Synthesis and evaluation of geometric textures
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Two-dimensional geometric textures are the geometric analogues of raster (pixel-based) textures and consist of planar distributions of discrete shapes with an inherent structure. These textures have many potential applications in art, computer graphics, and cartography. Synthesizing large textures by hand is generally a tedious task. In raster-based synthesis, many algorithms have been developed to limit the amount of manual effort required. These algorithms take in a small example as a reference and produce larger similar textures using a wide range of approaches. Recently, an increasing number of example-based geometric synthesis algorithms have been proposed. I refer to them in this dissertation as Geometric Texture Synthesis (GTS) algorithms. Analogous to their raster-based counterparts, GTS algorithms synthesize arrangements that ought to be judged by human viewers as “similar” to the example inputs. However, an absence of conventional evaluation procedures in current attempts demands an inquiry into the visual significance of synthesized results. In this dissertation, I present an investigation into GTS and report on my findings from three projects. I start by offering initial steps towards grounding texture synthesis techniques more firmly with our understanding of visual perception through two psychophysical studies. My observations throughout these studies result in important visual cues used by people when generating and/or comparing similarity of geometric arrangements as well a set of strategies adopted by participants when generating arrangements. Based on one of the generation strategies devised in these studies I develop a new geometric synthesis algorithm that uses a tile-based approach to generate arrangements. Textures synthesized by this algorithm are comparable to the state of the art in GTS and provide an additional reference in subsequent evaluations. To conduct effective evaluations of GTS, I start by collecting a set of representative examples, use them to acquire arrangements from multiple sources, and then gather them into a dataset that acts as a standard for the GTS research community. I then utilize this dataset in a second set of psychophysical studies that define an effective methodology for comparing current and future geometric synthesis algorithms.