AbstractÐSince the first shape-from-shading (SFS) technique was developed by Horn in the early 1970s, many different approaches have emerged. In this paper, six well-known SFS algorithms are implemented and compared. The performance of the algorithms was analyzed on synthetic images using mean and standard deviation of depth (Z) error, mean of surface gradient (p, q) error, and CPU timing. Each algorithm works well for certain images, but performs poorly for others. In general, minimization approaches are more robust, while the other approaches are faster. The implementation of these algorithms in C and images used in this paper are available by anonymous ftp under the pub/tech_paper/survey directory at eustis.cs.ucf.edu (132.170.108.42). These are also part of the electronic version of paper. Index TermsÐ Shape from shading, analysis of algorithms, Lambertian model, survey of shape from shading algorithms. 1
|
254
|
Illumination for Computer Generated Pictures
– Phong
- 1975
|
|
218
|
Theory for off-specular reflection from roughened surfaces
– Torrance, Sparrow
- 1967
|
|
133
|
Numerical shape from shading and occluding boundaries, Artif. Intell
– Ikeuchi, Horn
|
|
121
|
A viscosity solutions approach to shape-fromshading
– Rouy, Tourin
- 1992
|
|
112
|
A method for enforcing integrability in shape from shading algorithms
– Frankot, Chellappa
- 1988
|
|
81
|
Estimation of illuminant direction, albedo, and shape from shading
– Zheng, Chellappa
- 1991
|
|
63
|
Height and gradient from shading
– Horn
- 1990
|
|
63
|
Local shading analysis
– Pentland
- 1984
|
|
62
|
A.: Improved Methods of Estimating Shape from Shading Using the Light Source Coordinate System
– Lee, Rosenfeld
- 1985
|
|
61
|
from shading: A method for obtaining the shape of a smooth opaque object from one view. MAC-TR-79
– Horn
- 1970
|
|
56
|
M.J.: Shape and Source from Shading
– Horn, Brooks
|
|
53
|
Finding the Illuminant Direction
– Pentland
- 1982
|
|
46
|
Interpreting line drawings as three-dimensional surfaces
– Barrow, Tenenbaum
- 1981
|
|
40
|
A simple algorithm for shape from shading
– Bichsel, Pentland
- 1992
|
|
39
|
Local shape from specularity
– Healey, Binford
- 1987
|
|
34
|
Direct method for reconstructing shape from shading
– Dupuis, Oliensis
- 1991
|
|
33
|
The direct computation of height from shading
– Leclerc, Bobick
- 1991
|
|
31
|
The Eikonal equation: Some results applicable to computer vision,“J
– Bruss
- 1982
|
|
30
|
Shape from shading using linear approximation
– Tsai, Shah
- 1994
|
|
25
|
Mutual illumination
– Forsyth, Zisserman
- 1989
|
|
24
|
Shape from shading as a partially well-constrained problem
– Oliensis
- 1991
|
|
24
|
Surface descriptions from stereo and shading
– Blake, Zisserman, et al.
- 1989
|
|
23
|
Photometric motion
– Pentland
- 1991
|
|
23
|
Using Shadows in Finding Surface Orientations
– Shafer, Kanade
- 1983
|
|
20
|
Shape from shading with a linear triangular element surface model
– Lee, Kuo
- 1993
|
|
20
|
A global algorithm for shape from shading
– Oliensis, Dupuis
- 1993
|
|
18
|
Recovering three dimensional shape from a single image of curved objects
– Malik, Maydan
- 1989
|
|
18
|
Shape information from shading: A theory about human perception
– Pentland
- 1988
|
|
18
|
Reconstruction of three-dimensional surfaces from two-dimensional binary images
– RAVIV, PAO, et al.
- 1989
|
|
18
|
Dynamic Motion Vision
– Heel
- 1989
|
|
18
|
Perception of solid shape from shading
– Mingolla, Todd
- 1986
|
|
17
|
Fast shape from shading
– Szeliski
- 1991
|
|
14
|
Estimation of the light source distribution and its use in integrated shape recovery from stereo and shading
– Hougen, Ahuja
- 1993
|
|
13
|
Diffuse shading, visibility fields, and the geometry of ambient light
– Langer, Zucker
- 1993
|
|
13
|
Impossible shaded images
– Horn, Szeliski, et al.
- 1993
|
|
12
|
An optimal algorithm for the derivation of shape from shadows
– Hatzitheodorou, Kender
- 1988
|
|
11
|
Theory for O -Specular Re ection from Roughened Surfaces
– Torrance, Sparrow
- 1967
|
|
10
|
The entry-exit method of shadow boundary segmentation
– Hambrick, Loew, et al.
- 1987
|
|
10
|
Shape from shading via level sets
– Kimmel, Bruckstein
- 1992
|
|
9
|
Active Photometric Stereo
– Clark
- 1992
|
|
5
|
Shading logic: a heuristic approach to recover shape from shading
– Vega, Yang
- 1993
|
|
4
|
A provably convergent algorithm for shape from shading
– Lee
- 1985
|
|
3
|
Integration of Shape from X Modules: Combining Stereo and Shading
– Cryer, Tsai, et al.
- 1993
|
|
3
|
N.: Estimation of the Light Source Distribution and Its Use
– Hougen, Ahuja
- 1993
|
|
3
|
Surface Re ection: Physical and Geometrical Perspectives
– Nayar, Ikeuchi, et al.
- 1991
|
|
2
|
ªNumerical Shape from Shading and Occluding Boundaries,º
– Ikeuchi, Horn
- 1981
|
|
2
|
ªA Global Algorithm for Shape from Shading,º
– Oliensis, Dupuis
- 1993
|
|
2
|
A variational approach to sensor fusion using registered range and intensity data
– Pien, Gauch
- 1993
|
|
2
|
Segmentation between overlapping parts: The moving shadows approach
– Raviv, Pao, et al.
- 1989
|
|
2
|
Shape from interre ections
– Nayar, Ikeuchi, et al.
- 1990
|