Geometry Synthesis by Example Ares Lagae, Olivier Dumont, Philip Dutr´ e Department of Computer Science Katholieke Universiteit Leuven {ares,olivierd,phil}@cs.kuleuven.ac.be Abstract In this paper we present a method for geometry synthe- sis by example, inspired by techniques from texture synthe- sis. Given an example of input geometry, we synthesize new output geometry that is perceived similar to the input ge- ometry, but at the same time differs in its local appearance. We assume the input geometry satisfies the constraints of a Markov Random Field model, and represent the input ge- ometry by a hierarchical distance field. This allows us to perform fast matching between a target distance field that is partially synthesized, and the input distance field. Once the target distance field is completed, we copy the original corresponding geometry elements to the synthesized result. We show that automatically generating geometry by exam- ple can be achieved within reasonable computing times, and is able to produce convincing results. 1. Introduction Geometry synthesis relates to geometry modeling much like texture synthesis relates to texture modeling. Textures can be created by hand, generated procedurally, or synthe- sized from existing textures. Likewise, geometry can be modeled by hand, and specific types of geometry can be generated procedurally. However, there are not many tech- niques for generating geometry by example. The problem of geometry synthesis by example can be stated as follows: given an example of input geometry, syn- thesize new geometry that, when perceived by a human ob- server, appears to be similar to the input geometry. Figure 1 shows an example. To formalize this concept of similar- ity, we impose the Markov Random Field (MRF) model on our input geometry. This model assumes that the geome- try is the realization of a local and stationary stochastic pro- cess. This means that the geometry at each location is char- acterized by the geometry in a relatively small neighbor- hood around that location (locality), and that this character- ization is the same for each location on the geometry (sta- tionarity). The synthesized geometry is then perceived sim- Figure 1. The terrain geometry in the large im- age (TERRAIN1) was synthesized from the ex- ample geometry shown in the top left corner. ilar to the input geometry if they both seem to be generated by the same stochastic process. Our technique is a two-phase process. In the analysis phase, we compute the regularly sampled distance field of the input geometry, and organize its hierarchical represen- tation in a tree. In the synthesis phase, we use a tree search algorithm to find the best match for a partially synthesized neighborhood of distance field samples, and replace the un- synthesized samples with those of the best match. In paral- lel, we construct the final synthesized geometry. 2. Related Work Texture Synthesis Numerous approaches have been proposed for texture synthesis. In this overview we limit ourselves to texture syn- thesis techniques that assume a MRF texture model, since our method for geometry synthesis assumes a MRF geom- etry model. For a more complete survey of texture synthe- sis algorithms, we refer to Efros and Freeman [5] and Kwa- tra et al. [17].