Abstract Inferring unknown conic sections on the basis of noisy data is a challenging problem with applications in computer vision. A major limitation of the currently available methods for conic sections is that estimation methods rely on the underlying shape of the conics (being known to be ellipse, parabola, or hyperbola). A general purpose Bayesian hierarchical model is proposed for conic sections and corresponding estimation method based on noisy data is shown to work even when the specific nature of the conic section is unknown. The model, thus, provides probabilistic detection of the underlying conic section and inference about the associated parameters of the conic section. Through extensive simulation studies where the true conics may not be known, the methodology is demonstrated to have practical and methodological advantages relative to many existing techniques. In addition, the proposed method provides probabilistic measures of uncertainty of the estimated parameters. Furthermore, we observe high fidelity to the true conics even in challenging situations, such as data arising from partial conics in arbitrarily rotated and nonstandard form, and where a visual inspection is unable to correctly identify the type of conic section underlying the data. Supplementary materials for this article are available online.

中文翻译：

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从噪声数据中概率检测和估计圆锥截面

摘要 基于噪声数据推断未知圆锥截面是计算机视觉应用中的一个具有挑战性的问题。当前可用的圆锥截面方法的一个主要限制是估计方法依赖于圆锥的基本形状（已知为椭圆、抛物线或双曲线）。为圆锥截面提出了通用贝叶斯分层模型，并且即使在圆锥截面的特定性质未知时，基于噪声数据的相应估计方法也显示出工作。因此，该模型提供了基础圆锥截面的概率检测和关于圆锥截面的相关参数的推断。通过广泛的模拟研究，可能不知道真正的圆锥曲线，与许多现有技术相比，该方法被证明具有实际和方法论优势。此外，所提出的方法提供了估计参数的不确定性的概率度量。此外，即使在具有挑战性的情况下，我们也观察到对真实圆锥曲线的高保真度，例如由任意旋转和非标准形式的部分圆锥曲线产生的数据，以及目视检查无法正确识别数据基础圆锥截面的类型。本文的补充材料可在线获取。例如由任意旋转和非标准形式的部分圆锥产生的数据，以及目视检查无法正确识别数据下的圆锥截面类型的数据。本文的补充材料可在线获取。例如由任意旋转和非标准形式的部分圆锥产生的数据，以及目视检查无法正确识别数据下的圆锥截面类型的数据。本文的补充材料可在线获取。