I’m interested in the way artists use lines to indicate shape in drawings. Strictly speaking, my question is about human vision — how our brains interpret certain lines — but I’m asking it here because those working in shape perception might be able to suggest an answer. It concerns what my visual system thinks it’s seeing in the arrowed parts of drawings such as these, and how this relates to the geometrical properties of the objects and their projection onto two dimensions:
Before continuing with the question, I should add that after I posted it, “D.W.” put it on hold without consulting me, on the grounds that it’s not about computer science. I refer him or her to http: //gfx.cs.princeton.edu/proj/ld3d/ , “Line Drawings of 3D Shapes”. To quote from the top of that page:
This site describes recent research on line drawings of 3D shapes, including studies on how artists create drawings and how people interpret drawings.
So far, this work involves two studies. The first, “Where Do People Draw Lines?,” investigates how artists’ drawings of 3D shapes correlate with the mathematical properties of the shapes, and known computer graphics line drawing techniques. The second, “How Well Do Line Drawings Depict Shape?,” examines how people interpret line drawings, both hand-drawn and computer-generated, and when depiction succeeds and fails.
Note the bit about how drawings correlate with the mathematical properties of the shapes drawn. This is related to the cues that humans and programs use to infer 3-d shape from 2-d projections, which in turn are related to the way that 3-d shapes look when projected onto 2-d surfaces. An excellent writeup of the latter topic is given in http: //www.gestaltrevision.be/pdfs/koenderink/Shape.pdf , “Shadows of Shape” by Jan Koenderink, a mathematician and psychologist known for his researches on visual perception, computer vision, and geometry. I hope what I’ve said in bold shows that my question is relevant to computing, but if not, D.W., please ask a computer-vision expert.
The drawings are by Ken Reid. He drew for the Beano and other comics, and was known for strips such as Frankie Stein, Queen of the Seas, and The Nervs. His faces were often grotesque, with protrusions such as chins and Adam’s apples standing out clearly despite being drawn with very few lines. There are examples of his work on Lew Stringer’s blog at http://lewstringer.blogspot.co.uk/2012/07/ken-reid-genius.html , and a copy of a The Nervs strip at http://1.bp.blogspot.com/_448y6kVhntg/RhIjT_1lF0I/AAAAAAAAA3I/KtvcxEIE3F8/s1600-h/nervs_pg1.jpg . What interests me is why the lines he drew are so effective. What is the visual system interpreting them as?
The images above are from the above-linked strip. In the first image, the back of the knee, there’s an upward-curving line above a short vertical above two downward-curving lines. The higher downward-curving line is presumably the contour of the lower leg. It’s less obvious what the downward-curving line below it is, or whether it corresponds to any physical feature. Nevertheless, it certainly helps in giving a sense of three-dimensional form.
Similarly, in the second image, some of the three upward-curving lines could be folds where the chin presses back against itself. But is the visual system interpreting them all as folds? I don’t know, but again, they readily give a sense of form. Another example is here, from the very first frame in that strip:
As I said at the start, those working in shape perception might have an answer. I’d also be interested to hear from anyone whose vision programs happen to fit Reid’s conventions so well that they can actually deduce from those drawings the shapes he intended.
By the way, I and other readers have noticed that Reid’s drawings seem very “intense”. As one reader commented in a blog, “they seem to enter the subconscious and stick there for the rest of your life”. Why? That’s probably outside the scope of computer vision, but not necessarily. It might be that some classes of line, e.g. closely-spaced lines curving around a cylinder, happen to affect us particularly strongly. So it would be useful to know if there’s something special about the geometry of Reid’s lines.