Ligh%ng and Reflectance

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1 Ligh%ng and Reflectance

2 2

3 3

4 4

5 Ligh%ng Ligh%ng can have a big effect on how an object looks.

6 Modeling the effect of ligh%ng can be used for: Recogni%on par%cularly face recogni%on Shape reconstruc%on Mo%on es%ma%on Re-rendering / Re-ligh%ng

7 Ligh%ng is Complex Ligh%ng can come from any direc%on and at any strength Infinite degree of freedom

8 Capture ligh%ng varia%on Illuminate subject from many incident direc%ons From Ravi Ramamoorthi

9 Example images: From Ravi Ramamoorthi

10 Example images: From Ravi Ramamoorthi

11 Example images: = From Ravi Ramamoorthi

12 From Ravi Ramamoorthi

13 From Ravi Ramamoorthi

14 From Ravi Ramamoorthi

15 Ques%ons? 15

16 Image brightness What determines the brightness of an image pixel?

17 Image brightness What determines the brightness of an image pixel? Light source properties Surface properties ligh%ng Surface BRDF (local reflectance) Shadowing Inter-reflec%ons (global reflectance)

18 What is light? Electromagnetic radiation (EMR) moving along rays in space R(λ) is EMR, measured in units of power (watts) λ is wavelength Perceiving light How do we convert radiation into color? What part of the spectrum do we see?

19 Visible light We see electromagne%c radia%on in a range of wavelengths

20 Light spectrum The appearance of light depends on its power spectrum How much power (or energy) at each wavelength daylight tungsten bulb Our visual system converts a light spectrum into color This is a rather complex transformation

21 Light spectrum The appearance of light depends on its power spectrum How much power (or energy) at each wavelength daylight tungsten bulb Our visual system converts a light spectrum into color This is a rather complex transformation

22 Light spectrum The appearance of light depends on its power spectrum How much power (or energy) at each wavelength daylight tungsten bulb Our visual system converts a light spectrum into color This is a rather complex transformation

23 Light spectrum The appearance of light depends on its power spectrum How much power (or energy) at each wavelength daylight tungsten bulb Our visual system converts a light spectrum into color This is a rather complex transformation

24 Real response 24

25 Light sources Basic types Point source Distant point source Area source a union of point sources

26 Light field We can describe all of the light in the scene by specifying the radiation (or radiance along all light rays) arriving at every point in space and from every direction

27 The light field Known as the plenoptic function If you know R, you can predict how the scene would appear from any viewpoint.

28 The light field Known as the plenoptic function If you know R, you can predict how the scene would appear from any viewpoint. Usually drop λ and time parameters Assume radiance does not change along a ray

29 The light field Known as the plenoptic function If you know R, you can predict how the scene would appear from any viewpoint. Usually drop λ and time parameters Assume radiance does not change along a ray Down to 4 degrees of freedom

30 Stanford light field gantry

31 Spherical Gantry 4D Light Field Capture all the light leaving an object - like a hologram [ Don Fussel ]

32 Spherical Gantry 4D Light Field Capture all the light leaving an object - like a hologram [ Don Fussel ]

33 Spherical Gantry 4D Light Field Capture all the light leaving an object - like a hologram [ Don Fussel ]

34 Spherical Gantry 4D Light Field Capture all the light leaving an object - like a hologram [ Don Fussel ]

35 Spherical Gantry 4D Light Field Capture all the light leaving an object - like a hologram [ Don Fussel ]

36 Another light field representation The light field t is not time (different from above t!)

37 The light field The light field t is not time (different from above t!) Parameterize rays by intersection with two planes: How could you capture a light field?

38 Stanford Camera Array 38

39 Lytro FRANK O CONNELL/THE NEW YORK TIMES 13

40 Lytro ( 40

41 Ques%ons 41

42 What happens when a light ray hits an object? Some of the light gets absorbed converted to other forms of energy (e.g., heat) Some gets transmitted through the object possibly bent, through refraction a transmitted ray could possible bounce back Some gets reflected as we saw before, it could be reflected in multiple directions (possibly all directions) at once Let s consider the case of reflection in detail

43 Reflections ideal specular rough specular Lambertian from Steve Marschner

44 The BRDF The Bidirectional Reflection Distribution Function Given an incoming ray and outgoing ray what proportion of the incoming light is reflected along outgoing ray? surface normal Answer given by the BRDF:

45 Constraints on the BRDF Energy conserva%on Quan%ty of outgoing light quan%ty of incident light integral of BRDF 1 Helmholtz reciprocity reversing the path of light produces the same reflectance =

46 Diffuse (Lamber%an) reflec%on Diffuse reflec%on Dull, mace surfaces like chalk or latex paint Microfacets scacer incoming light randomly Effect is that light is reflected equally in all direc%ons

47 Diffuse reflection Diffuse reflection governed by Lambert s law L, N, V unit vectors

48 Diffuse reflection Diffuse reflection governed by Lambert s law Viewed brightness does not depend on viewing direction L, N, V unit vectors

49 Diffuse reflection Diffuse reflection governed by Lambert s law Viewed brightness does not depend on viewing direction Brightness does depend on direction of illumination This is the model most often used in computer vision L, N, V unit vectors

50 Diffuse reflection Diffuse reflection governed by Lambert s law Viewed brightness does not depend on viewing direction Brightness does depend on direction of illumination This is the model most often used in computer vision L, N, V unit vectors I e = outgoing radiance I i = incoming radiance Lambert s Law: BRDF for Lambertian surface

51 Specular reflection For a perfect mirror, light is reflected about N Near-perfect mirrors have a highlight around R common model:

52 Specular reflection Moving the light source Changing n s

53 Specular reflection Moving the light source Changing n s

54 Phong illumination model Phong approximation of surface reflectance Assume reflectance is modeled by three components Diffuse term Specular term Ambient term (to compensate for inter-reflected light) L, N, V unit vectors I e = outgoing radiance I i = incoming radiance I a = ambient light k a = ambient light reflectance factor (x) + = max(x, 0)

55 BRDF models Phenomenological Phong [75] Ward [92] Lafortune et al. [97] Ashikhmin et al. [00] Physical Cook-Torrance [81] Dichromatic [Shafer 85] He et al. [91] Here we re listing only some well-known examples

56 Shape reconstruction on diffuse surface 56

57 L Lambertian reflection

58 Lambertian reflection Lets assume that I i =1 is light source intensity to resolve scale ambiguity between kd and I i image intensity at a single point Ligh.ng direc%on (same for all points) Albedo at a point Surface normal at a point

59 Shape from shading Input: Output: - Single Image - 3D shape of the object in the image Problem is ill-posed: many shapes can give rise to same image. Common assumptions: - Lambertian reflectance + uniform albedo - Lighting is known (set as the camera direction)

60 We know (calibrate) L. For diffuse, V does not matter 60

61 Set L to be (0, 0, 1) For diffuse, V does not matter 61

62 Challenges in Shape from shading kd kd Ambiguous (family of solution on a cone) Not quite enough information to compute surface shape But can be if you add some additional info, for example Assume normals along the silhouette are known Constraints on neighboring normals integrability Smoothness

63 Surface Normal Estimate a surface z(x, y) A point on the surface: (x,y,z(x, y)) T Tangent directions t x = (1,0,z x ) T t y = (0,1,z y ) T N = t t x y t x t y = 1 ( z 2 x + z 2 y +1 z x, z y,1) T

64 Shape from shading I(x, y) = N L = l 1z x l 2 z y + l 3 z x 2 + z y 2 +1 From assump%on L= (0,0,1) T

65 Shape from shading I(x, y) = N L = l 1z x l 2 z y + l 3 z x 2 + z y 2 +1 From assump%on And get that L= (0,0,1) T I(x, y) = N L = 1 z x 2 + z y 2 +1

66 Shape from shading I(x, y) = N L = l 1z x l 2 z y + l 3 z x 2 + z y 2 +1 From assump%on L= (0,0,1) T And get that I(x, y) = N L = 1 z x 2 + z y 2 +1 Two unknowns per pixel z x One unknown for the en%re image z y

67 Shape from shading

68 Trick to make it work

69 Trick to make it work Pick the brightest point and assumes N = L Intensity there is equal to kd

70 Still heavily ambiguous I(x, y) = N L = 1 z x 2 + z y 2 +1

71 Shape from shading I(x, y) = N L = 1 z x 2 + z y 2 +1 Assume surface is integrable (integrability constraint): z xy = z yx

72 Shape from shading I(x, y) = N L = 1 z x 2 + z y 2 +1 Assume surface is integrable (integrability constraint): z xy = z yx argmin {zx, zy}

73 Shape from shading I(x, y) = N L = 1 z x 2 + z y 2 +1 Calculus of variation Assume surface is integrable (integrability constraint): z xy = z yx argmin {zx, zy}

74 Results

75 Shape from shading It is hard to get shape from shading work well in practice. The assumptions are quite restrictive But this is recovery of 3D from single 2D image

76 Bas Relief Ambiguity [ Belhumeur, Kriegman, Yuille ] 76

77 Bas Relief Ambiguity [ Belhumeur, Kriegman, Yuille ] 77

78 Bas Relief Ambiguity Uses ambiguity to show rich a 3D shape with low relief structure 78

79 79 [ ]

80 Shape from shading It is hard to get shape from shading work well in practice. The assumptions are quite restrictive But this is recovery of 3D from single 2D image Fewer assumptions are needed if we have several images of the same object under different lightings

81 Photometric stereo N L 3 L 2 V L 1 Can write this as a matrix equation:

82 Solving the equations

83 More than three lights Get better results by using more lights Least squares solution: Solve for N, k d as before What s the size of L T L?

84 Example Recovered albedo Recovered normal field Forsyth & Ponce, Sec. 5.4

85 Example

86 Results from Athos Georghiades

87 Limitations doesn t work for shiny things, semi-translucent things shadows, inter-reflections are difficult Single light source illumination camera and lights have to be distant calibration requirements measure light source directions, intensities camera response function

88 Limitations doesn t work for shiny things, semi-translucent things shadows, inter-reflections are difficult Single light source illumination camera and lights have to be distant calibration requirements measure light source directions, intensities camera response function Newer work addresses some of these issues Some pointers for further reading: Zickler, Belhumeur, and Kriegman, "Helmholtz Stereopsis: Exploiting Reciprocity for Surface Reconstruction." IJCV, Vol. 49 No. 2/3, pp Hertzmann & Seitz, Example-Based Photometric Stereo: Shape Reconstruction with General, Varying BRDFs. IEEE Trans. PAMI 2005 Basri, Jacobs and Kemelmacher Photometric Stereo with General Unknown Lighting, International Journal of Computer Vision (IJCV) 2007

89 Extra cool stuffs 89

90 Colored Photometric Stereo 90

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