Three-dimensional shape can be drawn using a variety of feature lines, but none of the current definitions alone seem to capture all visually-relevant lines. We introduce a new definition of feature lines based on two perceptual observations. First, human perception is sensitive to the variation of shading, and since shape perception is little affected by lighting and reflectance modification, we should focus on normal variation. Second, view-dependent lines better convey smooth surfaces. From this we define view-dependent curvature as the variation of the surface normal with respect to a viewing screen plane, and apparent ridges as the loci of points that maximize a view-dependent curvature. We present a formal definition of apparent ridges and an algorithm to render line drawings of 3D meshes. We show that our apparent ridges encompass or enhance aspects of several other feature lines.


Paper PDF (7 MB)
Video MOV (460MB)
Slides KEYNOTE (20MB) PDF (9MB) PPT (8MB)
Images ZIP (1.6MB)
Talk Siggraph Talk (slides with voiceover)
Code We have worked with Rusinkiewicz and DeCarlo to incorporate apparent ridges into their RTSC software. Download RTSC to work with apparent ridges, suggestive contours, ridges and valleys, contours and more.
Models Rounded Cube (80KB) Tablecloth (1.5MB) Column (18.5MB)


This work was supported by a NSF CAREER award 0447561 and Grant No. 0429739. Frédo Durand acknowledges a Microsoft Research New Faculty Fellowship and a Sloan Fellowship. Tilke Judd was supported by an NSF graduate fellowship. We thank Rusinkiewicz and DeCarlo for their rtsc software. We thank Yann LeTallec, MIT pre-reviewers and especially the SIGGRAPH reviewers for their extensive and insightful feedback on this work.


  author    = {Tilke Judd and
               Fr{\'e}do Durand and
               Edward H. Adelson},
  title     = {Apparent ridges for line drawing},
  journal   = {ACM Trans. Graph.},
  volume    = {26},
  number    = {3},
  year      = {2007},
  pages     = {19},
  ee        = {http://doi.acm.org/10.1145/1276377.1276401},
  bibsource = {DBLP, http://dblp.uni-trier.de}


INRIA, Grenoble, Dec 19, 2008, Host: Nicolas Holzschuch

ETH, Institute of Computational Science, Zurich Switzerland, July 11, 2007, Host: Markus Gross and Mark Pauly

University of Konstanz, Konstanz, Germany, July 9, 2007, Host: Oliver Deussen

Ecole Normal Superior, Paris, France June 29, 2007, Host: Jean Ponce

Harvard University, Cambridge MA, May 17, 2007, Maxwell Dworkin building, Hosts: Todd Zickler and Steven Gortler

Estonian translation provided by Valerie Bastiaan
Indonesian translation provided by Jordan Silaen
Slovak translation provided by Elze Gudmaniene