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Lecture 1 2

Lecture 1 2. Modules Employing Gradient Descent Computing Optical Flow Shape from Shading. is overflow. E/T is big. Gibbs Sampler. Gibbs Sampler. E max /T. that will overflow. = BIGGEST DOUBLE. 2 Modules that Employ Gradient Descent.

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Lecture 1 2

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  1. Lecture 12 Modules Employing Gradient Descent Computing Optical Flow Shape fromShading

  2. is overflow E/T is big Gibbs Sampler

  3. Gibbs Sampler Emax/T that will overflow = BIGGEST DOUBLE

  4. 2 Modules that Employ Gradient Descent • Computing Optical Flow for Motion Using Gradient Based Approach • Shape from Shading

  5. Optical Flow Motion Field in Image Plane

  6. Optical Flow 2 Methods: • Featured Based - similar to stereo where you solve - correspondence (matching) problem between 2 consecutive frames • Gradient of Intensity Based - No matching needed - Works well when images have much texture - Dense map of (u,v) at each pixel

  7. Gradient of Intensity Based - Spatial Resolution (x,y)pixels per cm - Temporal Resolution frames per second 1 2 3 I(x,y,t2) I(x,y,t1) I(x,y,t3) t I(x,y,t) 16/sec ALIASING

  8. Aliasing Problems noticeable when your sampling cannot truly estimate the underlying frequency Have to sample double the frequency

  9. Chain Rule: I(x,y,t) Assumption: “As an object moves, its intensity does not change”

  10. Specular Regions Specular regions are noise for Computer Vision 2 2

  11. Gradient of Intensity Based It Ix u Iy v

  12. Gradient of Intensity Based

  13. Gradient of Intensity Based Unknowns : u at each (x,y) v at each (x,y)

  14. Gradient of Intensity Based Use Gradient Descent : E(u,v) Update Rule Highly Textured Knowns : Ix, Iy, It at (x,y)

  15. Research Topics • Find (u,v) through gradient Method: Coarse-to-Fine • How to choose l1, l2 automatically • How to get the annealing schedule automatically T high Random Walk T low Greedy

  16. Shape from Shading Point Light at ∞ viewer ping-pong viewer Image Observed: f (viewer position, camera model, shape of object, material of object, light color, light model, light position)

  17. Material of Object • Color • Shiny • Transparency • Texture • Bumpy

  18. Light Model • Ambient – light (constant) at each point • Spot • Omni – Neon – All Direction • Point Light - “Sun”

  19. Light l = R,G,B Il(x,y) = Ambientl + Diffusel + Specularl = Ialkal + kdlIdlcosq + ksIsl(cosa)m Ia : Ambient Light Id : Diffuse Light – Main Light ka : Ambient Constant “glow in dark” kd : Main Color Diffuse Constant White is high , Black is low ks : Mirror Like, Specularity Constant ks = 0 for ping pong = 0.5 for apple = 1 for billioud

  20. Shininess Factor m = 20 m = 1 Sharp Shiny Blurry Shiny

  21. Shininess Factor • : angle between V and R • : angle between L and N cosq = L.N = |L||N|cosq = cosq

  22. Shininess Factor Diffuse = kd Id cosq cosq decrease I 85o 45o 0o brighter darker

  23. Shape Shape = Normal at a surface (Nx, Ny, Nz) unit

  24. Normal Equation of Plane

  25. Normal Normal is different at every point

  26. Light Direction L is the same at every point Contour of Constant Intensity

  27. SFS: Data Constraint Data Constraint

  28. SFS: Energy Function • Known : Ia, kd, (a,b,1), I(x,y) • Unknown : p,q

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