We introduce Delaunay Point Processes, a framework for the extraction of geometric structures from images. Our approach simultaneously locates and groups geometric primitives (line segments, triangles) to form extended structures (line networks, polygons) for a variety of image analysis tasks. Similarly to traditional point processes, our approach uses Markov Chain Monte Carlo to minimize an energy that balances fidelity to the input image data with geometric priors on the output structures. However, while existing point processes struggle to model structures composed of inter-connected components, we propose to embed the point process into a Delaunay triangulation, which provides high-quality connectivity by construction. We further leverage key properties of the Delaunay triangulation to devise a fast Markov Chain Monte Carlo sampler. We demonstrate the flexibility of our approach on a variety of applications, including line network extraction, object contouring, and mesh-based image compression.

中文翻译：

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使用 Delaunay 点过程提取图像中的几何结构


我们介绍 Delaunay Point Processes，一个从图像中提取几何结构的框架。我们的方法同时定位和分组几何基元（线段、三角形），以形成用于各种图像分析任务的扩展结构（线网络、多边形）。与传统的点过程类似，我们的方法使用马尔可夫链蒙特卡罗来最小化能量，以平衡输入图像数据的保真度与输出结构的几何先验。然而，虽然现有的点过程难以对由互连组件组成的结构进行建模，但我们建议将点过程嵌入到 Delaunay 三角剖分中，从而通过构造提供高质量的连接。我们进一步利用 Delaunay 三角剖分的关键属性来设计快速马尔可夫链蒙特卡罗采样器。我们在各种应用中展示了我们的方法的灵活性，包括线网络提取、对象轮廓和基于网格的图像压缩。