NoteNextra-origin/pages/CSE559A/CSE559A_L6.md

Lecture 6

Continue on Light, eye/camera, and color

BRDF (Bidirectional Reflectance Distribution Function)

\rho(\theta_i,\phi_i,\theta_o,\phi_o)

Diffuse Reflection

• Dull, matte surface like chalk or latex paint

• Most often used in computer vision

• Brightness does depend on direction of illumination

Diffuse reflection governed by Lambert's law: I_d = k_d N\cdot L I_i

• N: surface normal
• L: light direction
• I_i: incident light intensity
• k_d: albedo

\rho(\theta_i,\phi_i,\theta_o,\phi_o)=k_d \cos\theta_i

Photometric Stereo

Suppose there are three light sources, L_1, L_2, L_3, and we have the following measurements:

I_1 = k_d N\cdot L_1

I_2 = k_d N\cdot L_2

I_3 = k_d N\cdot L_3

We can solve for N by taking the dot product of N and each light direction and then solving the system of equations.

Will not do this in the lecture.

Specular Reflection

• Mirror-like surface

I_e=\begin{cases}
I_i & \text{if } V=R \\
0 & \text{if } V\neq R
\end{cases}

• V: view direction
• R: reflection direction
• \theta_i: angle between the incident light and the surface normal

Near-perfect mirror have a high light around R.

common model:

I_e=k_s (V\cdot R)^{n_s}I_i

• k_s: specular reflection coefficient
• n_s: shininess (imperfection of the surface)
• I_i: incident light intensity

Phong illumination model

• Phong approximation of surface reflectance
  • Assume reflectance is modeled by three compoents
    • Diffuse reflection
    • Specular reflection
    • Ambient reflection

I_e=k_a I_a + I_i \left[k_d (N\cdot L) + k_s (V\cdot R)^{n_s}\right]

• k_a: ambient reflection coefficient
• I_a: ambient light intensity
• k_d: diffuse reflection coefficient
• k_s: specular reflection coefficient
• n_s: shininess
• I_i: incident light intensity

Many other models.

Measuring BRDF

Use Gonioreflectometer.

• Device for measuring the reflectance of a surface as a function of the incident and reflected angles.
• Can be used to measure the BRDF of a surface.

BRDF dataset:

• MERL dataset
• CURET dataset

Camera/Eye

DSLR Camera

• Pinhole camera model
• Lens
• Aperture (the pinhole)
• Sensor
• ...

Digital Camera block diagram

Scanning protocols:

• Global shutter: all pixels are exposed at the same time
• Interlaced: odd and even lines are exposed at different times
• Rolling shutter: each line is exposed as it is read out