Suggestive Contours for Conveying Shape

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

Contours

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 Contour Generator = all p s.t.

n

(p) ٠

v

(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

Curvature

The curvature k(p) = The reciprocal of the radius of the circle that best approximates the curve at p.

w = The projection of v onto the tangent plane.

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

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 direction of w is positive: D w k r > 0 r in the

Equivalent Definitions

Definition II and III Suggestive Contour Generator (II) the direction of

w

.

= The set of minima of

n

٠

v

in ► 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 and k 2 Φ+ k 2 (p) sin 2 Φ for each point. k 1 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 camera origin.

v

by placing a diffuse light source at the 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 .

 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 Good results Very easy to implement - < 50 lines of code Object:    Faster Theoretically better results 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