A Novel Line Hatching Style through Conformal Mapping

Abstract

Pen-and-ink line hatching is a non-photorealistic rendering (NPR) image style typically characterized by monochrome, locally near-parallel lines. Our motivation was to generate line hatching images inspired by the Grendel image by Emil Antonucci. Antonucci's images are composed of many cells containing relatively short near-parallel lines. We develop an automatic NPR system that converts a photo into an output image portraying a novel line hatching style. One key characteristic of our approach is its use of conformal mapping to reshape segmented regions into a standardized shape. After drawing the lines on the standardized shape, we then transfer the lines back to the segment region. The transformation automatically distorts the lines to follow the segment region contours. Our process generates line hatching images that have short near-parallel lines, lines that change direction to represent feature boundaries, line density and line width variations to represent tone intensity, edge lines, and line perturbations.I would like to acknowledge my supervisor Professor David Mould. He has been my sounding board, my devil's advocate, and most of all my teacher. Without his direction and inspiration, this thesis would not have been possible. Any problems I encountered, he was my sounding board: What is the problem? What are potential solutions? Who has solved this problem before? His wealth of knowledge consistently got me unstuck. From his experience he exposed me to weird approaches and processes. Without him, I would not know about Barycentric coordinates, Conformal mapping, nor realize there is a difference between classical dithering and ordered dithering. Finally he always pushed for 100 percent in everything we did. I cannot say that I ever achieved this goal, however, I did learn a lot about graphics and myself in the pursuit.Many times I would feel lost or hit a wall. Sometimes I became extremely frustrated, failing to see the light at the end of the tunnel. In these situations Professor Sonia Chiasson, my wife, was there to drag me out of these ruts, to show me that there was an end to this journey, and that it was not as far as I thought. Without all her support, the thesis would not have been completed.Thank you to the defense committee members: Professor Anil Somayaji, Professor Robert Laganiere, and Professor Lianying Zhao. I thank you for spending your precious time reading through my thesis and for providing feedback. Each of you brought a unique perspective and your contributions improved the end result.