Sparse representation of terrains for procedural modeling

In this paper, we present a simple and efficient method to represent terrains as elevation functions built from linear combinations of landform features (atoms). These features can be extracted either from real world data‐sets or procedural primitives, or from any combination of multiple terrain models. Our approach consists in representing the elevation function as a sparse combination of primitives, a concept which we call Sparse Construction Tree , which blends the different landform features stored in a dictionary. The sparse representation allows us to represent complex terrains using combinations of atoms from a small dictionary, yielding a powerful and compact terrain representation and synthesis tool. Moreover, we present a method for automatically learning the dictionary and generating the Sparse Construction Tree model. We demonstrate the efficiency of our method in several applications: inverse procedural modeling of terrains, terrain amplification and synthesis from a coarse sketch.