  Digital terrain models (DTMs) are pivotal in remote sensing, cartography, and
landscape management, requiring accurate surface representation and topological
information restoration. While topology analysis traditionally relies on smooth
manifolds, the absence of an easy-to-use continuous surface model for a large
terrain results in a preference for discrete meshes. Structural representation
based on topology provides a succinct surface description, laying the
foundation for many terrain analysis applications. However, on discrete meshes,
numerical issues emerge, and complex algorithms are designed to handle them.
This paper brings the context of terrain data analysis back to the continuous
world and introduces ImplicitTerrain (Project homepage available at
https://fengyee.github.io/implicit-terrain/), an implicit neural representation
(INR) approach for modeling high-resolution terrain continuously and
differentiably. Our comprehensive experiments demonstrate superior surface
fitting accuracy, effective topological feature retrieval, and various
topographical feature extraction that are implemented over this compact
representation in parallel. To our knowledge, ImplicitTerrain pioneers a
feasible continuous terrain surface modeling pipeline that provides a new
research avenue for our community.
