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

http://www.cse.wustl.edu/~ayan/courses/cse559a/

Sep 20, 2018

Administrivia

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


  • Problem Set due Tuesday


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

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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 \(\lambda\)

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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