4. RECONSTRUCTION AND OPTIMIZATION
4.2 Optimization
4.2.3 Optimization Flow Chart
Fig.19 Optimization flow chart Reflectance (kd, normal) Initial positions
(Structured light system) +
Light and Camera location
Positions (pos z)
Reflectance (kd,ks,alpha)
Positions (pos z)
Reflectance (σs,σa,η)
Positions (pos z) Lambertian
Optimization
Specular Optimization
Sub-Surface Scattrering Optimization
Phase1
Phase2 Phase2
Chapter 5. Experiment and Result
In this chapter, we describe our experiment and results. There are two kinds of experiments. The first one is a synthesis experiment. We use a bunny from Standford PLY file.
We rendered the bunny with reflectance model and add noise to z values of each point as initial position guesses. Then, we perform our algorithm to evaluate the benefit of shading information. Second, we scanned a real data, a marble statue, and optimized it with our algorithm. The framework is implemented in C++, OpenGL and WIN 32 library with a Pentium4 3.20GHz CPU and 1.5 G RAM. The proposed system is show in Fig 20:
Fig.20 The proposal System
5.1 A Bunny Table1.
data information
Vertex number 35,947 Polygon number 69,451
Original data
(a)
(b)
Fig. 21 Bunny original image (a) frontal view, (b) rear view
Noise Model
(a)
(b)
Fig.22 Bunny with position noise (random noise per vertex)
Synthesis Reflectance
(a)
Phong Model: kd=0.8,ks=0.2,alpha=0.5 Camera(0,0,1000) Light(0,0,1000) (b)
Fig.23 Synthetic bunny images
Optimization with – Phong Model Phase 1-Diffuse Optimization
Cost Error Initial: 9.000712 per pixel Current: 0.019035 per pixel Reflectance parameters: kd=1.236784
(a) Reflectance
initial position cost error=42.584771 per pixel last position cost error=38.288401 per pixel
smooth weight = 0.1 (b)Positions
Fig.24 Phase 1 Optimization
Phase 2 – Specular Optimization
Cost Error Initial: 0.019035 per pixel Current: 0.003346 per pixel Reflectance parameters: kd=0.779817,ks=0.177215,shiness=0.598451
(a)Reflectance
initial position cost error=3.5548330 per pixel last position cost error=3.4629534 per pixel
(b) Positions
Fig.25 Round 2 reflectance optimized data
Optimization with – BSSRDF Model Synthesis Reflectanc
(a)
(b)
BSSRDF Model σs=(2.19,2.62,3.0),σz=(0.0021,0.0041,0.0071),η=1.5 reference by Jensen 2001 [3] Marble Material
Camera(0,0,2900) Light(-45,-20,2730) Fig.26 Synthetic bunny image (by BSSRDF model)
Optimize Synthesis-BSSRDF model
cost error = 0.32 per point (a) Phase1
final cost error = 0.29 per point (b)Phase 2
5.2 A marble statue
5.2.1 Stereo positions
Fig.28 Input structured light images.
Table2
data information
Vertex number 81,027
Reconstruction Result
(a) (b) Fig.29 (a)an input reflectance image (b) scanned data
5.2.2 Optimized Result
Optimization with Phong reflection model
Reflectance parameters:
Initial: kd=0.8, ks=0.2, alpha=0.5, error= 0.127580 per-point
Optimize: kd=0.6428, ks=-0.164, alpha=4.41, error= 0.006225 per-point
Fig.30 The left image shows real reflectance color, and the right image shows optimized reflectance color
Phong Position Optimization
Position error:
Initial: 0.261 per point Optimizing: 0.258 per point
Fig.31 The result of Phong optimized position
Chapter 6. Conclusion and Future work
6.1 Conclusion
This thesis proposes a reconstruction approach that makes use of the reflectance properties to optimize both the stereo positions and the reflectance parameters. The Phong and the BSSRDF model are used as our reflectance model. Therefore, the details of non-lambertian and the sub-surface scattering objects can be reconstructed by our approach.
There are three stages in our approach: First, we utilize the projective calibration to reconstruct a 3D stereo position. Then, the Phong and the BSSRDF reflectance model are used to estimate the reflectance parameters. Last, the estimated reflectance parameters are further utilized to optimize the stereo positions. Our contributions are as follows:
(d) Improving the scanning accuracy of non-lambertian and sub-surface scattering objects.
(e) Utilizing only inexpensive devices.
(f) The reflectance parameters are also estimated. We can use them to render the object from different views and lighting conditions.
6.2 Future work
Our system can be further improved from the following aspects. Our stereo structured light system is not accurate enough but easy to implement. The accurate 3D scanner can be applied for more accurate initial guesses. The BSSRDF reflectance model that we utilize requires heavy computation. Therefore, we only use it for partial detail improvement. Recently, many simplified BSSRDF models are proposed, these reflectance models may also be integrated in to our approach.
Reference
[1] D. Nehab, S. Rusinkiewicz, J. Davis, R. Ramamoorthi,” Efficiently Combining Positions and Normals for Precise 3D Geometry.”, Proceedings of ACM SIGGRAPH, pp. 536 – 543,2005.
[2] T. Yu, N. Xu, N. Ahuja, "Recovering Shape and Reflectance Model of Non-Lambertian Objects from Multiple Views," CVPR, pp. 226-233, 2004.
[3] H. Jensen, S. Marschner, M. Levoy, and P. Hanrahan, "A Practical Model for Subsurface Light Transport", Proceedings of SIGGRAPH, pages 511-518, 2001.
[4] D. Huynh,”Calibration of a Structured Light System: A Projective Approach”, CVPR , Page: 225, 1997.
[5] C. H. Chen and A. C. Kak. “Modeling and Calibration of a Structured Light Scanner for 3-D Robot Vision”. In Proc. IEEE Conf. Robotics and Automation, volume 2, pp. 807-815, 1987.
[6] L. Zhang, B. Curless, and S. M. Seitz. “Spacetime Stereo: Shape Recovery for Dynamic Scenes”. In Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), Madison, W, pp. 367-374, I, June, 2003
[7] A. Hertzmann, S. M. Seitz. “Shape and Materials by Example: A Photometric Stereo Approach”. Proc. IEEE CVPR 2003. Madison, WI. June 2003. Vol. 1. pp. 533-540, 2003.
[8] H. Fang and J. C. Hart. “Textureshop: Texture Synthesis as a Photograph Editing Tool.”
Proc. SIGGRAPH, 2004.
[9] F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. “Limperis.
Geometric considerations and nomenclature for reflectance”. Monograph 161, National Bureau of Standards (US), October 1977.
Eurographics Symposium on Rendering, pages 409-417, ACM Transactions on Graphics (SIGGRAPH'2005), pp. 1032-1039, 2005.
[11] K. M. Lee, C. J. Kuo, “Shape from Shading with a Generalized Reflectance Map Model”, Computer vision and image understanding, Vol. 67, No. 2, pp. 143–160, Aug.1997.
[12] A. Hertzmann, S. Seitz, “Shape and Materials by Example: A Photometric Stereo Approach”, Computer Vision and Pattern Recognition, 2003. Proceedings. Vol. 1, pp.
533-540, June 2003
[13] G. Vogiatzis, P. H. S. Torr, R., ” Volumetric graph-cut”, Cipolla,Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) , 2005.
[14] S.R. Marschner, “Inverse Rendering for Computer Graphics,” Ph.D. Thesis, Cornell University, Aug. 1998.
[15] P. Debevec, T. Hawkins, C. Tchou, H.P. Duiker, W. Sarokin, and M. Sagar. “Acquiring the reflectance field of a human face”, Proceedings of the 27th annual conference on
Computer graphics and interactive techniques, pp. 145– 156. 2000
[16] R.C. Love. “Surface Reflection Model Estimation from Naturally Illuminated Image Sequences”, PhD thesis, The University of Leeds, Sep. 1997.
[17] J. I. Apricio, J.G.Garcia-Bermejo, “An Approach for Determining Phong Reflectance Parameters from Real Objects,” Pattern Recognition, 2000. Proceedings. 15th International Conference on, pp. 568 -571 vol.3 Sept. 2000
[18] R. Ramamoorthi and P. Hanrahan, “A Signal-Processing Framework for Inverse Rendering”, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp.117-128, 2001
[19] Y. Sato, M. D. Wheeler, and K. Ikeuchi. “Object shape and reflectance modeling from observation”, Proceedings of the 24th annual conference on Computer graphics and
interactive techniques, pp. 379–388, 1997.