We propose a new shape analysis approach based on the non-local analysis of
local shape variations. Our method relies on a novel description of shape
variations, called Local Probing Field (LPF), which describes how a local
probing operator transforms a pattern onto the shape. By carefully optimizing
the position and orientation of each descriptor, we are able to capture shape
similarities and gather them into a geometrically relevant dictionary over
which the shape decomposes sparsely. This new representation permits to handle
shapes with mixed intrinsic dimensionality (e.g. shapes containing both
surfaces and curves) and to encode various shape features such as boundaries.
Our shape representation has several potential applications; here we
demonstrate its efficiency for shape resampling and point set denoising for
both synthetic and real data.

提出了一种新的形状分析方法，基于局部形状变化的非局部分析。该方法使用一种称为局部探测场的新颖形状变化描述来描述局部探测算子如何将模式变换为形状，通过优化每个描述符的位置和方向，能够捕捉形状之间的相似性并将其聚集到几何相关的词典中，从而对具有混合内在维度（例如包含曲面和曲线的形状）的形状进行处理，并编码各种形状特征，例如边界。该形状表示法有多种潜在应用，在合成和真实数据中展示了其用于形状重采样和点集去噪的效率。