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UCF REU Week 3

This document explores the Shape from Shading (SfS) technique using a Lambertian reflectance model defined as E = k * p * cos(q), with k and p set to 1. It examines the relationship between surface gradients (p, q) and image intensity. Key topics include the computation of intensity I, camera positioning, and the formulation of Lambertian Reflectance Maps at specified points. Optimization techniques for enhancing computation efficiency and ensuring smoothness in solutions are discussed, along with practical examples demonstrating these methods.

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UCF REU Week 3

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  1. UCF REU Week 3 Lam Tran

  2. Shape From Shading

  3. Lambertian Model E = k*p*COS q Let k=p=1, I = COS q = N*L/(|N||L|) Camera (0,0,1) (-p,-q,1) q (-ps,-qs,1)

  4. Lambertian Reflectance Map ps=0 qs=0

  5. Lambertian Reflectance Map ps=0.7 qs=0.3

  6. Shape From Shading with MRF • Solve I(x,y) = R(p,q), p and q are the surface gradient Local horizontal and vertical cost Smoothness horizontal and vertical cost

  7. Optimization Techniques Less computation Guarantee Smoothness

  8. Optimization Example (1)

  9. Optimization Example (2) Approximation Exact

  10. Another Example

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