# SALD: Sign Agnostic Learning with Derivatives Source: [SALD: Sign Agnostic Learning with Derivatives]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:56:44.720Z Authors: Matan Atzmon, Yaron Lipman Published: 2020-06-09T16:54:57.000Z ## Abstract Learning 3D geometry directly from raw data, such as point clouds, triangle soups, or unoriented meshes is still a challenging task that feeds many downstream computer vision and graphics applications. In this paper, we introduce SALD: a method for learning implicit neural representations of shapes directly from raw data. We generalize sign agnostic learning (SAL) to include derivatives: given an unsigned distance function to the input raw data, we advocate a novel sign agnostic regression loss, incorporating both pointwise values and gradients of the unsigned distance function. Optimizing this loss leads to a signed implicit function solution, the zero level set of which is a high quality and valid manifold approximation to the input 3D data. The motivation behind SALD is that incorporating derivatives in a regression loss leads to a lower sample complexity, and consequently better fitting. In addition, we prove that SAL enjoys a minimal length property in 2D, favoring minimal length solutions. More importantly, we are able to show that this property still holds for SALD, i.e., with derivatives included. We demonstrate the efficacy of SALD for shape space learning on two challenging datasets: ShapeNet that contains inconsistent orientation and non-manifold meshes, and D-Faust that contains raw 3D scans (triangle soups). On both these datasets, we present state-of-the-art results. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Surface Reconstruction on 20 real-scanned meshes 1.0 (test)](): Surface Reconstruction; 20 real-scanned meshes 1.0 (test); Chamfer Distance (dc): 31.13. - [Unconditional Implicit Shape Generation on Human (test)](): Unconditional implicit shape generation; Human (test); Error Rate (ER): 7.21. - [Unconditional implicit shape generation on Animal (test)](): Unconditional implicit shape generation; Animal (test); ER: 8.12. ## Original sources and implementation [Original paper]() [PDF]()