Redeeming Valleys and Ridges for Line-Drawing

Abstract

This paper presents a new method of line drawing based on the hypothesis that artists draw the lines that decompose the object into parts, and the lines that help convey the shapes of the parts. But they draw these lines differently depending on the viewpoint. Contours are the most obvious part-decomposing lines. Valley lines, which typically delimit convex parts, are also part-decomposing lines. As shape-conveying lines, ridge lines on each part are chosen; they are good at conveying the shape of parts in that they are maxima of the principal curvatures on the part surface. So, valley and ridge lines are good candidates in line-drawing. But they have been dismissed because they are view-independent unlike contours. But because of their shape-conveying capability, they have a strong intuitive appeal as candidates for line-drawing. So we propose a way to ”redeem” them by making them view-dependent: Valley and ridge lines are given strengths depending on how the view direction relates to the surface normals to the lines. On the other hand, when valleys and ridges are extremely strong, for example, when they are sharp edge lines, they are drawn regardless of viewpoint. We have found that the view-dependent valley and ridge lines are quite stable with respect to viewpoint change.