DETC 2017 67564 ROBUST RECOVERY OF 3 D GEOMETRIC PRIMITIVES FROM POINT CLOUD
A robust method for surface fitting in 3D point cloud is presented as an application of the robust estimation of multiple inlier structures algorithm [1] The geometric primitives such as planes, spheres and cylinders are detected from the point samples in the noisy dataset, without regenerating surface normals or mesh. The inlier points of different surfaces are classified and segmented, with the tolerance of error for each surface estimated adaptively from the input data. From the segmented points, designers can interact with the geometric primitives conveniently. Direct modification of 3D point cloud and inverse design of solid model can be applied. Both synthetic and real point cloud datasets are tested for the use of the robust algorithm. INTRODUCTION The 3D point cloud is one of the most accepted data formats obtained from the 3D data acquisition techniques. The information of an object is then captured by the 3D coordinates of the points. Two major approaches of the 3D reconstruction exist to generate the point cloud. The 3D scanning [2] actively interfere with the surfaces of the physical parts by using range finding devices, like the laser range sensors. The passive methods, such as the photogrammetric approach based on multiple view geometry [3] rebuilds the point cloud using a sequence of 2D images from different views. The 3D data then can be used in the 3D visualization, rapid prototyping, 3D printing, and the ComputerAided Design (CAD) systems [4] Accurate 3D point samples can be reconstructed using the point cloud data format, but it does not explicitly represent the geometric features. Reusing the obtained model in an inverse CAD problem is very inconvenient even if only simple modification of the data is required. Instead of the 3D point samples, designers of solid modeling prefer the information captured by geometric primitives (Fig. 1) such as lines, planes, cylinders etc. which describes the model through geometric elements. Systems like Automatic Feature Recognition (AFR) can evaluate the characteristics in a solid model only if the geometric features are available [5] The highlevel geometric or topological properties in CAD models, such as the extrusion and the revolving procedures, are recognized only when geometric primitives are recovered first. The solid model containing parametric features is the standard format of the mechanical design. Ideally, the 3D surfaces can be directly recovered from the dense reconstructed point cloud. The STL (STereoLithography) file [6] used in rapid prototyping and 3D printing, consists of the 1 Copyright c (c) 2017 by ASME FIGURE 1. To rebuild the solid model, the geometric primitives should be recovered first from the point cloud. unit normal and vertices of each triangulated surface to uniquely define a closed solid model [7] This file format can be generated from many advanced 3D scanners, and the interpolation problem introduced by the scattered data can be solved by the dense sampling. In paper [8] the geometric primitives were detected and segmented from the 3D range data containing thousands of points, with the surface normals explicitly provided. A 3D point cloud does not necessarily capture the accurate information of a surface when the point samples are corrupted by noise, the model contains concave shapes, or a large area of surface is missing due to the scene occlusion. This problem was mentioned in [9] that the point cloud generated from multi view stereo reconstruction may not be used for inverse CAD as it suffers from noise and large reconstruction holes. Since the evaluation of the normals requires smoothing over a small area, the sharp edges and surface flatness may not be preserved without considering the missing data. Overfitting of a surface can also happen and results in redundant meshes, which may not provide accurate information for the surface extraction. In Fig. 2 we show an example generated by the Autodesk ReMake [10] where these problems appear. The conversion from the point cloud to the solid model is usually done by using the 3D cloud data only as a reference. The solid models are redrawn following no systematic approach and the robustness relies on the designer instead of the input data. This is an error prone process since all the geometric measurement are carried out manually. The quality of the result is heavily dependent on the experience of the designer and the functionalities of the software. When the design task involves new or unfamiliar objects, the robustness may not be consistent every time. The RANdom SAmple Consensus (RANSAC) algorithm [11] is implemented in several commercial CAD software [12] This estimation process does not require the user to manually select a group of good points as inliers for the surface fitting. Instead, RANSAC discards the outliers from the input data, where they could come from another surface or be the noise points acquired mistakenly in the data acquisition procedure. The major drawback of RANSAC is that the user has to assign an empirical scale before the robust fitting. Generally, only FIGURE 2. The planes can be recovered directly from the point cloud with robust surface fitting, while a mesh model can be inaccurate and