영상처리에 있어서 하프변환에 관한 연구 = (A) study on the Hough transform in image processing

다국어 초록 (Multilingual Abstract)

One of the important computer applications is image understanding, which is a Little different from image processing. Image understanding is the explicit description of image, while image processing is the study of image to image transforms. Image understanding is the technique which is more necessary to practical engineering application than image processing. The latter however is a prerequisite for the former.
The image which is the substitution of an object is usually recognized by the differences in the intensity of brightness. Intensity discontinuities in an image appear to the human eyes as boundaries or edges of objects, which are the fundamentals of recognition. The edge detection is the first step to image understanding. Various methods for edge detection have been reported and are being extensively studied, Edges represented by binary value have the shape of line or curves many of which can be expressed with analytic geometry. A line has two parameters namely the slope and intercept. A circle has three parameters, center coordinate (x_(0),y_(0)) and radius, and an ellipse has five parameters center coordinate, major and minor axis, and rotation angle. A curve is expressed by parameters.
Hough transform which is well known as a robust method for line detection (i.e. two parameters determination) has gradually extended it's applicaion to the detection of circle, ellipse and other curves. And yet, the usage of Hough transform as the detector of circle and ellipse has been limited by slow speed and excessive memory since the calculation and memory requirement exponentially increases as the number of parameters to be determined increases.
In this study, the methods for ellipse detection are proposed to reduce calculation cost and memory requirement. In this method, 8 points are selected so that those points may be approximately evenly distributed on the ellipse, and used to determine the five parameters by the least square method. 8 points are the tangential coordinates at the direction of 0˚ 45˚ , 90˚ 135˚ . Hough transform is used to find the tangential lines in only 4 directions. Tests for some kinds of ellipses prove that remarkable reduction is achieved in calculation and memory requirement with little error increase. This is because that memory requirement is for 8 points, coefficient matrix of 3 simultaneous equations including image itself and Hough transform is carried out only for 4 directions using only a fraction of original points.

목차 (Table of Contents)

• 목차 = ⅰ
• List of tables = ⅲ
• List of figures = ⅳ
• ABSTRACT = ⅷ
• Ⅰ. 서론 = 1
• Ⅱ. 디지탈 영상 = 4
• A. 영상의 표현 = 4
• B. 샘플링 및 양자화 = 6
• C. 픽셀의 관련성 = 6
• D. 디지탈 영상 시스템 = 7
• Ⅲ. 전처리 = 10
• A. 공간영역 방법 = 10
• B. 주파수영역 방법 = 12
• C. 최소자승법 = 13
• D. 히스토그램 처리 = 14
• E. 잡음제거 = 16
• 1. 잡음을 제거 하기 위한 구조적인 메카니즘 = 16
• 2. 평활화 = 17
• 3. 메디안 필터링 = 18
• F. 에지검출 = 20
• 1. 그래디언트 연산자 = 21
• 2. 라플라스 연산자 = 23
• 3. 문턱값 결정 = 23
• Ⅳ. 하프변환의 특성 = 27
• A. 라돈변환 = 27
• B. 파라미터 변환의 특성 = 29
• C. 양자화 = 37
• D. 이동, 회전, 크기 변화에 따른 기하학적 특성 = 39
• 1. 이동 = 39
• 2. 회전 = 40
• 3. 크기변화 = 41
• E. 곡선 검출 = 42
• F. R-table = 47
• G. 후처리 = 48
• 1. 나비형 성질 = 49
• 2. 정합 마스크 = 51
• Ⅴ. 타원 검출 알고리즘 = 52
• A. 타원의 기하학적 성질 = 52
• B. 4점범 = 59
• C. 8점법 = 62
• Ⅵ. 실험 및 고찰 = 66
• A. 직선 및 타원 검출 실험 = 66
• 1. 직선의 검출 = 66
• 2. 타원 검출 = 70
• B. 실험 결과 고찰 = 89
• 1. 혼합 에지에서의 직선 검출 = 89
• 2. 타원 검출 = 89
• a. 4점범 = 91
• b. 8점법 = 91
• Ⅶ. 결론 = 92
• References = 94