Constructing an Optimal Decision Tree for FAST Corner Point Detection

In this paper, we consider a problem that is originated in computer vision: determining an optimal testing strategy for the corner point detection problem that is a part of FAST algorithm [11,12]. The problem can be formulated as building a decision tree with the minimum average depth for a decision table with all discrete attributes. We experimentally compare performance of an exact algorithm based on dynamic programming and several greedy algorithms that differ in the attribute selection criterion.

[1]  Wei-Yin Loh,et al.  Classification and regression trees , 2011, WIREs Data Mining Knowl. Discov..

[2]  Igor Chikalov,et al.  Consecutive Optimization of Decision Trees Concerning Various Complexity Measures , 2004, Fundam. Informaticae.

[3]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .

[4]  Ronald L. Rivest,et al.  Constructing Optimal Binary Decision Trees is NP-Complete , 1976, Inf. Process. Lett..

[5]  Antti Oulasvirta,et al.  Computer Vision – ECCV 2006 , 2006, Lecture Notes in Computer Science.

[6]  Tom Drummond,et al.  Machine Learning for High-Speed Corner Detection , 2006, ECCV.

[7]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[8]  Tom Drummond,et al.  Fusing points and lines for high performance tracking , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[9]  Yuri Breitbart,et al.  A branch-and-bound algorithm to obtain an optimal evaluation tree for monotonic Boolean functions , 2004, Acta Informatica.

[10]  Mukesh K. Mohania,et al.  Decision trees for entity identification: approximation algorithms and hardness results , 2007, TALG.

[11]  M. Garey Optimal Binary Identification Procedures , 1972 .

[12]  Bernard M. E. Moret,et al.  The Activity of a Variable and Its Relation to Decision Trees , 1980, TOPL.

[13]  Kenneth C. Sevcik,et al.  The synthetic approach to decision table conversion , 1976, CACM.

[14]  Micah Adler,et al.  Approximating Optimal Binary Decision Trees , 2008, APPROX-RANDOM.