  We investigate the problem of pixelwise correspondence for deformable
objects, namely cloth and rope, by comparing both classical and learning-based
methods. We choose cloth and rope because they are traditionally some of the
most difficult deformable objects to analytically model with their large
configuration space, and they are meaningful in the context of robotic tasks
like cloth folding, rope knot-tying, T-shirt folding, curtain closing, etc. The
correspondence problem is heavily motivated in robotics, with wide-ranging
applications including semantic grasping, object tracking, and manipulation
policies built on top of correspondences. We present an exhaustive survey of
existing classical methods for doing correspondence via feature-matching,
including SIFT, SURF, and ORB, and two recently published learning-based
methods including TimeCycle and Dense Object Nets. We make three main
contributions: (1) a framework for simulating and rendering synthetic images of
deformable objects, with qualitative results demonstrating transfer between our
simulated and real domains (2) a new learning-based correspondence method
extending Dense Object Nets, and (3) a standardized comparison across
state-of-the-art correspondence methods. Our proposed method provides a
flexible, general formulation for learning temporally and spatially continuous
correspondences for nonrigid (and rigid) objects. We report root mean squared
error statistics for all methods and find that Dense Object Nets outperforms
baseline classical methods for correspondence, and our proposed extension of
Dense Object Nets performs similarly.
