We introduce an orientation-preserving landmark-based distance for continuous curves, which can be viewed as an alternative to the \Frechet or Dynamic Time Warping distances. This measure retains many of the properties of those measures, and we prove some relations, but can be interpreted as a Euclidean distance in a particular vector space. Hence it is significantly easier to use, faster for general nearest neighbor queries, and allows easier access to classification results than those measures. It is based on the \emph{signed} distance function to the curves or other objects from a fixed set of landmark points. We also prove new stability properties with respect to the choice of landmark points, and along the way introduce a concept called signed local feature size (slfs) which parameterizes these notions. Slfs explains the complexity of shapes such as non-closed curves where the notion of local orientation is in dispute -- but is more general than the well-known concept of (unsigned) local feature size, and is for instance infinite for closed simple curves. Altogether, this work provides a novel, simple, and powerful method for oriented shape similarity and analysis.

翻译：我们为连续曲线引入了基于方向保存地标的距离, 这可以被视为 \ Frechet 或动态时间扭曲距离的替代物。 这一测量方法保留了这些措施的许多特性, 我们证明了某些关系, 但可以被解释为特定矢量空间中的欧几里德距离。 因此, 使用这种距离比一般近邻查询要快得多, 并且比这些措施更容易获得分类结果。 它基于固定的一组地标点对曲线或其他对象的距离函数 \ emph{ mitted} 。 我们还证明在选择地标点方面具有新的稳定性, 并沿路径引入一个名为签名本地地物大小( slfs) 的概念, 以参数化这些概念。 Slfs 解释了各种形状的复杂性, 例如非封闭的曲线, 当地方向的概念有争议 -- 但比众所周知的( 未签名的) 本地地物大小概念更为笼统, 并且对于封闭的简单曲线来说是无限的。 总之, 这项工作提供了一种新颖、 简单和强大的方法, 用于方向相似性分析 。