  Learning-based isosurface extraction methods have recently emerged as a
robust and efficient alternative to axiomatic techniques. However, the vast
majority of such approaches rely on supervised training with axiomatically
computed ground truths, thus potentially inheriting biases and data artifacts
of the corresponding axiomatic methods. Steering away from such dependencies,
we propose a self-supervised training scheme for the Neural Dual Contouring
meshing framework, resulting in our method: Self-Supervised Dual Contouring
(SDC). Instead of optimizing predicted mesh vertices with supervised training,
we use two novel self-supervised loss functions that encourage the consistency
between distances to the generated mesh up to the first order. Meshes
reconstructed by SDC surpass existing data-driven methods in capturing
intricate details while being more robust to possible irregularities in the
input. Furthermore, we use the same self-supervised training objective linking
inferred mesh and input SDF, to regularize the training process of Deep
Implicit Networks (DINs). We demonstrate that the resulting DINs produce
higher-quality implicit functions, ultimately leading to more accurate and
detail-preserving surfaces compared to prior baselines for different input
modalities. Finally, we demonstrate that our self-supervised losses improve
meshing performance in the single-view reconstruction task by enabling joint
training of predicted SDF and resulting output mesh. We open-source our code at
https://github.com/Sentient07/SDC
