Parameters using Fourier Analysis Alban Fichet Imari Sato Nicolas - PowerPoint PPT Presentation

Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis Alban Fichet Imari Sato Nicolas Holzschuch Inria – Univ Grenoble Alpes – LJK – CNRS Inria – Univ Grenoble Alpes – LJK – CNRS National Institute of Informatics alban.fichet@inria.fr imarik@nii.ac.jp nicolas.holzschuch@inria.fr

Representing opaque materials • BRDF - 4D function: • Incoming light (elevation θ i & azimuth φ i ) • Observation point (elevation θ o & azimuth φ o ) • Spatially varying material SVBRDF: • + 2 dimensions: u, v Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 3

Representing opaque materials Diffuse component Anisotropy direction Roughness α x α y Specular component Anisotropic highlight Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 4

Representing opaque materials Diffuse Specular Shading Anisotropy Roughness normal direction α x / α y ( α x + α y )/2 3 dimensions: 3 dimensions: 2 dimensions: 1 dimension: 2 dimensions: • • Elevation θ n Direction φ a Horizontal α x Red Red • • • • • Green Green Azimuth φ n Vertical α y • • • • Blue Blue Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 5

Related work BRDF acquisition Spatially Varying BRDF Capture under varying Gathering sparse and illumination dense measurements [ Matusik et al – 2003 ] [ Gardner et al – 2003 ] [ Ren et al – 2011 ] Isotropic [ Holroyd et al – 2010 ] [ Ngan et al – 2005 ] [ Tunwattanapong et al – 2013 ] [ Wang et al – 2008 ] Anisotropic [ Filip et al – 2014 ] [ Aittala et al – 2015 ] [ Dong et al – 2010 ] Lighting system complexity Easy Average Difficult Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 6

Related work [ Gardner et al – 2003 ] Linear Light Source Reflectometry The linear light source apparatus Diffuse, Specular intensity, Specular roughness Rendering Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 7

Related work [ Tunwattanapong et al – 2013 ] Acquiring Reflectance and Shape from Continuous Spherical Harmonics Illumination Acquisition Setup Rendered 3D Model Reflectance Maps Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 8

Contribution • Capturing material with a simple setup • Easy and cheap to reproduce setup • Fast acquisition time • Few samples needed ( 20 used in our example ) • Simple and flexible • Dealing with anisotropic Spatially-Varying material • No assumption on surrounding pixels • Works with high frequency patterns (amulet dataset) Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 9

Overview of our technique Capture Analysis Rendering Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 10

Analysis • Each pixel treated independently Reflectance intensity Light azimuthal angle φ i Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 12

Analysis • Anisotropy → Two peaks • Shading normal → Maximum difference x Light azimuthal angle φ i Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 13

Analysis • Fourier transform • Fundamental – average Magnitude [ log( signal ) ] • Harmonics – complex numbers c 1   2     c 2 ni c s ( ) e d h n h h 0 • Frequency domain • Argument – offset • Magnitude – contribution Light azimuthal angle φ i Harmonics Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 14

Analysis • Initial estimation of • Anisotropy direction φ a • Normal azimuth φ n • 3-step minimization process 1. Even rank harmonics – Anisotropy / Specular 2. First harmonic & fundamental – Normal / Diffuse 3. Fit on signal itself • Loop back Light azimuthal angle φ i Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 15

Limitations • Constrained to almost planar surfaces • Shading normal in a limited range variation • Miss of high specularity or diffuse details • 20 samples used – Nyquist-Shannon sampling theorm • Single exposure images @14bits • Fresnel term ignored • Gazing angles issues Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 20

Conclusion & Future work • Technique for retrieving anisotropic SVBRDF • Based on Fourier analysis • Simple capture setup and modular analysis • Application to non-planar objects • Extension to more advanced anisotropy patterns • Gathering similar pixels to improve accuracy Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 22

Alban Fichet Imari Sato Nicolas Holzschuch alban.fichet@inria.fr imarik@nii.ac.jp nicolas.holzschuch@inria.fr Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 23

Capture setup • Nikon D7100 camera • AF-S Nikkor 18-105mm 1:3.5- 5.6G lens • Captured in NEF 14 bits • Rotating arm with light • Computer controlled synchronized with camera shoot • Sample stage Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 24

Representation • Incoming light vector i • Outgoing light vector o h = i + o • Half vector i + o • Anisotropy direction x Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 25

BRDF model • Cook-Torrance ) = k d ( r i , o p æ ö æ ö ( ) G i , o ( ) F cos q d cos 2 j h + sin 2 j h + k s ç ÷ D tan 2 q h ç ÷ ç ÷ ç ÷ a x a y 4cos q i cos q o a x a y 2 2 è ø è ø • GGX Isotropic NDF GGX Anisotropic NDF a g 2 c + ( m × c + ( m × n ) n ) D ( i , o ) = D ( i , o ) = 2 + tan 2 q h ( ) æ ö æ ö 2 2 p cos 4 q h a g cos 2 j h + sin 2 j h ç ÷ ç ÷ p cos 4 q h a x a y 1 + tan 2 q h ç ÷ ç ÷ a x a y 2 2 è ø è ø Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis 26