Irradiation direction from texture.

We present a theory of image texture resulting from the shading of corrugated (three-dimensional textured) surfaces, Lambertian on the micro scale, in the domain of geometrical optics. The derivation applies to isotropic Gaussian random surfaces, under collimated illumination, in normal view. The theory predicts the structure tensors from either the gradient or the Hessian of the image intensity and allows inferences of the direction of irradiation of the surface. Although the assumptions appear prima facie rather restrictive, even for surfaces that are not at all Gaussian, with the bidirectional reflectance distribution function far from Lambertian and vignetting and multiple scattering present, we empirically recover the direction of irradiation with an accuracy of a few degrees.

[1]  M. Levoy,et al.  The light field , 1939 .

[2]  M. Longuet-Higgins.  The statistical analysis of a random, moving surface , 1957, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[3]  M. Berry,et al.  Umbilic points on Gaussian random surfaces , 1977 .

[4]  Azriel Rosenfeld,et al.  Improved Methods of Estimating Shape from Shading Using the Light Source Coordinate System , 1985, Artif. Intell..

[5]  Berthold K. P. Horn,et al.  Shape from shading , 1989 .

[6]  D C Knill,et al.  Estimating illuminant direction and degree of surface relief. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[7]  Rama Chellappa,et al.  Estimation of illuminant direction, albedo, and shape from shading , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[8]  M. Chantler.  Why illuminant direction is fundamental to texture analysis , 2022 .

[9]  M. Carter.  Computer graphics: Principles and practice , 1997 .

[10]  Thomas Ertl,et al.  Computer Graphics - Principles and Practice, 3rd Edition , 2014 .

[11]  Martin J. Wainwright,et al.  Scale Mixtures of Gaussians and the Statistics of Natural Images , 1999, NIPS.

[12]  Shree K. Nayar,et al.  Reflectance and texture of real-world surfaces , 1999, TOGS.

[13]  Mike J. Chantler,et al.  The response of texture features to illuminant rotation , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[14]  Andrea J. van Doorn,et al.  Image Processing Done Right , 2002, ECCV.

[15]  Maria Petrou,et al.  The Effect of Illuminant Rotation on Texture Filters: Lissajous's Ellipses , 2002, ECCV.

[16]  Andrea J. van Doorn,et al.  Local structure of gaussian texture , 2003 .

[17]  J. Koenderink,et al.  Bidirectional Texture Contrast Function , 2004, International Journal of Computer Vision.

[18]  Kristin J. Dana,et al.  Texture histograms as a function of irradiation and viewing direction , 1999, International Journal of Computer Vision.

[19]  Jitendra Malik,et al.  Representing and Recognizing the Visual Appearance of Materials using Three-dimensional Textons , 2001, International Journal of Computer Vision.

[20]  Alex Pentland.  Linear shape from shading , 2004, International Journal of Computer Vision.