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This paper studies a problem of learning surface mesh via implicit functionsin an emerging field of deep learning surface reconstruction, where implicitfunctions are popularly implemented as multi-layer perceptrons (MLPs) withrectified linear units (ReLU). To achieve meshing from learned implicitfunctions, existing methods adopt the de-facto standard algorithm of marchingcubes; while promising, they suffer from loss of precision learned in the MLPs,due to the discretization nature of marching cubes. Motivated by the knowledgethat a ReLU based MLP partitions its input space into a number of linearregions, we identify from these regions analytic cells and analytic faces thatare associated with zero-level isosurface of the implicit function, andcharacterize the theoretical conditions under which the identified analyticfaces are guaranteed to connect and form a closed, piecewise planar surface.Based on our theorem, we propose a naturally parallelizable algorithm ofanalytic marching, which marches among analytic cells to exactly recover themesh captured by a learned MLP. Experiments on deep learning meshreconstruction verify the advantages of our algorithm over existing ones.

Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks