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Technical Perspective: Where Do People Draw Lines?

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Once upon a time, computer graphics focused exclusively on realism and the generation of synthetic images that follow the laws of optics. The field eventually realized that other pictorial styles, such as line drawing, offer compelling depictions that can be more visually economical, better at focusing attention and abstracting out unimportant areas, and be more aesthetically pleasing. After all, a significant amount of the pictures generated by artists and designers are not photorealistic; indeed, a great many of them are line drawings. For example, educational diagrams and user manuals often use such simplified style to better eliminate superfluous detail and focus attention. The breadth of situations in which line drawings are used makes it important to develop algorithms to generate them either automatically or in a user-assisted manner.

Inspired by artists' work, a new subfield called non-photorealistic rendering has emerged that seeks to imitate traditional media such as pencil drawing or oil painting. Whereas this new area has contributed exciting algorithms and vastly broadened the variety of visual styles that can be created with computers, the establishment of clear problem statements and evaluation metrics has proven challenging.

In contrast to photorealistic computer graphics, which can be formulated as the solution of the light propagation equation, non-photorealistic styles are elusive. Consider line drawing. What is a set of line strokes that can convey a 3D shape from a given viewpoint? This issue touches upon art and perception, but these two fields offer few answers. The effectiveness of line drawing has been demonstrated with perceptual studies, but the question of what lines should be drawn was ignored and such studies relied on hand-drawn pictures for which the mathematical link between lines and shape cannot be easily investigated.

Computer graphics researchers have had to base line drawing algorithms on hypotheses and intuitions about the relationship between local properties of a shape and the location of appropriate lines. Before computer graphics became interested in the issue, the great mathematician David Hilbert hypothesized that differential geometry holds the answer and that lines should be drawn at so-called parabolic curves. However, once computers enabled the automatic extraction of such curves from 3D models, it became clear they do not lead to compelling drawings. New definitions of lines based on a variety of differential geometry properties were proposed and the quality of computer-generated drawings improved.

We now have many available mathematical feature-line definitions, but the crucial question remains the precise characterization of where skilled human artists place lines to convey a 3D shape. This is the issue tackled by Cole et al. in the following paper. The central challenge to relate artists' drawings and shape is registration. One need not only a drawing of a known shape, but also the precise spatial registration of stroke locations onto the shape. Tracing the drawing on top of a photorealistic rendering of the shape could solve registration but would likely bias artists. The authors address this by asking artists to first draw the shape on white paper, and then reproduce their drawing by tracing it on top of a photorealistic rendering of the shape. This method enabled the gathering of a set of precisely registered drawings and shapes.

The following study is exciting not only for computer graphics, but also for the understanding of human perception and art.

This study is exciting not only for computer graphics, but also for the understanding of human perception and art. Line drawings are intriguing because they offer stimuli that are very different from real scenes, and that our ancestors have not encountered during their evolution. Understanding their effectiveness at conveying scenes might shed light on the strategy used by our visual system and what locations of a shape carry more visual information.

One might argue that handmade pictures are just one baseline and that the real metric should be the effectiveness at conveying shape, regardless of how similar a drawing is to that of the artist's. The authors have studied this question as well in a companion paper entitled "How Well Do Line Drawings Depict Shape?," which I highly recommend. Together, these two papers dramatically enhance our understanding of line drawing and will lead to more effective algorithms.

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Frédo Durand ( is an associate professor in Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, and a member of the Computer Science and Artificial Intelligence Laboratory.

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