Uncalibrated Neural Inverse Rendering for Photometric Stereo of General Surfaces

This paper presents an uncalibrated deep neural network framework for the photometric stereo problem. For training models to solve the problem, existing neural network-based methods either require exact light directions or ground-truth surface normals of the object or both. However, in practice, it is challenging to procure both of this information precisely, which restricts the broader adoption of photometric stereo algorithms for vision application. To bypass this difficulty, we propose an uncalibrated neural inverse rendering approach to this problem. Our method first estimates the light directions from the input images and then optimizes an image reconstruction loss to calculate the surface normals, bidirectional reflectance distribution function value, and depth. Additionally, our formulation explicitly models the concave and convex parts of a complex surface to consider the effects of interreflections in the image formation process. Extensive evaluation of the proposed method on the challenging subjects generally shows comparable or better results than the supervised and classical approaches.

[1]  Ronen Basri,et al.  Solving Uncalibrated Photometric Stereo Using Fewer Images by Jointly Optimizing Low-rank Matrix Completion and Integrability , 2017, Journal of Mathematical Imaging and Vision.

[2]  David J. Kriegman,et al.  Reflections on the generalized bas-relief ambiguity , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[3]  Bailin Deng,et al.  Lightweight Photometric Stereo for Facial Details Recovery , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[4]  Kai Han,et al.  PS-FCN: A Flexible Learning Framework for Photometric Stereo , 2018, ECCV.

[5]  Yin Zhang,et al.  Fixed-Point Continuation for l1-Minimization: Methodology and Convergence , 2008, SIAM J. Optim..

[6]  Paolo Favaro,et al.  A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima , 2013, International Journal of Computer Vision.

[7]  Tai-Pang Wu,et al.  Photometric Stereo via Expectation Maximization , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[9]  James F. Blinn,et al.  Models of light reflection for computer synthesized pictures , 1977, SIGGRAPH.

[10]  Denis Laurendeau,et al.  Deep SVBRDF Estimation on Real Materials , 2020, 2020 International Conference on 3D Vision (3DV).

[11]  Changchang Wu,et al.  Structure from Motion Using Structure-Less Resection , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[12]  Yasuyuki Matsushita,et al.  Learning to Minify Photometric Stereo , 2019, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[13]  Zhe Wu,et al.  A Benchmark Dataset and Evaluation for Non-Lambertian and Uncalibrated Photometric Stereo , 2019, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[14]  Takanori Maehara,et al.  Neural Inverse Rendering for General Reflectance Photometric Stereo , 2018, ICML.

[15]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[16]  Satoshi Ikehata,et al.  CNN-PS: CNN-based Photometric Stereo for General Non-Convex Surfaces , 2018, ECCV.

[17]  Mike J. Chantler,et al.  Can two specular pixels calibrate photometric stereo? , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[18]  Keenan Crane Conformal Geometry Processing , 2013 .

[19]  Christian Wöhler,et al.  An introduction to image-based 3D surface reconstruction and a survey of photometric stereo methods , 2011 .

[20]  Richard Szeliski,et al.  Computer Vision - Algorithms and Applications , 2011, Texts in Computer Science.

[21]  Jean Ponce,et al.  Accurate, Dense, and Robust Multiview Stereopsis , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[23]  Tianqi Chen,et al.  Empirical Evaluation of Rectified Activations in Convolutional Network , 2015, ArXiv.

[24]  Imari Sato,et al.  A Microfacet-Based Model for Photometric Stereo with General Isotropic Reflectance , 2021, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Andrew Zisserman,et al.  SilNet : Single- and Multi-View Reconstruction by Learning from Silhouettes , 2017, BMVC.

[26]  Takahiro Okabe,et al.  Uncalibrated Photometric Stereo for Unknown Isotropic Reflectances , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[27]  Yasuyuki Matsushita,et al.  Deep Photometric Stereo Network , 2017, 2017 IEEE International Conference on Computer Vision Workshops (ICCVW).

[28]  Takeshi Shakunaga,et al.  Analysis of photometric factors based on photometric linearization. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[29]  Kiyoharu Aizawa,et al.  Photometric Stereo Using Constrained Bivariate Regression for General Isotropic Surfaces , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[30]  Wojciech Matusik,et al.  A data-driven reflectance model , 2003, ACM Trans. Graph..

[31]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

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

[33]  Steven M. Seitz,et al.  Schematic surface reconstruction , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[34]  Roberto Cipolla,et al.  A Differential Volumetric Approach to Multi-View Photometric Stereo , 2018, 2019 IEEE/CVF International Conference on Computer Vision (ICCV).

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

[36]  Yasuyuki Matsushita,et al.  Self-Calibrating Deep Photometric Stereo Networks , 2019, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

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

[38]  Svorad Stolc,et al.  A Review of Depth and Normal Fusion Algorithms , 2018, Sensors.

[39]  Yu Ji,et al.  A Neural Rendering Framework for Free-Viewpoint Relighting , 2019, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[40]  Daniel Cremers,et al.  A Non-convex Variational Approach to Photometric Stereo under Inaccurate Lighting , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[41]  Yasuyuki Matsushita,et al.  Multiview Photometric Stereo Using Planar Mesh Parameterization , 2013, 2013 IEEE International Conference on Computer Vision.

[42]  Katsushi Ikeuchi,et al.  Median Photometric Stereo as Applied to the Segonko Tumulus and Museum Objects , 2009, International Journal of Computer Vision.

[43]  Hongdong Li,et al.  Superpixel Soup: Monocular Dense 3D Reconstruction of a Complex Dynamic Scene , 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[44]  Yasuyuki Matsushita,et al.  What Is Learned in Deep Uncalibrated Photometric Stereo? , 2020, ECCV.

[45]  Hongdong Li,et al.  Monocular Dense 3D Reconstruction of a Complex Dynamic Scene from Two Perspective Frames , 2017, 2017 IEEE International Conference on Computer Vision (ICCV).

[46]  Kun Li,et al.  GPS-Net: Graph-based Photometric Stereo Network , 2020, NeurIPS.

[47]  Xi Wang,et al.  Non-Lambertian Photometric Stereo Network Based on Inverse Reflectance Model With Collocated Light , 2020, IEEE Transactions on Image Processing.

[48]  Ping Tan,et al.  A Benchmark Dataset and Evaluation for Non-Lambertian and Uncalibrated Photometric Stereo , 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  Kiyoharu Aizawa,et al.  Photometric Stereo Using Sparse Bayesian Regression for General Diffuse Surfaces , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[50]  Zhe Wu,et al.  Calibrating Photometric Stereo by Holistic Reflectance Symmetry Analysis , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[51]  Xudong Jiang,et al.  SPLINE-Net: Sparse Photometric Stereo Through Lighting Interpolation and Normal Estimation Networks , 2019, 2019 IEEE/CVF International Conference on Computer Vision (ICCV).

[52]  Ignas Budvytis,et al.  A CNN Based Approach for the Near-Field Photometric Stereo Problem , 2020, BMVC.

[53]  David J. Kriegman,et al.  The Bas-Relief Ambiguity , 2004, International Journal of Computer Vision.

[54]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[55]  David J. Kriegman,et al.  Isotropy, Reciprocity and the Generalized Bas-Relief Ambiguity , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[56]  King-Sun Fu,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence Publication Information , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[57]  Takeo Kanade,et al.  Shape from interreflections , 2004, International Journal of Computer Vision.

[58]  Edward H. Adelson,et al.  Shape estimation in natural illumination , 2011, CVPR 2011.

[59]  Paolo Favaro,et al.  A New Perspective on Uncalibrated Photometric Stereo , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[60]  Boxin Shi,et al.  Multi-View Photometric Stereo: A Robust Solution and Benchmark Dataset for Spatially Varying Isotropic Materials , 2020, IEEE Transactions on Image Processing.

[61]  Yi Ma,et al.  The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices , 2010, Journal of structural biology.

[62]  Kiriakos N. Kutulakos,et al.  Photometric Stereo via Discrete Hypothesis-and-Test Search , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

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

[64]  Yasuyuki Matsushita,et al.  Deep Photometric Stereo for Non-Lambertian Surfaces , 2020, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[65]  Jiaya Jia,et al.  Efficient photometric stereo on glossy surfaces with wide specular lobes , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[66]  Ignas Budvytis,et al.  PX-NET: Simple, Efficient Pixel-Wise Training of Photometric Stereo Networks , 2020, ArXiv.

[67]  Luca Antiga,et al.  Automatic differentiation in PyTorch , 2017 .

[68]  Suryansh Kumar,et al.  Jumping Manifolds: Geometry Aware Dense Non-Rigid Structure From Motion , 2019, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[69]  Steven M. Seitz,et al.  Shape and spatially-varying BRDFs from photometric stereo , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[70]  David J. Kriegman,et al.  Resolving the Generalized Bas-Relief Ambiguity by Entropy Minimization , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[71]  Yasuyuki Matsushita,et al.  Self-calibrating photometric stereo , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[72]  Katsushi Ikeuchi,et al.  Ieee Transactions on Pattern Analysis and Machine Intelligence Bi-polynomial Modeling of Low-frequency Reflectances , 2022 .

[73]  G. Sapiro,et al.  A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography. , 2013, Journal of structural biology.

[74]  Kalyan Sunkavalli,et al.  Deep 3D Capture: Geometry and Reflectance From Sparse Multi-View Images , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[75]  Yoichi Sato,et al.  SymPS: BRDF Symmetry Guided Photometric Stereo for Shape and Light Source Estimation , 2018, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[76]  Yasuyuki Matsushita,et al.  Deep Near-Light Photometric Stereo for Spatially Varying Reflectances , 2020, ECCV.

[77]  Carlos D. Castillo,et al.  SfSNet: Learning Shape, Reflectance and Illuminance of Faces 'in the Wild' , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[78]  Athinodoros S. Georghiades,et al.  Incorporating the Torrance and Sparrow model of reflectance in uncalibrated photometric stereo , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[79]  In-So Kweon,et al.  Partial Sum Minimization of Singular Values in RPCA for Low-Level Vision , 2013, 2013 IEEE International Conference on Computer Vision.