  We present a framework for learning 3D object shapes and dense cross-object
3D correspondences from just an unaligned category-specific image collection.
The 3D shapes are generated implicitly as deformations to a category-specific
signed distance field and are learned in an unsupervised manner solely from
unaligned image collections and their poses without any 3D supervision.
Generally, image collections on the internet contain several intra-category
geometric and topological variations, for example, different chairs can have
different topologies, which makes the task of joint shape and correspondence
estimation much more challenging. Because of this, prior works either focus on
learning each 3D object shape individually without modeling cross-instance
correspondences or perform joint shape and correspondence estimation on
categories with minimal intra-category topological variations. We overcome
these restrictions by learning a topologically-aware implicit deformation field
that maps a 3D point in the object space to a higher dimensional point in the
category-specific canonical space. At inference time, given a single image, we
reconstruct the underlying 3D shape by first implicitly deforming each 3D point
in the object space to the learned category-specific canonical space using the
topologically-aware deformation field and then reconstructing the 3D shape as a
canonical signed distance field. Both canonical shape and deformation field are
learned end-to-end in an inverse-graphics fashion using a learned recurrent ray
marcher (SRN) as a differentiable rendering module. Our approach, dubbed TARS,
achieves state-of-the-art reconstruction fidelity on several datasets:
ShapeNet, Pascal3D+, CUB, and Pix3D chairs. Result videos and code at
https://shivamduggal4.github.io/tars-3D/
