基于最小二次拟合的点云通用基元检测
Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits
摘要：
我们提出了一种新的和有效的方法来检测3D图元在杂乱，无组织的点云，没有腋窝分割或类型规范。我们认为二次曲面封装我们的环境的基本构建块-平面，球体，椭球体，圆锥体或圆柱体，在一个统一的方式。此外，二次曲面允许我们对更高自由度的形状进行建模，例如可以在非刚性设置中使用的双曲面或抛物面。我们首先贡献两个新的二次拟合目标的3D点集，赋予切线空间信息。基于将二次曲面梯度与曲面法线对齐的想法，我们的第一个公式是精确的，并且需要低至四个定向点。第二个拟合近似于第一个拟合，并减少了计算工作量。我们从理论上分析这些符合严格，并给出代数和几何参数。接下来，通过重新参数化的解决方案，我们设计了一个新的本地Hough投票方案的零空间系数，结合RANSAC，减少复杂性从$O(N^4)$到$O(N^3)$（三点）。据我们所知，这是第一种能够在困难场景中执行通用交叉型多对象基元检测而无需分割的方法。我们广泛的定性和定量的结果表明，我们的方法是有效的，灵活的，以及是准确的。
英文摘要：
We present a novel and effective method for detecting 3D primitives in cluttered, unorganized point clouds, without axillary segmentation or type specification. We consider the quadric surfaces for encapsulating the basic building blocks of our environments - planes, spheres, ellipsoids, cones or cylinders, in a unified fashion. Moreover, quadrics allow us to model higher degree of freedom shapes, such as hyperboloids or paraboloids that could be used in non-rigid settings. We begin by contributing two novel quadric fits targeting 3D point sets that are endowed with tangent space information. Based upon the idea of aligning the quadric gradients with the surface normals, our first formulation is exact and requires as low as four oriented points. The second fit approximates the first, and reduces the computational effort. We theoretically analyze these fits with rigor, and give algebraic and geometric arguments. Next, by re-parameterizing the solution, we devise a new local Hough voting scheme on the null-space coefficients that is combined with RANSAC, reducing the complexity from $O(N^4)$ to $O(N^3)$ (three points). To the best of our knowledge, this is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes without segmentation. Our extensive qualitative and quantitative results show that our method is efficient and flexible, as well as being accurate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
