  In this paper, we propose U-RED, an Unsupervised shape REtrieval and
Deformation pipeline that takes an arbitrary object observation as input,
typically captured by RGB images or scans, and jointly retrieves and deforms
the geometrically similar CAD models from a pre-established database to tightly
match the target. Considering existing methods typically fail to handle noisy
partial observations, U-RED is designed to address this issue from two aspects.
First, since one partial shape may correspond to multiple potential full
shapes, the retrieval method must allow such an ambiguous one-to-many
relationship. Thereby U-RED learns to project all possible full shapes of a
partial target onto the surface of a unit sphere. Then during inference, each
sampling on the sphere will yield a feasible retrieval. Second, since
real-world partial observations usually contain noticeable noise, a reliable
learned metric that measures the similarity between shapes is necessary for
stable retrieval. In U-RED, we design a novel point-wise residual-guided metric
that allows noise-robust comparison. Extensive experiments on the synthetic
datasets PartNet, ComplementMe and the real-world dataset Scan2CAD demonstrate
that U-RED surpasses existing state-of-the-art approaches by 47.3%, 16.7% and
31.6% respectively under Chamfer Distance.
