Abstract
This article concerns a new type of photometric stereo algorithm for which outliers such as highlights and shadows, including attached and cast shadow, are mixed with Lambertian data. The underlying motivation behind this algorithm is very simple: an axial symmetrical setup in 6-light photometric stereo can be used to offer advantages. We investigate why an axial symmetrical setup is useful and how it can be used to improve standard photometric stereo. The main result is summarized as a combinatorial photometric stereo algorithm which embeds a non-Lambertian detection procedure. To apply this algorithm, it involves three steps. First, it combines a group of reflectance intensities to make five virtual images, whose equivalence is guaranteed due to the axial symmetrical setup of the 6-source photometric stereo system. Second, comparison between these virtual images generates a five by five skew-symmetric matrix. The Frobenius norm of this matrix is then employed as an index to determine whether there is a non-Lambertian pixel present among the six pixels. Finally, after identification of non-Lambertian pixels, standard photometric stereo is performed to realize 3D modeling. Validation of this algorithm has been conducted with both synthetic and real images. The real images were obtained from a newly designed 3D imaging device, the Skin Analyzer, for clinical inspection of melanoma. Experimental study shows that combinatorial photometric stereo gives promising results in suppressing shadows and highlights, while improving 3D reconstruction results. Furthermore, error analysis illustrates how to determine an appropriate threshold value to enable the algorithm to achieve optimal performance.
Similar content being viewed by others
References
Woodham, R.: Photometric stereo: a reflectance map technique for determining surface orientation from image. In: Proceedings of the SPIE (1978)
Coleman E.N., Jain R.: Obtaining 3-dimensional shape of textured and specular surfaces using four-source photometry. Comput. Graph. Image Underst. 18, 309–328 (1982)
Nayar S.K., Ikeuchi K., Kanade T.: Determining shape and reflectance of hybrid surfaces by photometric sampling. IEEE Trans. Robot. Autom. 6(4), 418–430 (1990)
Belhumeur, P.N., Kriegman, D.J.: What is the set of images of an object under all possible lighting conditions? IEEE Int. Conf. Comput. Vis. Pattern Recognit. (1996)
Belhumeur P.N., Kriegman D.J., Yuille A.: The bas-relief ambiguity. Int. J. Comput. Vis. 35(1), 33–44 (1991)
Mukaigawa Y., Ishii Y., Shakunaga T.: Analysis of photometric factors based on photometric linearization. J. Opt. Soc. Am. A 24(10), 3326–3334 (2007)
Hayakawa H.: Photometric stereo under a light source with arbitrary motion. J. Opt. Soc. Am. A 11(11), 3079–3089 (1994)
Basri R., Jacobs D. et al.: Photometric stereo with general, unknown lighting. Int. J. Comput. Vis. 72(3), 239–257 (2007)
Basri R., Jacobs D.: Lambertian reflectance and linear subspaces. IEEE Trans. Pattern Anal. Mach. Intell. 25, 218–233 (2003)
Hertzmann A., Seitz S.: Example-based photometric stereo: shape reconstruction with general, varying BRDFs. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1254–1264 (2005)
Zhou Z., Tan P.: Ring-Light Photometric Stereo. In: Daniilidis, K., Maragos, P., Paragios, N. (eds) Computer vision—ECCV 2010, pp. 265–279. Springer, Berlin (2010)
Tagare H., deFigueiredo R.: A theory of photometric stereo for a class of diffuse non-Lambertian surfaces. IEEE Trans. Pattern Anal. Mach. Intell. 13(2), 133–152 (1991)
Tan P., Lin S., Quan L.: Subpixel photometric stereo. IEEE Trans. Pattern Anal. Mach. Intell. 30(8), 1460–1471 (2008)
Zhou S.K., Aggarwal G., Chellappa R., Jacobs D.W.: Appearance Characterization of Linear Lambertian Objects, Generalized Photometric Stereo, and Illumination-Invariant Face Recognition. IEEE Trans. Pattern Anal. Mach. Intell. 29(2), 230–245 (2007)
Alldrin, N.G., Kriegman D.J.: Toward reconstructing surfaces with arbitrary isotropic reflectance: a stratified photometric stereo approach. In: IEEE 11th International Conference on Computer Vision (2007)
Holroyd M., Holroyd M. et al.: A photometric approach for estimating normals and tangents. ACM Trans. Graph. 27(5), 1–9 (2008)
Park, J.S., Tou, J.T.: Highlight separation and surface orientations for 3-D specular objects. In: Proceedings of 10th International Conference on Pattern Recognition, NJ USA, vol. 1, pp. 331–335 (1990)
Chandraker M.K., Agarwal S., Kriegman D.J.: ShadowCuts: Photometric Stereo with Shadows. CVPR, Minneapolis (2007)
Zhu S.C., Yuille A.: Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 18(9), 884–900 (1996)
Yu Y.H., Chang J.T.: Shadow graphs and 3D texture reconstruction. Int. J. Comput. Vis. 62(1–2), 35–60 (2005)
Barsky S., Petrou M.: The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1239–1252 (2003)
Sun J., Smith M., Smith L., Midha S., Bamber J.: Object Surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities. Image Vis. Comput. 25, 1050–1057 (2007)
Miyazaki D., Hara K., Ikeuchi K.: Median Photometric Stereo as Applied to the Segonko Tumulus and Museum objects. Int. J. Comput. Vis. 86(2–3), 229–242 (2010)
Higo, T., Matsushita Y., et al.: Consensus photometric stereo. In: IEEE International Conference on Computer Vision and Pattern Recognition (2010)
Sun J., Smith M., Smith L., Coutts L., Dabis R., Harland C., Bamber J.: Reflectance of human skin using colour photometric stereo: with particular application to pigmented lesion analysis. Skin Res. Technol. 14(2), 173–179 (2007)
Shashua, A.: Geometry and Photometry in 3D Visual Recognition. Massachusetts Institute of Technology, Cambridge (1992)
Fischler M., Bolles R.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24(6), 381–395 (1981)
Frankot R., Chellappa R.: A method for enforcing integrability in shape from shading algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 439–451 (1988)
Wu, L., Ganesh, A., et al.: Robust photometric stereo via low-rank matrix completion and recovery. In: Proceedings of the ACCV (2010)
Marsden J.E., Tromba A.J.: Vector Calculus (4th edn.). W. H. Freeman and Company, San Francisco (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhou, Y., Smith, M.L., Smith, L. et al. Combinatorial photometric stereo and its application in 3D modeling of melanoma. Machine Vision and Applications 23, 1029–1045 (2012). https://doi.org/10.1007/s00138-011-0356-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00138-011-0356-6