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Structure learning for 3D shapes is vital for 3D computer vision.State-of-the-art methods show promising results by representing shapes usingimplicit functions in 3D that are learned using discriminative neural networks.However, learning implicit functions requires dense and irregular sampling in3D space, which also makes the sampling methods affect the accuracy of shapereconstruction during test. To avoid dense and irregular sampling in 3D, wepropose to represent shapes using 2D functions, where the output of thefunction at each 2D location is a sequence of line segments inside the shape.Our approach leverages the power of functional representations, but without thedisadvantage of 3D sampling. Specifically, we use a voxel tubelization torepresent a voxel grid as a set of tubes along any one of the X, Y, or Z axes.Each tube can be indexed by its 2D coordinates on the plane spanned by theother two axes. We further simplify each tube into a sequence of occupancysegments. Each occupancy segment consists of successive voxels occupied by theshape, which leads to a simple representation of its 1D start and end location.Given the 2D coordinates of the tube and a shape feature as condition, thisrepresentation enables us to learn 3D shape structures by sequentiallypredicting the start and end locations of each occupancy segment in the tube.We implement this approach using a Seq2Seq model with attention, calledSeqXY2SeqZ, which learns the mapping from a sequence of 2D coordinates alongtwo arbitrary axes to a sequence of 1D locations along the third axis.SeqXY2SeqZ not only benefits from the regularity of voxel grids in training andtesting, but also achieves high memory efficiency. Our experiments show thatSeqXY2SeqZ outperforms the state-ofthe-art methods under widely usedbenchmarks.

SeqXY2SeqZ: Structure Learning for 3D Shapes by Sequentially Predicting 1D Occupancy Segments From 2D Coordinates