The process of aligning a pair of shapes is a fundamental operation in
computer graphics. Traditional approaches rely heavily on matching
corresponding points or features to guide the alignment, a paradigm that
falters when significant shape portions are missing. These techniques generally
do not incorporate prior knowledge about expected shape characteristics, which
can help compensate for any misleading cues left by inaccuracies exhibited in
the input shapes. We present an approach based on a deep neural network,
leveraging shape datasets to learn a shape-aware prior for source-to-target
alignment that is robust to shape incompleteness. In the absence of ground
truth alignments for supervision, we train a network on the task of shape
alignment using incomplete shapes generated from full shapes for
self-supervision. Our network, called ALIGNet, is trained to warp complete
source shapes to incomplete targets, as if the target shapes were complete,
thus essentially rendering the alignment partial-shape agnostic. We aim for the
network to develop specialized expertise over the common characteristics of the
shapes in each dataset, thereby achieving a higher-level understanding of the
expected shape space to which a local approach would be oblivious. We constrain
ALIGNet through an anisotropic total variation identity regularization to
promote piecewise smooth deformation fields, facilitating both partial-shape
agnosticism and post-deformation applications. We demonstrate that ALIGNet
learns to align geometrically distinct shapes, and is able to infer plausible
mappings even when the target shape is significantly incomplete. We show that
our network learns the common expected characteristics of shape collections,
without over-fitting or memorization, enabling it to produce plausible
deformations on unseen data during test time.

本文提出一种基于深度神经网络的形状对齐方法，利用形状数据集学习形状感知的先验，以解决传统方法在缺失重要形状部分时失效的问题，并通过各向异性全变分正则化对 ALIGNet 进行约束，从而使其适用于不完整的目标形状。我们展示了 ALIGNet 学习了形状集合的通用期望特征，能够在测试时产生合理的形变。