MCS: Research on Detection and Classification of 2D and 3D Shapes in Cluttered Point Clouds

在我们的数字社会中，图像是最大的数据和信息来源。许多应用领域，如医疗诊断、国土安全、军事监视和互联网通信，都可以受益于用于分析图像的自动化技术，特别是用于检测、分类和分析图像中的对象的自动化技术。图像中目标检测的快速技术通常分为两个步骤：(1)使用快速技术从图像中提取某些基本原语（突出点，边缘，弧线等）；(2)在这些提取的原语中收集感兴趣的对象。第二步——在2D和3D点云中基于形状发现物体的统计框架——是本研究的重点。由于提取的原语可能属于对象或背景，因此给定的数据既嘈杂又混乱。简单来说，这个问题类似于在繁星满天的夜晚寻找天空中的北斗七星。简单的组合搜索是不可能的，因为将点组织成多边形的计算成本是令人望而却步的。这里提出的框架是通过综合分析：首先合成连续形状Ð二维轮廓和三维表面——对于感兴趣的形状类别，并将这些形状采样到点集中。然后（概率上）将这些合成的点集与给定的点云进行比较，以确定图像中是否存在形状类。本研究将采用贝叶斯方法进行形状分类，其中估计给定点云中存在的不同形状类别的后验概率。这涉及到整合某些讨厌变量的基本步骤：(i)数据中存在的未知物体形状，（ii）它在场景中出现的未知姿势和比例，以及（iii）连续形状的未知采样到离散点。研究人员将开发特定类别的统计模型来捕获这些令人讨厌的变量的可变性，并将使用蒙特卡罗方法从这些模型中模拟来近似所需的后验。该框架依赖于以下要素：(1)统计形状模型：首先，研究人员将推导形状（曲线和曲面）的数学表示，在其形状空间上施加黎曼度量，并开发计算测地线的算法。其次，他们将在生成的形状空间上定义和估计概率模型，并从这些模型中模拟用于生成随机推断的形状。由于形状空间通常是无限维的非线性流形，因此对形状进行有效统计推断的前景既新颖又具有挑战性。(2)形状采样：为了合成一个假设的点集，取一个连续的形状，用有限个数的点对其进行采样。研究人员将为这一抽样过程开发数学表示和随机模型。(3)似然评估：最后需要计算给定点云的似然。这涉及到最优地注册和转换（旋转、平移和缩放）合成点集以匹配给定数据。代价函数是基于观测噪声和背景杂波的概率模型。这个项目将研究、开发和实现这些在点云中寻找形状的基本成分。将测试该框架在检测和分类图像中的目标方面的性能和效率。

Images form the largest source of data and information in our digital society. Many application domains, such as medical diagnostics, homeland security, military surveillance, and Internet communication, can benefit from automated techniques for analyzing images and, in particular, for detection, classification, and analysis of objects in images. Fast techniques for object detection in images often work in two steps: (1) Extract certain basic primitives (prominent points, edges, arcs, etc) from images using fast techniques and, (2) glean objects of interest in these extracted primitives. This second step -- a statistical framework for shape-based discovery of objects in 2D and 3D point clouds -- is the focus of this research. Since the extracted primitives may belong either to objects or backgrounds, the given data is both noisy and cluttered. In simple terms, this problem is akin to finding the big dipper in the sky on a starry night. A simple combinatorial search is impossible, as the computational cost of organizing points into polygonal shapes are prohibitive. The framework proposed here is analysis by synthesis: one starts by synthesizing continuous shapes Ð contours for 2D and surfaces for 3D -- for the shape classes of interest and samples these shapes into sets of points. These synthesized point sets are then (probabilistically) compared with the given point cloud to decide if a shape class is present in the image. This research will take a Bayesian approach to shape classification where one estimates the posterior probabilities of different shape classes being present in the given point cloud. This involves a fundamental step of integrating out certain nuisance variables: (i) the unknown shape of object present in the data, (ii) the unknown pose and scale at which it appears in the scene, and (iii) the unknown sampling of a continuous shape into discrete points. The investigators will develop class-specific statistical models to capture variability of these nuisance variables, and will use a Monte Carlo approach that simulates from these models to approximate the desired posterior. This framework relies on the following ingredients: (1) Statistical shape models: Firstly, the investigators will derive mathematical representations of shapes (of curves and surfaces), impose Riemannian metrics on their shape spaces and develop algorithms for computing geodesics. Secondly, they will define and estimate probability models on the resulting shape spaces and simulate shapes from those models for use in generating stochastic inferences. Since shape spaces are typically infinite-dimensional, nonlinear manifolds, the prospect of efficient statistical inferences of shapes is both novel and challenging. (2) Shape Sampling: To synthesize a hypothesized point set, one takes a continuous shape and samples it with a finite number of points. The researchers will develop mathematical representations and stochastic models for this sampling process. (3) Likelihood Evaluation: Lastly, one needs to calculate the likelihood of the given point cloud. This involves optimally registering and transforming (rotating, translating, and scaling) the synthetic point set to match the given data. The cost function is based on probability models for the observation noise and the background clutter. This project will research, develop, and implement these fundamental ingredients for finding shapes in point clouds. The proposed framework will be tested for performance and efficiency in detecting and classifying objects in images.