Sorce: Suggestive Contours for Conveying Shape. (SIGGRAPH 2003) Doug DeCarlo, Adam Finkelstein, Szymon Rusinkiewicz, Anthony Santella. 1 Suggestive Contours for Conveying Shape CS 174 Robert Li May 24, 2004

Contours Contour Generator = all p s.t. n(p)٠v(p) = 0 set of points on the surface such that the unit surface normal is perpendicular to the view vector. Contour = The visible portions of the contour generator projected onto the image plane S = a smooth closed surface n(p) = unit surface normal at p v(p) = c - p, the view vector p = a point on S c = the camera

Curvature The curvature k(p) = The reciprocal of the radius of the circle that best approximates the curve at p. The radial plane = Plane defined by the vectors n, w and the point p. The radial curve = The set of points in S intersect the radial plane. w = The un-normalized projection of v onto the tangent plane at p w = The projection of v onto the tangent plane.

Suggestive Contours Definition I Suggestive Contour Generator (I): The set of points on the surface at which its radial curvature k r is 0, and the directional derivative of k r in the direction of w is positive: D w k r > 0

Equivalent Definitions Definition II and III Suggestive Contour Generator (II) = The set of minima of n ٠ v in the direction of w. ► Suggestive Contour Generator (III) The set of points on the contour generator of a nearby viewpoint (of radial distance less than 90 degrees) that are not in radial correspondence with points on the contour generators of any (radially) closer viewpoint ► Additionally

Object Space Algorithm Test each triangle for two vertices whose sign of n dot v is different. Interpolate to get the zero crossing (Hertzmann zero crossing algorithm for smooth surfaces) Find k r (p) = k 1 (p) cos 2 Φ+ k 2 (p) sin 2 Φ for each point. k 1 and k 2 are the principle curvatures of the face and Φ is the angle between w(p) and the principle curvature direction corresponding to k 1 Find the zeros of k r (p) using the zero crossing algorithm These should be loops on the surface Calculate D w k r and make sure it is positive Handle numerical errors

Image Space Algorithm Approximate n ٠ v by placing a diffuse light source at the camera origin. Search image for valleys in intensity by finding stable minima of (n ٠ v) /||v|| : For pixel i with intensity p i, define the pixel of the greatest intensity in a radius r around p i to be p max. For pixel i with intensity p i, define the pixel of the greatest intensity in a radius r around p i to be p max. Label i a valley if two conditions are met: no more than a certain percentage s of the pixels in this disk are strictly darker than p i ; and p max - p i exceeds a fixed threshold d. Label i a valley if two conditions are met: no more than a certain percentage s of the pixels in this disk are strictly darker than p i ; and p max - p i exceeds a fixed threshold d. Remove small irregularities with a median filter of radius r.

Results from Paper Contours image space object space

My Results

Comparison

Comparison Between Algorithms Image: Slower Slower Good results Good results Very easy to implement - < 50 lines of code Very easy to implement - < 50 lines of codeObject: Faster Faster Theoretically better results Theoretically better results Much harder to implement – several hundred lines of code Much harder to implement – several hundred lines of code

Future Directions Improve object space algorithm. Need less parameters. Implement algorithms on the GPU by using vertex and pixel shaders. Work better with smooth surfaces