Photometric Stereo Using Constrained Bivariate Regression for General Isotropic Surfaces

This paper presents a photometric stereo method that is purely pixelwise and handles general isotropic surfaces in a stable manner. Following the recently proposed sum-of-lobes representation of the isotropic reflectance function, we constructed a constrained bivariate regression problem where the regression function is approximated by smooth, bivariate Bernstein polynomials. The unknown normal vector was separated from the unknown reflectance function by considering the inverse representation of the image formation process, and then we could accurately compute the unknown surface normals by solving a simple and efficient quadratic programming problem. Extensive evaluations that showed the state-of-the-art performance using both synthetic and real-world images were performed.

[1]  Donald P. Greenberg,et al.  Non-linear approximation of reflectance functions , 1997, SIGGRAPH.

[2]  Robert L. Cook,et al.  A Reflectance Model for Computer Graphics , 1987, TOGS.

[3]  Barry Smith,et al.  Semi-nonparametric estimation with Bernstein polynomials , 2005 .

[4]  David J. Kriegman,et al.  Photometric stereo with non-parametric and spatially-varying reflectance , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[5]  Katsushi Ikeuchi,et al.  Elevation Angle from Reflectance Monotonicity: Photometric Stereo for General Isotropic Reflectances , 2012, ECCV.

[6]  Katsushi Ikeuchi,et al.  A biquadratic reflectance model for radiometric image analysis , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[7]  Shree K. Nayar,et al.  Generalization of Lambert's reflectance model , 1994, SIGGRAPH.

[8]  George G. Lorentz,et al.  Deferred Bernstein polynomials , 1951 .

[9]  J. Wang,et al.  Shape restricted nonparametric regression with Bernstein polynomials , 2012, Comput. Stat. Data Anal..

[10]  Rama Chellappa,et al.  What Is the Range of Surface Reconstructions from a Gradient Field? , 2006, ECCV.

[11]  Gregory J. Ward,et al.  Measuring and modeling anisotropic reflection , 1992, SIGGRAPH.

[12]  Yongtian Wang,et al.  Robust Photometric Stereo via Low-Rank Matrix Completion and Recovery , 2010, ACCV.

[13]  Robert J. Woodham,et al.  Photometric method for determining surface orientation from multiple images , 1980 .

[14]  Kiyoharu Aizawa,et al.  Robust photometric stereo using sparse regression , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Steven M. Seitz,et al.  Shape and Spatially-Varying BRDFs from Photometric Stereo , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Ravi Ramamoorthi,et al.  What an image reveals about material reflectance , 2011, 2011 International Conference on Computer Vision.

[17]  Katsushi Ikeuchi,et al.  Consensus photometric stereo , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  I. van Mechelen,et al.  Simple and multiple P-splines regression with shape constraints. , 2006, The British journal of mathematical and statistical psychology.

[19]  Peter Shirley,et al.  An Anisotropic Phong BRDF Model , 2000, J. Graphics, GPU, & Game Tools.

[20]  Paolo Favaro,et al.  A closed-form solution to uncalibrated photometric stereo via diffuse maxima , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.