Computing Shape From Depth Discontinuities

根据深度不连续性计算形状

• 批准号: 0729126
• 负责人: Gabriel Taubin
• 金额: $ 26万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0729126&HistoricalAwards=false
• 关键词: Computing; Shape; Depth; Discontinuities

Piecewise smooth surfaces are used to describe the boundary shape of solid objects, such as those that can be fabricated with machine tools. They are composed of smooth surface patches meeting along piecewise smooth patch boundary curves called feature lines, across which the surface normal fields can be discontinuous. Structured lighting triangulation systems (e.g. based on lasers, or coded pattern projection) are used to capture the location of points on smooth surface patches, but are unable to sample feature lines. As a result, postprocessing operations are used to detect the feature lines lost in the clouds of sample points. Unfortunately, reconstructing feature lines from these samples is intrinsically impossible, because a continuous function with discontinuous derivatives is not a band-limited signal. This project introduces a new primal-dual framework for representation, capture, processing, and display of piecewise smooth surfaces, based on a new dual representation for piecewise smooth surfaces in the space of oriented 3D lines, or rays. In alternative dual representations tangent planes are used. An image capture process detects depth discontinuities, for example using multi-flash photography, from a generalized camera moving with respect to the object, or from a static camera and a moving object. Articulated and deformable objects, as well as real-time capture for 3D cinematography applications, will be considered in later phases of the project. A depth discontinuity sweep is a surface in dual space composed of the time-dependent family of depth discontinuity curves span as the camera pose describes a curved path in 3D space. Only part of this surface is visible and measurable from the moving camera. Silhouettes are included in the visible depth discontinuities. Locally convex points deep inside concavities can be estimated from the additional information, but not locally concave point laying at the bottom of concavities, resulting in holes in the reconstructed surface. New methods to fill these holes are proposed. One of these extrapolates the non-visible depth discontinuity curves from the visible ones by exploiting symmetries in the captured data. A second approach is based on interpreting the data as captured with a cylindrical camera looking at a fully visible toroidal surface. A new highly compressed surface representation composed of simple curve primitives in dual space will be developed. While sampling is regular for triangulation-based systems in primal space, in the dual space of rays samples are highly concentrated in the vicinity of high curvature points. Feature line points, which are highly localized in primal space, are easy to estimate in dual space because they correspond to extended and smooth curve segments. The investigators will implement hybrid systems combining depth discontinuities with triangulation-based systems, as well as photometric stereo, to achieve more accurate reconstructions of solid objects bound by piecewise smooth surfaces with accuracy guarantees for metrology applications. The proposed research includes applications ranging from reverse engineering to real-time 3D cinematography, and development of variational algorithms to fit watertight piecewise smooth implicit surfaces to the capture data, as well as isosurface algorithms to triangulate these implicit surfaces preserving feature lines.

分段光滑曲面用于描述固体物体的边界形状，例如那些可以用机床制造的物体。它们由光滑曲面片组成，这些曲面片沿着称为特征线的分段光滑曲面片边界曲线相交，曲面法向场可以在特征线上不连续。 结构化照明三角测量系统（例如，基于激光或编码图案投影）用于捕获光滑表面块上的点的位置，但不能对特征线进行采样。因此，后处理操作用于检测在样本点云中丢失的特征线。不幸的是，从这些样本重建特征线本质上是不可能的，因为具有不连续导数的连续函数不是带限信号。该项目介绍了一个新的原始对偶框架表示，捕捉，处理和显示分段光滑表面，基于一个新的对偶表示分段光滑表面在空间中的定向3D线，或射线。 在替代的对偶表示中，使用切平面。图像捕获过程例如使用多闪光摄影从相对于对象移动的广义相机或从静态相机和移动对象检测深度不连续性。 铰接和可变形物体，以及3D电影摄影应用的实时捕捉，将在项目的后期阶段考虑。深度不连续性扫描是对偶空间中的表面，其由深度不连续性曲线跨度的时间依赖族组成，因为相机姿势描述3D空间中的弯曲路径。从移动的摄像机中只能看到和测量到该表面的一部分。 可见的深度不连续性中包括轮廓。根据附加信息可以估计凹部内部深处的局部凸点，但不能估计位于凹部底部的局部凹点，从而导致重构表面中的孔洞。提出了填补这些空洞的新方法。其中之一是通过利用捕获数据中的对称性从可见深度不连续曲线外推不可见深度不连续曲线。第二种方法是基于解释的数据捕捉与圆柱相机看一个完全可见的环面。 提出了一种新的由对偶空间中简单曲线基元组成的高度压缩的曲面表示方法。虽然在原始空间中基于三角测量的系统的采样是规则的，但在射线的对偶空间中，样本高度集中在高曲率点附近。特征线点在原始空间中是高度局部化的，在对偶空间中很容易估计，因为它们对应于扩展和光滑的曲线段。研究人员将实施混合系统，将深度不连续性与基于三角测量的系统以及光度立体相结合，以实现对由分段光滑表面约束的固体物体的更准确重建，并为计量应用提供准确性保证。拟议的研究包括应用程序，从逆向工程到实时3D电影，和发展的变分算法，以适应水密分段光滑隐式曲面的捕获数据，以及等值面算法三角形这些隐式曲面保留特征线。