Detecting ellipses poses a challenging low-level task indispensable to many image analysis applications. Existing ellipse detection methods commonly encounter two fundamental issues. First, inferior detection accuracy could be incurred on a small ellipse than that on a large one; this introduces the scale issue. Second, inferior detection accuracy could be yielded along the minor axis than along the major one of the same ellipse; this leads to the anisotropy issue. To address these issues simultaneously, a novel anisotropic scale-invariant (ASI) ellipse detection methodology is proposed. Our basic idea is to perform ellipse detection in a transformed image space referred to as the ellipse normalization (EN) space, in which the desired ellipse from the original image is ‘normalized’ to the unit circle. With the establishment of the EN-space, an analytical ellipse fitting scheme and a set of distance measures are developed. Theoretical justifications are then derived to prove that both our ellipse fitting scheme and distance measures are invariant to anisotropic scaling, and thus each ellipse can be detected with the same accuracy regardless of its size and ellipticity. By incorporating these components into two recent state-of-the-art algorithms, two ASI ellipse detectors are finally developed and exploited to verify the effectiveness of our proposed methodology.

中文翻译：

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各向异性尺度不变椭圆检测

检测椭圆提出了许多图像分析应用中不可或缺的具有挑战性的低级任务。现有的椭圆检测方法通常遇到两个基本问题。首先，小椭圆的检测精度可能比大椭圆的检测精度差；这就引入了规模问题。其次，同一椭圆沿短轴的检测精度可能比沿长轴的检测精度低；这导致了各向异性问题。为了同时解决这些问题，提出了一种新颖的各向异性尺度不变（ASI）椭圆检测方法。我们的基本思想是在称为椭圆归一化（EN）空间的变换图像空间中执行椭圆检测，其中原始图像中所需的椭圆被“归一化”为单位圆。随着 EN 空间的建立，开发了分析椭圆拟合方案和一组距离测量。然后得出理论依据，证明我们的椭圆拟合方案和距离测量对于各向异性缩放都是不变的，因此无论其大小和椭圆率如何，都可以以相同的精度检测每个椭圆。通过将这些组件合并到两个最新的最先进算法中，最终开发并利用了两个 ASI 椭圆检测器来验证我们提出的方法的有效性。