11 Photometric StereoGiven multiple images taken with varying illumination, recover albedo and normals.take pictures in dark room with varying illumination.estimate lighting directions L.recover albedo and normals.
12 Side note 1: How to get the lighting direction? Put a shiny sphere in the sceneSphere’s geometry (normals) are knownFind specular highlight
13 Side-note 2: Why “Stereo”? Surface normals provide constraints on depth differences
14 Photometric StereoIf L is known, and albedo is grayscale this is a linear problem.I = ρ(L N)= ρ (Lx Nx + Ly Ny + Lz Nz )= Lx Nxρ + Ly Nyρ + Lz Nzρ= Lx a + Ly b + Lz c
15 For each pixel: I = ρ(L N) = Lx a + Ly b + Lz c I1 Lx1 Ly1 Lz1 I2 …Lxn Lyn LznI1I2I3Inabc=Then:ρ = sqrt(a2 + b2 + c2)N = (a,b,c) / ρ
29 Radiometric Camera Calibration If you can control the exposure…Take two pictures with different known exposures (e.g. 0.5 second and 1 second):Observed2 = f (e2 RAW)Observed1 = f (e1 RAW)f -1 (Observed1) = e1 RAWf -1 (Observed2) = e2 RAWf -1 (Observed1) e1f -1 (Observed2) e2=Solve for the best f -1 that fits your model
30 Heliometric Stereo I = f (e ρ (S L N + a)) The following should hold for each pixel in each image:I = f (e ρ (S L N + a))f : the camera’s response curvee: that image’s exposure valuea: that image’s ambient lightS: 0 if that pixel is in shadow at that time, 1 otherwiseN: that pixel’s surface normalρ: that pixel’s albedo
31 Heliometric Stereo I = f (e ρ (S L N + a)) Step 1: pixel-level thresholding to find shadowsStep 2: initialize all variablesI = f (e ρ (S L N + a))
32 Heliometric Stereo I = f (e ρ (S L N + a)) I = f (e ρ (S L N + a)) Step 3: fix f, e, and a, solve for ρ and N.Step 4: fix ρ and N, solve for f, e, and a.Step 5: goto 3.I = f (e ρ (S L N + a))I = f (e ρ (S L N + a))
34 BRDF Bi-Directional Reflectance Distribution Function given incoming and outgoing rays, what proportion of light is reflected?just a big word that describes how light’s energy is transferred upon hitting a surface
35 BRDF Almost nobody actually tries to model a full BRDF. Why? Build a lighting model with fewer parameters that approximate the BRDFDiffuse lighting model is very common
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