[论文解读] Learning shape correspondence with anisotropic convolutional neural networks

Davide Boscaini, Jonathan Masci+2 more|arXiv (Cornell University)|May 20, 2016

Image Retrieval and Classification Techniques被引用 169

一句话总结

ACNN 通过在流形上应用各向异性热核基的补片来学习密集的内在形状对应，从而在具有挑战性的非刚性形状基准测试中实现了最先进的性能。

ABSTRACT

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the presence of topological noise and missing parts, mainly due to the limited capability to model such deformations axiomatically. Several recent works showed that invariance to complex shape transformations can be learned from examples. In this paper, we introduce an intrinsic convolutional neural network architecture based on anisotropic diffusion kernels, which we term Anisotropic Convolutional Neural Network (ACNN). In our construction, we generalize convolutions to non-Euclidean domains by constructing a set of oriented anisotropic diffusion kernels, creating in this way a local intrinsic polar representation of the data (`patch'), which is then correlated with a filter. Several cascades of such filters, linear, and non-linear operators are stacked to form a deep neural network whose parameters are learned by minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks.

研究动机与目标

• 激励在非等距变形、拓扑噪声和缺失部分下的鲁棒密集内在形状对应。
• 引入一个使用各向异性扩散核在3D形状上形成局部补片的内在CNN框架（ACNN）。
• 端到端学习任务特定过滤器以预测可变形形状之间的密集对应。

提出的方法

• 使用各向异性热核定义补片算子，在每个点周围创建局部极坐标表示。
• 在CNN框架中，将内在卷积构造成带可学习滤波器的补片加权和。
• 使用多项回归损失进行训练，以产出每点的软对应。
• 通过从高置信对应计算功能映射并重新估计逐点匹配来精炼对应关系。
• 将各向异性拉普拉斯算子在网格上离散化以便实际计算。
• 在CNN架构中加入全连接、内在卷积、dropout和批量归一化等层。

实验结果

研究问题

• RQ1 否能基于各向异性扩散的补片在非刚性变形和噪声下支持鲁棒的密集内在对应？
• RQ2 如何在非欧几里得域上定义并学习内在卷积，以跨越不同形状表示（网格、点云等）实现泛化？
• RQ3 在具有挑战性的对应基准上，ACNN 是否优于之前的内在学习方法（GCNN, ADD, LSCNN）？
• RQ4 网络是否能产生可靠的软对应并被精炼为准确的点对点映射？
• RQ5 需要哪些离散化和实现选择来将 ACNN 扩展到实用的3D形状？

主要发现

• ACNN 提供了基于各向异性热核的本征、定向补片算子，使在流形上的局部特征提取更有效。
• 根据摘要，该架构在具有挑战性形状对应基准上实现了最先进的结果。
• ACNN 将空间补片与可学习滤波器相结合，在跨表示的适用性和对补片的可解释性方面，优于先前的内在CNN。
• 该方法支持可通过功能映射方法精炼的逐点软对应输出。
• 在三角网格上以主曲率方向离散化，使得计算在不依赖于可同值半径的情况下也可实现。