Rotation invariance is an important requirement for point shape analysis. To
achieve this, current state-of-the-art methods attempt to construct the local
rotation-invariant representation through learning or defining the local
reference frame (LRF). Although efficient, these LRF-based methods suffer from
perturbation of local geometric relations, resulting in suboptimal local
rotation invariance. To alleviate this issue, we propose a Local-consistent
Transformation (LocoTrans) learning strategy. Specifically, we first construct
the local-consistent reference frame (LCRF) by considering the symmetry of the
two axes in LRF. In comparison with previous LRFs, our LCRF is able to preserve
local geometric relationships better through performing local-consistent
transformation. However, as the consistency only exists in local regions, the
relative pose information is still lost in the intermediate layers of the
network. We mitigate such a relative pose issue by developing a relative pose
recovery (RPR) module. RPR aims to restore the relative pose between adjacent
transformed patches. Equipped with LCRF and RPR, our LocoTrans is capable of
learning local-consistent transformation and preserving local geometry, which
benefits rotation invariance learning. Competitive performance under arbitrary
rotations on both shape classification and part segmentation tasks and
ablations can demonstrate the effectiveness of our method. Code will be
available publicly at this https URL

通过学习局部一致性变换和保留局部几何关系，我们在点形状分析中提出了一种具有旋转不变性的局部一致变换学习策略，并通过相对姿态恢复模块来解决中间层网络中相对姿态丢失的问题，实现了在形状分类和部分分割任务中具备任意旋转下的竞争性性能。

基于本地一致的旋转不变点云分析变换学习

Local-consistent Transformation Learning for Rotation-invariant Point  Cloud Analysis

The majority of descriptor-based methods for geometric processing of
non-rigid shape rely on hand-crafted descriptors. Recently, learning-based
techniques have been shown effective, achieving state-of-the-art results in a
variety of tasks. Yet, even though these methods can in principle work directly
on raw data, most methods still rely on hand-crafted descriptors at the input
layer. In this work, we wish to challenge this practice and use a neural
network to learn descriptors directly from the raw mesh. To this end, we
introduce two modules into our neural architecture. The first is a local
reference frame (LRF) used to explicitly make the features invariant to rigid
transformations. The second is continuous convolution kernels that provide
robustness to sampling. We show the efficacy of our proposed network in
learning on raw meshes using two cornerstone tasks: shape matching, and human
body parts segmentation. Our results show superior results over baseline
methods that use hand-crafted descriptors.

通过引入局部参考框架和连续卷积核，本文提出了一种神经网络框架，可以从原始网格中学习特征，并在非刚性形状匹配和人体部位分割两项任务中取得了优异的结果。

学习三维形状的连续测地卷积

Continuous Geodesic Convolutions for Learning on 3D Shapes

Recognizing 3D objects in the presence of noise, varying mesh resolution,
occlusion and clutter is a very challenging task. This paper presents a novel
method named Rotational Projection Statistics (RoPS). It has three major
modules: Local Reference Frame (LRF) definition, RoPS feature description and
3D object recognition. We propose a novel technique to define the LRF by
calculating the scatter matrix of all points lying on the local surface. RoPS
feature descriptors are obtained by rotationally projecting the neighboring
points of a feature point onto 2D planes and calculating a set of statistics
(including low-order central moments and entropy) of the distribution of these
projected points. Using the proposed LRF and RoPS descriptor, we present a
hierarchical 3D object recognition algorithm. The performance of the proposed
LRF, RoPS descriptor and object recognition algorithm was rigorously tested on
a number of popular and publicly available datasets. Our proposed techniques
exhibited superior performance compared to existing techniques. We also showed
that our method is robust with respect to noise and varying mesh resolution.
Our RoPS based algorithm achieved recognition rates of 100%, 98.9%, 95.4% and
96.0% respectively when tested on the Bologna, UWA, Queen's and Ca' Foscari
Venezia Datasets.

本研究提出了一种基于 RoPS 和 LRF 的 3D 物体识别算法，通过计算散布矩阵和投影统计学方法对邻域进行特征描述，从而实现对噪声和网格分辨率的鲁棒性，取得了比现有技术更好的表现。