利用二次曲線近似法來計算二階段霍夫轉換來偵測數位影像中的直線和圓

Abstract

本論文提出一種新的二階段霍夫轉換(two-stages Hough Transform)來偵測影像中的直線和圓。此種霍夫轉換最主要的特色是利用二次曲線疊代的方式先算出影像中特徵點的法線向量，進而把n維參數空間分解成n-1維的參數空間。我們利用此種方法來偵測圓並且延伸此種方法來偵測直線。在複雜影像中，大多部分的情況是只有直線和曲線。利用曲線疊代的方式，不只可以計算出特徵點的法線方向也可以計算出曲率。利用直線和曲線的曲率不同的特性，在二階段的直線霍夫轉換裡，可以有效的壓抑曲線不去進行投票，而只讓直線進行投票。在實驗中可以獲得很好的結果。我們並且把這些技術應用在CAD和其他實際的圖形中，發覺效果很好。

A new two-stages Hough transform for detecting lines and circles in digital image is proposed here. The main feature of the new two-stages Hough transform is to evaluate the normal direction of the feature point by using quadratic polynomial fitting and decompose n dimension parameter array into n-1 dimension parameter array. The method is extended to detect lines in the digital image. In complicated images, the most curves are straight lines and circles and arcs. By using quadratic polynomial fitting, the normal direction and the curvature would be computed. By using the property of the different curvature between the lines and arcs, the non-straight lines are suppressed not to vote and only let the straight lines to vote in the two-stages Hough transform with quadratic polynomial fitting. The approach would get good performance in the experiment. The technique would be applied in CAD image and real pattern to get good results.