CSE 559A: Computer Vision

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Fall 2018: T-R: 11:30-1pm @ Lopata 101

Instructor: Ayan Chakrabarti (ayan@wustl.edu).
Course Staff: Zhihao Xia, Charlie Wu, Han Liu

Sep 20, 2018

• Recitation Tomorrow
• Jolley Hall 309. 10:30AM - Noon

• Problem Set due Tuesday

• Office Hours Monday: Again in Jolley 217, 5:30-6:30pm.

# Angles

Bi-directional Reflectance Distribution Function

$L_o(\theta_o,\phi_o) = \int~\rho(\theta_i,\phi_i,\theta_o,\phi_o)L_i(\theta_i,\phi_i) \cos\theta_i~d\omega_i$

• So, the BRDF describes how every incoming ray gets reflected by the surface.
• How much energy in which direction
• This is actually a function of wavelength $$\lambda$$

Bi-directional Reflectance Distribution Function

Properties

• Positivity: $$\rho(\theta_i,\phi_i,\theta_o,\phi_o) \geq 0$$

• Helmholtz Reciprocity: $$\rho(\theta_i,\phi_i,\theta_o,\phi_o) = \rho(\theta_o,\phi_o,\theta_i,\phi_i)$$

• Total Energy leaving surface is less than total energy arriving

$\int L_i(\theta_i,\phi_i) \cos\theta_i~d\omega_i \geq \int \left[\int~\rho(\theta_i,\phi_i,\theta_o,\phi_o)L_i(\theta_i,\phi_i) \cos\theta_i~d\omega_i\right] \cos \theta_o d\omega_o$

# Next Up

• Model Light Sources and Lighting Environments
• Use to relate observed intensity to surface normals
• Recover shape from intensity