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A new method that allows capturing shapes from an input image using an optimisation-based approach is presented. An objective function is designed by introducing two terms: the first term is used to minimise the difference between the shading of the reconstructed shape and the input image, and the second term is to apply smoothness constraints to the reconstructed shape. To achieve shape reconstruction in high quality, the authors propose weighted smoothness constraint, which is designed to be anti-proportional to the intensity gradients in the input image. Under this constraint, flat image areas make more contribution towards the smoothness of the reconstructed shape, while the fine details from the image areas with large intensity gradients are preserved in the reconstructed result. Given the objective function, wavelets are used to obtain the solution effectively. Since wavelets accurately preserve high-frequency data, they can be used to solve the objective function with the advantage of allowing for a good recovery of fine details from the input image. The authors have chosen to use the Daubechies wavelets, which are orthonormal and compactly supported. Here the formulation of the algorithm based on the mathematical details is provided. Finally, the authors present experimental results on a number of different images and compare them against some well-known methods and ground truth (where available). The comparison shows that the method is effective and offers good results.
References
-
-
1)
-
Hsieh, J., Liao, H.M., Ko, M., Fan, K.: `Wavelet-based shape from shading', Proc. ICIP-94., IEEE Int. Conf. Image Processing, 1994, p. 125–129.
-
2)
-
Latto, A., Resnikoff, H.L., Tenenbaum, E.: `The evaluation of connect coefficients of compactly supported wavelets', Proc. USA-French Workshop on wavelet and Turbulence, 1991, Princeton University.
-
3)
-
Dupuis, P., Oliensis, J.: `Direct method for reconstructing shape from shading', IEEE Proc. Computer Vision and Pattern Recognition, 1992, p. 453–458.
-
4)
-
Durou, J.D., Falcone, M., Sagona, M.: `A survey of numerical methods shading', Technical, 2004, IRIT, Université Paul Sabatier, Toulouse.
-
5)
-
B.K.P. Horn
.
Height and gradient from shading.
Int. J. Comput. Vis.
,
1 ,
584 -
595
-
6)
-
J. Oliensis
.
Shape from shading as a partially well-constrained problem.
Comput. Vis. Graph. Image Process. Image Underst.
,
163 -
183
-
7)
-
R. Kozera ,
R. Klette
.
Finite difference based algorithms in linear shape from shading.
Mach. Graph. Vis.
,
2 ,
157 -
201
-
8)
-
Zhang, R., Tsai, P., Cryer, J.E., Shah, M.: `Analysis of shape from shading techniques', IEEE CVPR-94, 1994, Seattle, Washington, p. 377–384.
-
9)
-
P.L. Worthington ,
E.R. Hancock
.
New constraints on data-closeness and needle map consistency for shape-from-shading.
IEEE Trans. Pattern Anal. Mach. Intell.
,
12 ,
1250 -
1267
-
10)
-
J. Malik ,
D. Maydan
.
Recovering three-dimensional shape from a single image of curved objects.
IEEE Trans. Pattern Anal. Mach. Intell.
,
6 ,
555 -
566
-
11)
-
H. Ragheb ,
E.R. Hancock
.
Surface radiance correction for shape from shading.
Pattern Recognit.
,
1574 -
1595
-
12)
-
Y. Zhang ,
Y.H. Yang
.
Multiple illuminant direction detection with application to image synthesis.
IEEE Trans. Pattern Anal. Mach. Intell.
,
8 ,
915 -
920
-
13)
-
A. Pentland
.
Photometric motion.
IEEE Trans. Pattern Anal. Mach. Intell.
,
9 ,
879 -
890
-
14)
-
Q. Zheng ,
R. Chellappa
.
Estimation of illuminant direction, albedo, and shape from shading.
IEEE Trans. Pattern Anal. Mach. Intell.
,
7 ,
680 -
702
-
15)
-
Horn, B.K.P.: `Shape from shading: a method for obtaining the shape of a smooth opaque object from one view', 1970, PhD, MIT.
-
16)
-
T. Okatani ,
K. Deguchi
.
Shape reconstruction from an endoscope image by shape from shading technique for a point light source at the projection center.
Comput. Vis. Image Underst.
,
2 ,
119 -
131
-
17)
-
A.P. Pentland
.
Local shading analysis.
IEEE Trans. Pattern Anal. Mach. Intell.
,
2 ,
170 -
187
-
18)
-
Leclerc, Y.G., Bobick, A.F.: `The direct computation of height from shading', Proc. IEEE Conf. Computer Vision and Pattern Recognition, June 1991, Maui, Hawaii, USA, p. 552–558.
-
19)
-
Pentland, A.: `Shape information from shading: a theory about human perception', Proc. Int. Conf. Computer Vision, 1988, p. 404–413.
-
20)
-
Brooks, M.J., Horn, B.K.P.: `Shape and source from shading', Proc. Int. Joint Conf. Artificial Intelligence, 1985, p. 932–936.
-
21)
-
G. Beylkin
.
On the representation of operators in bases of compactly supported wavelets.
SIAM J. Numer. Anal.
,
1716 -
1740
-
22)
-
B.K.P. Horn ,
P.H. Winston
.
(1975)
Obtaining shape from shading information, The psychology of computer vision.
-
23)
-
G. Ulich
.
Provably convergent methods for the linear and nonlinear shape from shading problem.
J. Math. Imaging Vis.
,
1 ,
69 -
82
-
24)
-
Tsai, P.S., Shah, M.: `A simple shape from shading algorithm', CVPR-92, 1992, p. 734–736.
-
25)
-
R.T. Frankot ,
R. Chellappa
.
A method for enforcing integrability in shape from shading algorithms.
IEEE Trans. Pattern Anal. Mach. Intell.
,
4 ,
439 -
451
-
26)
-
Zhang, R., Tsai, P., Cryer, J., Shah, M.: `A survey of shape from shading methods', CS-TR-97-15, Technical, 1997, Computer Science Department University of Central Florida.
-
27)
-
E. Prados ,
F. Camilli ,
O. Faugeras
.
A unifying and rigorous shape from shading method adapted to realistic data and applications.
J. Math. Imaging Vis.
,
307 -
328
-
28)
-
White, R., Forsyth, D.A.: `Combining cues: shape from shading and texture', Proc. CVPR, 2006, p. 1809–1816.
-
29)
-
Daubechies, I.: `Ten lectures on wavelets', CBMS-NSFReg. Conf. Ser. Appl. Math. 61, Philadelphia, Soc. Ind. Appl. Math., 1992.
-
30)
-
Tan, R.T., Nishino, K., Ikeuchi, K.: `Separating diffuse and specular reflection components based on surface color ratio and chromaticity', Proc. Int. Assoc. Pattern Recognition Workshop Machine Vision Applications, 2002, p. 14–19.
-
31)
-
Daniel, P., Durou, J.D.: `From deterministic to stochastic methods for shape from shading', Proc. 4th Asian Conf. Computer Vision, January 2000, Taipei, Taiwan, p. 187–192.
-
32)
-
Pentland, A.P.: `The perception of shape from shading', Proc. OSA Annual Meeting, 1982, Tucson, AZ.
-
33)
-
K.M. Lee ,
C.-C.J. Ku
.
Shape from shading with a linear triangular element surface model.
IEEE Trans. Pattern Anal. Mach. Intell.
,
8 ,
815 -
822
-
34)
-
Kimmel, R., Bruckstein, A.M.: `Global shape from shading', Proc. 12th Int. Conf. Pattern Recognition, October 1994, Jerusalem, Israel, I, p. 120–125.
-
35)
-
I. Shimishoni ,
Y. Moses ,
M. Lindenbaum
.
Shape reconstruction of 3D bilaterally symmetric surfaces.
Int. J. Comput. Vis.
,
97 -
110
-
36)
-
C.H. Lee ,
A. Rosenfeld
.
Improved methods of estimating shape from shading using the light source coordinate system.
Artif. Intell.
,
125 -
143
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