Abstract
The paper presents a new approach for shape recovery based on integrating geometric and photometric information. We consider 3D bilaterally symmetric objects, that is, objects which are symmetric with respect to a plane (e.g., faces), and their reconstruction from a single image. Both the viewpoint and the illumination are not necessarily frontal. Furthermore, no correspondence between symmetric points is required.
The basic idea is that an image taken from a general, non frontal viewpoint, under non-frontal illumination can be regarded as a pair of images. Each image of the pair is one half of the object, taken from different viewing positions and with different lighting directions. Thus, one-image-variants of geometric stereo and of photometric stereo can be used. Unlike the separate invocation of these approaches, which require point correspondence between the two images, we show that integrating the photometric and geometric information suffice to yield a dense correspondence between pairs of symmetric points, and as a result, a dense shape recovery of the object. Furthermore, the unknown lighting and viewing parameters, are also recovered in this process.
Unknown distant point light source, Lambertian surfaces, unknown constant albedo, and weak perspective projection are assumed. The method has been implemented and tested experimentally on simulated and real data.
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References
Basri, R. and Moses, Y. 1999. When is it possible to identify 3D objects from single images using class constraints? Int. J. of Comp. Vision, 33(2):1–22.
Blake, A., Zisserman, A., and Knowles, G. 1985. Surface description from stereo and shading. Image Vision Computation, 3(4):183–191.
Cham, T. and Cipolla, R. 1995. Symmetry detection through local skewed symmetries. Image and Vision Computing Journal, 5:439–450.
Cryer, J.E., Tsai, P.S., and Shah, M. 1995. Integration of shape from shading and stereo. PR, 28(7):1033–1043.
Faugeras, O.D. 1993. Three-Dimensional Computer Vision. MIT Press: Boston MA.
Freiberg, S.A. 1986. Finding axes of skewed symmetry. Computer Vision Graphics and Image Processing, 34:138–155.
Fua, P. and Leclerc, Y. 1993. Object-centered surface reconstruction: Combining multi-image stereo and shading. In Proc. DARPA Image Understanding Workshop, pp. 1097–1120.
Gofman, Y. and Kiryati, N. 1996. Detecting symmetry in grey level images: The global optimization approach. In ICPR, p. A94.2.
Gordon, G.G. 1989. Shape from symmetry. In Proc. of SPIE Intellent Robots And Computer Vision VIII, Vol. 1192, Nov.
Gross, A.D. and Boult, T.E. 1996. Recovery of SHGCs from a single intensity view. IEEE Trans. Patt. Anal. Mach. Intell., 18(2):161–180.
Hayakawa, H. 1994. Photometric stereo under a light-source with arbitrary motion. J. Opt. Soc. Am. A, 11(11):3079–3089.
Horn, B.K.P. 1986. Computer Vision. MIT Press: Cambridge, Mass.
Horn, B.K.P. and Brooks, M.J. 1986. The variational approach to shape from shading. Comp. Vis. Graph. Im. Proc., 33:174–203.
Horn, B.K.P. and Brooks, M.J. 1989. Shape fromShading. MITPress.
Hougen, D.R. and Ahuja, N. 1993. Estimation of the light source distribution and its use in integrated shape recovery from stereo and shading. In Proc. Int. Conf. Comp. Vision, pp. 148–155.
Moses, Y. and Ullman, S. 1998. Generalization to novel views: Universal, class-based, and model-based processing. Int. J. of Comp. Vision, 29(3):233–253.
Mukherjee, D.P., Zisserman, A., and Brady, J.M. 1993. Shape from symmetry–detecting and exploiting symmetry in affine images. Technical Report, Report No. OUEL 1988/93. University of Oxford, Department of Engineering Science.
Onn, R. and Bruckstein, A.M. 1990. Integrability disambiguates surface recovery in two-image photometric stereo. IJCV, 5(1):105–113.
Ponce, J. 1990. On characterizing ribbons and finding skewed symmetries. Comp. Vis. Graph. Im. Proc., 52:328.–340.
Rothwell, C.A. 1995. Object Recognition Through Invariant Indexing. Oxford University Press.
Shimshoni, I., Moses, Y., and Lindenbaum, M. 1997. Auto photometric/geometric stereo from a single image or class based reconstruction of bilaterally symmetric objects. Technical Report CIS-9710-1997, The Technion.
Shimshoni, I., Moses, Y., and Lindenbaum, M. 1999. Shape reconstruction of 3D bilaterally symmetric surfaces. In Proc. Int. Conf. Image Ana. and Proc., pp. 76–81.
Takacs, B. and Wechsler, H. 1997. Detection of faces and facial landmarks using iconic filter banks. PR, 30(10):1623–1636.
Woodham, R.J. 1978. Photometric stereo: A reflectance map technique for determining surface orientation from image intensity. Proc. SPIE, 155:136–143.
Zabrodsky, H. 1993. Computational aspects of pattern characterization–continuous symmetry. PhD Thesis, Hebrew University, Jerusalem.
Zhang, Z. and Tsui, H.T. 1998. 3D reconstruction from a single view of an object and its image in a plane mirror. In Proc. International Conf. Patt. Recog., p. SAP1.
Zisserman, A., Forsyth, D., Mundy, J., Rothwell, C., Liu, J., and Pillow, N. 1995. 3D object recognition using invariance. AI, 78(12):239–288.
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Shimshoni, I., Moses, Y. & Lindenbaum, M. Shape Reconstruction of 3D Bilaterally Symmetric Surfaces. International Journal of Computer Vision 39, 97–110 (2000). https://doi.org/10.1023/A:1008118909580
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DOI: https://doi.org/10.1023/A:1008118909580