[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 176

一句话总结

本文提出各向异性卷积神经网络（ACNN），利用各向异性热核作为空间补丁，在非欧几里得域上学习密集的内在形状对应，并在具有挑战性的基准测试中达到最先进的结果。

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

• 在非刚性形变和数据瑕疵下，激发并解决密集的内在形状对应问题。
• 开发一种内在的、对变形不变的 CNN 框架，适用于网格和点云。
• 利用各向异性扩散形成方向性局部补丁，从而实现对对应关系的鲁棒学习。

提出的方法

• 定义基于各向异性热核的补丁算子 D(x)f，带有方向 (\u0013 θ) 和尺度 t，使用 h_{\\,αθ t}(x,ξ) 。
• 使用补丁构造内在卷积： (f * a)(x) = ∫ a(θ,t) (D(x)f)(θ,t) dtdθ。
• 将 ACNN 组装为包含以下层次的网络：全连接层、内在卷积层、Dropout、Batch Normalization，以及用于密集对应的 Softmax。
• 通过最小化多项式回归损失来训练，以在形状之间产生软对应 f_Θ(x,y)。
• 通过使用自信点的函数映射方法来细化对应关系，求解 Φ_I C = Ψ_I 并重新推导逐点匹配。

实验结果

研究问题

• RQ1 如何在非欧几里得曲面上定义内在的、方向感知的卷积，以学习密集的对应关系？
• RQ2 与现有的内在 CNN 相比，基于各向异性扩散的补丁是否能够提高对非等距形变和拓扑噪声的鲁棒性？
• RQ3 ACNN 框架是否能跨形状表示（网格、点云）进行泛化，并在基准测试中超越现有的内在方法？
• RQ4 ACNN 学到的软对应是否可以通过函数映射进一步细化为精确的密集映射？

主要发现

• ACNN 使在非欧几里得域上进行内在、对变形不变的学习成为可能，使用各向异性热核来构造补丁。
• 该框架结合了现有内在模型的优点，同时避免其缺点，包括对可积半径和网格特定图等的依赖。
• 相对于 GCNN 和 ADD 变体，ACNN 在具有挑战性的密集对应基准上实现了最先进的结果。
• 该方法产生可靠的软对应，可以通过基于函数映射的细化，得到更密集、更准确的逐点映射。