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Modeling and 3D object reconstruction by implicitly defined surfaces with sharp features

机译:通过隐式定义的具有锐利特征的曲面进行建模和3D对象重建

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We propose a new method for describing sharp features (i.e., edges and vertices) of implicitly defined surfaces. We consider an initial implicitly defined surface, which is represented as the zero set of a C~1 smooth scalar field with non-vanishing gradients. In order to represent sharp edges and vertices, this surface is augmented by adding new types of implicit representations, called edge descriptors and vertex descriptors. They are denned with the help of the distance field of edge curves. In our implementation, we use circular splines to describe these edge curves, since they support a fast and non-iterative closest point computation.rnAfter adding the edge and vertex descriptors to the initial scalar field, the zero set of the augmented function contains the sharp features. We apply the new representation to surface modeling by implicitly defined surfaces with sharp features and to object reconstruction. In the latter case we describe an algorithm for detecting the sharp curves and vertices of a shape which is given by an unorganized point cloud, which are then approximated by circular splines, in order to define the edge and vertex descriptors.
机译:我们提出了一种新的方法来描述隐式定义的曲面的尖锐特征(即边缘和顶点)。我们考虑一个初始隐式定义的表面,该表面表示为具有不消失梯度的C〜1光滑标量场的零集。为了表示尖锐的边缘和顶点,通过添加称为边缘描述符和顶点描述符的新型隐式表示来增强该表面。通过边缘曲线的距离场可以确定它们。在我们的实现中,我们使用圆形样条来描述这些边缘曲线,因为它们支持快速且非迭代的最近点计算。在将边缘和顶点描述符添加到初始标量字段之后,增强函数的零集包含特征。我们将新的表示形式应用于具有清晰特征的隐式定义曲面的曲面建模以及对象重建。在后一种情况下,我们描述了一种算法,该算法用于检测由无序点云给出的形状的尖锐曲线和顶点,然后通过圆形样条曲线对其进行逼近,以定义边缘和顶点描述符。

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