Discrete Element Texture Synthesis

A variety of natural and man-made phenomena can be characterized by repetitive discrete elements. Examples include a stack of fruits, a plate of dish, or a stone sculpture. Although certain results can be produced via existing methods based on procedural or physical simulation, these are often designed for specific applications. Some of these methods can also be hard to control.

We present discrete element texture synthesis, a data-driven method for placing repetitive discrete elements within a given large-scale structure. Our main goal is to provide a general approach that works for a variety of phenomena instead of just specific scenarios, including different dimensionality, different element properties and distributions, different number of element types, as well as physically realistic or artistic phenomena. We also want it easy to use, as the user only needs to specify an input exemplar for the detailed elements and the overall output structure, and our approach will produce the desired combination. Our method is inspired by texture synthesis, a methodology tailored for generating repetitions. However, existing texture synthesis methods cannot adequately handle discrete elements, often producing unnaturally broken or merged elements. Our method not only preserves the individual element properties such as color, shape, size, and orientation, but also their aggregate distributions. It also allows certain application specific controls, such as boundary constraints for physically realistic appearance. Our key idea is a new neighborhood metric for element distribution as well as an energy formulation for synthesis quality and control. As an added benefit, our method can also be applied for editing element distributions.