Efficient prior specification in procedural 3D modelling

Abstract

Procedural modelling programs can be used to generate 3D scenes of infinite variety, alleviating the need for manual repetitive tasks in 3D modelling. We utilize a probabilistic programming interpretation of controlled procedural modelling programs, and address the issue of prior misspecification, which can hinder the accurate representation of 3D models. We are interested in cases where prior knowledge is available as probabilistic tail bounds on global, high-level features of the 3D scene. In general, specifying the prior parameters satisfying the aforementioned high-level prior knowledge requires a parameter space search. However, programs with a large number of random variables, 3D scenes described by multiple procedural modelling programs and the need for repeated prior predictive checks might necessitate a prolonged prior parameter search. We reduce the time complexity of prior parameter search, and thus improve the process of modelling 3D scenes, by replacing computationally expensive computations of tail bounds constraints with the lower bounds provided by Selberg’s inequality. We present the theoretical underpinnings of our method and a detailed feasibility problem formulation that can be solved numerically. We compare our method to related approaches in the literature, and finally, we demonstrate its application in the procedural generation of 3D scenes in the agricultural domain.