graph. Pattern Recognition Lett. 18(1997) 507–513CrossRefGoogle Scholar
  17. 17.
    Strela V., Heller P. N., Strang G., Topiwala P., Heil C: The Application of Multi-wavelet Filterbanks for Image Processing. IEEE Trans. on Image Processing 8(1999) 548–563CrossRefGoogle Scholar
  18. 18.
    Trier Ø. D., Jain A. K.: Goal-Directed Evaluation of Binarization Methods. IEEE Trans, on Pattern Anal. and Mach. Intel. 17(1995) 1191–1201CrossRefGoogle Scholar
  19. 19.
    Vapnik V. N.: Estimation of Dependencies Based on Empirical Data. Springer-Verlag, Berlin Heidelberg (1982)Google Scholar
  20. 20.
    Zadeh L. A.: Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets Syst. 1(1978) 3–28zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Uri Lipowezky
    • 1
  • Victor Shenkar
    • 1
  1. 1.Tiltan System Engineering LtdBeney — BeraqIsrael

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