Active Random Hypersurface Models: Simultaneous Shape and Pose Tracking of Extended Objects in Noisy Point Clouds

基于物体表面的噪声点云测量来跟踪快速移动的扩展3D物体的姿态是几个应用中的重要问题。这些应用包括汽车安全、娱乐设备的创新控制、远程呈现应用和工业生产线。测量数据由激光扫描仪、深度相机、多相机设置或雷达设备等传感器获取。一般来说，由于遮挡效应，在给定的时间步长，只有对象的某些部分可见。此外，根据对象相对于传感器的位置，测量次数及其质量也会发生很大变化。为了准确地估计姿态，必须在对象处于运动中的同时随时间顺序地收集对象的若干测量。跟踪姿态还需要连续确定其形状，即使目标对象的形状不是主要兴趣，以便联合收割机从不同视角组合信息。对于形状建模，将结合随机超曲面模型（RHM）和活动轮廓的成熟概念，从而产生ARHM。这将形成贝叶斯跟踪算法的基础，该算法同时递归地估计对象的形状和姿态。使用RHM，噪声测量与对象参数相关，使用具有乘性噪声的显式测量方程。其关键思想是通过根据概率分布对基本形状进行变换来描述对象。例如，圆柱体可以被描述为通过挤压变形的圆形基础形状。该模型允许从点云的测量中提取信息，而不需要知道确切的源点是在哪里生成的。该提案的主要研究贡献是将RHM扩展到三维对象。这包括三种新型RHM的开发，它们可以组合起来描述更复杂的对象以及铰接结构。对称性和变换不变性的应用避免了表示中的冗余，甚至允许使用少量参数来描述复杂的形式。参数化表面与正则化约束一起允许对尚未观察到的零件进行建模。这个概念是基于活动轮廓的想法。RHM和活动轮廓的非平凡组合将产生能够使用参数化形式可靠地跟踪扩展3D对象的姿态的估计方法，从而产生允许以封闭形式导出估计过程的有效模型。此外，我们希望我们提出的想法和算法能够对3D对象跟踪领域做出重大贡献，因为我们的方法基于坚实的数学基础，但仍然是直观的。

Tracking the pose of quickly moving extended 3D-objects based on noisy point cloud measurements from the surface of the object is an important problem in several applications. These include automobile safety, innovative control for entertainment devices, telepresence applications, and industrial production lines.Measurements are acquired by sensors such as laser scanners, depth cameras, multi-camera setups, or radar devices. In general, due to occlusion effects, only certain parts of the object are visible at a given time step. In addition, depending on where the object is located relative to the sensor, the number of measurements and their quality strongly varies. In order to accurately estimate the pose, several measurements of the object have to be sequentially collected over time while the object is in motion. Tracking the pose also requires the continuous determination of its shape, even if the shape of the target object is not the primary interest, in order to combine information from different perspectives. For shape modeling, the well-established concept of Random Hypersurface Models (RHMs) and Active Contours will be combined, resulting in the ARHMs. This will form the basis of a Bayesian tracking algorithm, which recursively estimates the shape and pose of an object simultaneously. Using RHMs, noisy measurements are related to the object parameters using explicit measurement equations with multiplicative noise. The key idea is to describe the object by applying transformations on a base shape according to a probability distribution. For example, a cylinder can be described as a circular base shape being transformed by an extrusion. This model allows information to be extracted from measurements of a point cloud without knowing where the exact source points were generated. The main research contribution of the proposal is the extension of RHMs to three-dimensional objects. This consists of the development of three new types of RHMs, which can be combined to describe more complex objects, as well as articulated structures. The application of symmetries and transformation invariances avoids redundancies in the representation, allowing even complex forms to be described using a small amount of parameters. The parametrized surface, together with regularization constraints, allows modeling of parts that have not been observed. This concept is based on ideas from Active Contours. The non-trivial combination of RHMs and Active Contours will yield an estimation method capable of reliably tracking the pose of extended 3D-objects using a parametrized form, resulting in an efficient model that allows the derivation of estimation procedures in closed form. In addition, we expect our proposed ideas and algorithms to result in a significant contribution to the field of 3D-object tracking, as our approach is based on solid mathematical fundaments, yet will still be intuitive.