Computing Shape From Depth Discontinuities

分段光滑表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。它们由光滑的表面斑块组成，这些光滑的表面斑块沿着被称为特征线的光滑斑块边界曲线相遇，表面法线场可以是不连续的。结构化照明三角测量系统（例如基于激光或编码模式投影）用于捕获光滑表面斑块上点的位置，但无法对特征线进行采样。因此，使用后处理操作来检测丢失在样本点云中的特征线。不幸的是，从这些样本中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。该项目引入了一个新的原始对偶框架，用于表示、捕获、处理和显示分段光滑表面，该框架基于定向3D线或射线空间中分段光滑表面的新对偶表示。在可选的对偶表示中使用切平面。图像捕获过程检测深度不连续，例如使用多闪光灯摄影，从相对于物体移动的广义相机，或从静态相机和移动物体。铰接和可变形的物体，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。深度不连续扫描是由相机姿态在三维空间中描述弯曲路径时跨越的随时间变化的深度不连续曲线族组成的对偶空间表面。移动的摄像机只能看到和测量到这个表面的一部分。轮廓包含在可见深度不连续中。从附加信息中可以估计出凹坑内部深处的局部凸点，但不能估计出凹坑底部的局部凹点，从而导致重建表面出现孔洞。提出了填补这些孔洞的新方法。其中一种方法是利用捕获数据中的对称性，从可见深度不连续曲线中推断出不可见深度不连续曲线。第二种方法是基于用一个圆柱形摄像机观察一个完全可见的环面来解释捕获的数据。在对偶空间中，提出了一种由简单曲线基元组成的高度压缩曲面表示。基于三角剖分的系统在原始空间中采样是规则的，而在射线对偶空间中，样本高度集中在高曲率点附近。特征线点在原始空间中高度局域化，在对偶空间中由于对应于扩展的光滑曲线段而易于估计。研究人员将实施混合系统，将深度不连续与基于三角测量的系统以及光度立体相结合，以实现更精确的固体物体重建，这些物体由分段光滑表面绑定，并保证计量应用的精度。提出的研究包括从逆向工程到实时3D电影摄影的应用，以及开发变分算法以适应捕获数据的水密分段光滑隐式表面，以及对这些隐式表面进行三角剖分的等面算法，以保留特征线。

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.