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일반화된 허프변환의 임계값 선택을 위한 확률적 접근방식

A Selection of Threshold for the Generalized Hough Transform: A Probabilistic Approach

  • 장지영 (광주대학교 자율.융복합전공학부)
  • Chang, Ji Y. (Division of Self-Designed and Open Majors, Gwangju University)
  • 투고 : 2013.07.24
  • 발행 : 2014.01.25

초록

허프변환은 이미지 영역에서 패러미터 영역으로의 변환을 통해 주어진 이미지에서 모델 인스턴스를 추출해내는 방식으로 허프변환된 결과는 패러미터 영역 좌표에 해당하는 Cell 카운터들의 히스토그램 형태가 된다. 다음 단계로 임계값을 정한 후 이를 상회하는 카운터 값에 해당하는 패러미터 값을 통해 모델 인스턴스를 추출하게 되는데 일반적으로 그 임계값은 최고 Cell 카운터 값의 일정 부분에 해당하는 값을 주로 선택하게 된다. 임계점이 너무 낮을 경우 잘못된 모델 인스턴스를 추출할 가능성이 있으며(false positives) 반대로 너무 높은 임계점을 선택할 경우 존재하는 모델 인스턴스를 추출해내지 못하는 오류(false negatives)를 초래하게 된다. 본 논문에서는 일반화된 허프변환(Generalized Hough Transform) 적용 시 패러미터 영역에서의 Cell 카운터 값의 임계점 선택을 위한 방법으로 확률적인 접근방식을 제시하며 이를 위해 Cell 카운터 분포에 해당하는 조건부 확률을 도출하여 과학적인 임계점 선택이 가능함을 입증한다.

When the Hough transform is applied to identify an instance of a given model, the output is typically a histogram of votes cast by a set of image features into a parameter space. The next step is to threshold the histogram of counts to hypothesize a given match. The question is "What is a reasonable choice of the threshold?" In a standard implementation of the Hough transform, the threshold is selected heuristically, e.g., some fraction of the highest cell count. Setting the threshold too low can give rise to a false alarm of a given shape(Type I error). On the other hand, setting the threshold too high can result in mis-detection of a given shape(Type II error). In this paper, we derive two conditional probability functions of cell counts in the accumulator array of the generalized Hough transform(GHough), that can be used to select a scientific threshold at the peak detection stage of the Ghough.

키워드

참고문헌

  1. P. V. C. Hough, "Method and means for recognizing complex patterns," U.S. Patent 3,069,654, 1962.
  2. R. O. Duda and P. E. Hart, "Use of the Hough transform to detect lines and curves in pictures," Communications of the ACM, vol.15, pp.11-15, 1972. https://doi.org/10.1145/361237.361242
  3. C. Kimme, D. H. Ballard, and J. Sklansky, " Finding circles by an array of accumulators," Communications of the ACM, vol.18, pp120-122, 1975. https://doi.org/10.1145/360666.360677
  4. P. M. Merlin and D. J. Farber, "A parallel mechanism for detecting curves in pictures," IEEE Transactions on Computers, vol.24, pp.96-98, 1975.
  5. D. H. Ballard, "Generalizing the Hough transform to detect arbitrary shapes," Pattern Recognition, vol.13, pp.111-122, 1981. https://doi.org/10.1016/0031-3203(81)90009-1
  6. J. Illingworth and J. Kittler, "A survey of the Hough transform," Computer Vision, Graphics and Image Processing, vol.44, pp.87-116, 1988 https://doi.org/10.1016/S0734-189X(88)80033-1
  7. F. F. Ping and S. L. Wing, "Randomized generalized Hough transform for 2-D grayscale object detection," Proc. of International Conf. of Pattern Recognitions, Vienna, Austria, pp.511-515, 1996
  8. D. M. Tsai, "An improved generalized Hough transform for the recognition of overlapping objects," Image and Vision Computing, vol.15, no.12, pp.877-888, 1997 https://doi.org/10.1016/S0262-8856(97)00033-4
  9. P. Tipwai and S. Madarasmi, "A modified generalized Hough transform for image search," IEICE Transactions on Information and Systems, vol.E90-D, no.1, pp165-172, 2007 https://doi.org/10.1093/ietisy/e90-1.1.165
  10. E. Montiel, A. S. Aguado and M. Nixon, "Improving the Hough transform gathering procesfor affine transformations," Pattern Recognition Letters, vol.22, no.9, pp.959-969, 2001 https://doi.org/10.1016/S0167-8655(01)00039-3
  11. A.S. Aguado, E. Montiel and M. Nixon, "Invariant characterisation of the Hough transform for pose estimation of arbitrary shapes," Pattern Recognition, vol.35, no.5, pp.1083-1097, 2002 https://doi.org/10.1016/S0031-3203(01)00099-1
  12. K. S. Hahn, Y. J. Han, H. S. Hahn, "Line Segment Based Randomized Hough Transform," Journal of the Institute of Electronics Engineers of Korea, vol.44, SC, no.6, Nov. 2007
  13. K. H. Baek, H. S. Lee, "A Study on Improving Generalized Hough Transform with Chromatic Informations, Suited for 2D Object Recognition," in Proc. of the Institute of Electronics Engineers of Korea, vol.26, no.26, pp. 1984-1987, July 2003.
  14. Sheldon M. Ross, Introduction to Probability Models. Academic Press, 1981.

피인용 문헌

  1. Performance Evaluation of the Generalized Hough Transform vol.7, pp.6, 2014, https://doi.org/10.22156/cs4smb.2017.7.6.143