3-D Shape from Shading - PowerPoint PPT Presentation

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3-D Shape from Shading

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Image formation and the shape from shading problem. 1-2. 3D shape from shading ... radiance. surface radiance. surface irradiance. 1-5. Reflectance functions ... – PowerPoint PPT presentation

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Title: 3-D Shape from Shading


1
3-D Shape from Shading
  • Image formation and the shape from shading problem

2
3D shape from shading
Prados Faugeras, 2005
3
Image intensities depend on
  • 3-D surface shape
  • Surface reflectance properties
  • Illumination in the scene
  • Viewing geometry

Compute explicitly
General assumptions
4
Viewing geometry
What fraction of the incident light is reflected
toward the viewer?
radiance
irradiance
Reflectance Function F(i,e,g)
surface radiance surface irradiance
5
Reflectance functions
Fmirror(i,e,g) 1 if i e i e g
0 otherwise
Fmatte(i,e,g) ? cos i if i lt 90 0
otherwise ? albedo
6
Representing surface orientation using
stereographic projection
sphere has radius 1
g
f
(f,g) (0, 2)
(f,g) (2, 0)
viewer
7
Given surface brightness, can we determine
surface orientation?
8
Reflectance Map R(f,g)
Given (1) light source (2) viewer position (3)
surface reflectance properties
R(f,g) relates brightness to surface orientation
Image Irradiance Equation I(x,y) I0 ?(x,y)
R(f,g)
9
Ikeuchi Horn shape-from-shading algorithm
  • Three sources of constraint
  • (1) image intensity I(x,y)
  • (2) surface smoothness
  • e.g. minimize total variation in surface
  • (3) points of known surface orientation
  • e.g. occluding boundaries, shadow boundaries

(known viewer direction, light source direction,
surface reflectance properties)
I(x,y) I0 ?(x,y) R(f,g)
10
Boundaries influence shape perception
Ramachandran, 1988
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