Injective 3d deformations based on 2d mesh deformations

Abstract

Aspects and features of the present disclosure relate to providing injective three-dimensional (3D) deformations based on two-dimensional (2D) mesh deformations. For example, a method involves defining at least one 2D mesh deformation based on a designated position of an object represented by an input neural radiance field (NeRF). The method also involves applying the 2D mesh deformation(s) to a 3D piecewise-linear map that operates over a plane and preserves a normal direction to produce prismatic maps. The method further involves composing a 3D deformation for the object from layers defined by the prismatic maps, and parameterizing the 3D piecewise-linear map. The method additionally involves storing or rendering, using the 3D piecewise-linear map, a deformed NeRF injectively representing the object in the designated position. Aspects also include computer systems, apparatus, and computer programs configured to perform the method.