Illumination and Reflectance

Transcription

1 COMP 546 Lecture 12 Illumination and Reflectance Tues. Feb. 20,

2 Illumination and Reflectance Shading Brightness versus Lightness Color constancy

3 Shading on a sunny day N(x) L N L Lambert s (cosine) Law: I X = N(X) L

4 Unit Surface Normal N Z X Z Y Z X, Z Y, 1 N 4

5 Shading on a sunny day 5

6 Cast and Attached Shadows attached : N(X) L < 0 L cast : N(X) L > 0 but light is occluded

7 Shading models sunny day (last lecture) sunny day + low relief cloudy day

8 Examples of low relief surfaces (un)crumpled paper

9 Low relief surface Z Z Suppose and are both small. Thus, X 0 Y 0 N Z X Z Y Z X, Z Y,

10 Linear shading model for low relief I X, Y Z X, Z Y, 1 L X, L Y, L Z shadows can still occur one equation per point but two unknowns 10

11 Example: curtains X Z Z X, Y = Z 0 + a sin( k X X ) L N

12 Example: curtains X Z Z X, Y = Z 0 + a sin( k X X ) Z X = a k X cos k X X, Z Y = 0

13 Example: curtains I X, Y Z Z,, 1 L X, L Y, L Z X Y Z X, Y = Z 0 + a sin( k X X ) Z X = a k X cos k X X, Z Y = 0 I X, Y = a k X cos k X X L X L Z

14 Example: curtains X Z X, Y = Z 0 + a sin( k X X ) Z I X, Y = L Z + a k X L X cos k X X L = (L X, L Y, L Z ) N Q: where do the intensity maxima and minima occur?

15 Shading on a cloudy day (my Ph.D. thesis) 15

16 Shading on a Cloudy Day (x) Shadowing effects cannot be ignored.

17 Shading on a Cloudy Day Shading is determined by shadowing and surface normal. 17

18 Shading on a Sunny Day Shading determined by surface normal only.

19 Shape from shading Q: What is the task? What problem is being solved? A: Estimate surface slant, tilt, curvature. How to account for (or estimate) the lighting? 19

20 Illumination and Reflectance Shading [Shading and shadowing models assume that intensity variations on a surface are entirely due to illumination. But surfaces have reflectance variations too. ] Brightness versus Lightness Color constancy

21 Which paper is lighter? Paper on the left is in shadow. It has lower physical intensity and it appears darker. But do both papers seem to be of same (white) material? 21

22 Which paper is lighter? Image is processed so that the right paper is given same image intensities as left paper. Now, right paper appears to be made of different material. Why? 22

23 I x, y = illumination x, y reflectance (x, y) Real example Abstract version

24 Physical quantities luminance I x, y = illumination x, y reflectance (x, y) shading & shadows material

25 I x, y = illumination x, y reflectance (x, y) low reflectance, high illumination low reflectance, low illumination high reflectance, low illumination

26 Perceptual quantities brightness I x, y = illumination x, y reflectance (x, y) (no standard term for perceived illumination) lightness

27 Adelson s corrugated plaid illusion. All four indicated squares have same intensity. What is the key difference between the two configurations?

28 Lightness perception Q: What is the task? What problem is being solved? A:

29 Lightness perception Q: What is the task? What problem is being solved? A: Estimate the surface reflectance, by discounting the illumination. I x, y = illumination x, y reflectance (x, y)?

30 Lightness perception: solution sketch Q: What is the task? What problem is being solved? A: Estimate the surface reflectance, by discounting illumination effects. Compare points that have same illumination. I x 1, y 1 = illumination reflectance (x 1, y 1 ) = I x 2, y 2 = illumination reflectance (x 2, y 2 )

31 Illumination and Reflectance Shading Brightness versus Lightness Color constancy

32 Recall lecture 3 - color Absorption by photoreceptors (fraction) Illumination Surface Reflectance (fraction) There are three different spectra here. 32

33 LMS cone responses Cone response I x, y, λ C LMS (λ) dλ I x, y, λ = illumination x, y, λ reflectance x, y, λ

34 Surface Color Perception Q: What is the task? What is the problem to be solved? A: illumination Surface Reflectance 34

35 Surface Color Perception Q: What is the task? What is the problem to be solved? A: Estimate the surface reflectance, by discounting the illumination. illumination Surface Reflectance I x, y, λ = illumination x, y, λ reflectance x, y, λ 35

36 For simplicity, let s ignore the continuous wavelength λ and just consider RGB (LMS). Cone response I x, y, λ C LMS (λ) dλ λ I RGB x, y = illumination RGB x, y reflectance RGB (x, y)

37 Color Constancy Task: estimate the surface reflectance, by discounting the illumination illumination Surface Reflectance I RGB x, y = illumination RGB x, y reflectance RGB (x, y) 37

38 Why we need color constancy object recognition skin evaluation (health, emotion, ) food quality

39 Example 1: spatially uniform illumination = * I RGB x, y = illumination RGB x, y reflectance RGB (x, y) Given this, how to estimate this?

40 Solution 1: max-rgb Adaptation = * I RGB x, y = illumination RGB x, y reflectance RGB (x, y) Divide each I RGB channel by the max value of I RGB in each channel. When does this give the correct answer?

41 Example 2: non-uniform illumination sun + blue sky only blue sky = * I RGB x, y = illumination RGB x, y reflectance RGB x, y Solution: See Exercises.

42 Illumination and Reflectance Shape from Shading Brightness versus Lightness Color constancy Different solutions require different underlying assumptions. This is separate issue from how we can code up a solution using neural circuits.