Download
1 / 28
280 likes | 415 Views
This lecture explores the application of gradient descent in computing optical flow and shape from shading. We discuss two primary methods: feature-based and gradient of intensity-based approaches, outlining their respective advantages in motion estimation. Key concepts include the importance of sampling frequency to mitigate aliasing, handling specular regions, and deriving gradients to update motion parameters. Additionally, we cover topics such as coarse-to-fine strategies, automatic l1 and l2 selection, and efficient light modeling techniques in computer vision applications.
E N D
Lecture 12 Modules Employing Gradient Descent Computing Optical Flow Shape fromShading
is overflow E/T is big Gibbs Sampler
Gibbs Sampler Emax/T that will overflow = BIGGEST DOUBLE
2 Modules that Employ Gradient Descent • Computing Optical Flow for Motion Using Gradient Based Approach • Shape from Shading
Optical Flow Motion Field in Image Plane
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
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
Aliasing Problems noticeable when your sampling cannot truly estimate the underlying frequency Have to sample double the frequency
Chain Rule: I(x,y,t) Assumption: “As an object moves, its intensity does not change”
Specular Regions Specular regions are noise for Computer Vision 2 2
Gradient of Intensity Based It Ix u Iy v
Gradient of Intensity Based Unknowns : u at each (x,y) v at each (x,y)
Gradient of Intensity Based Use Gradient Descent : E(u,v) Update Rule Highly Textured Knowns : Ix, Iy, It at (x,y)
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
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)
Material of Object • Color • Shiny • Transparency • Texture • Bumpy
Light Model • Ambient – light (constant) at each point • Spot • Omni – Neon – All Direction • Point Light - “Sun”
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
Shininess Factor m = 20 m = 1 Sharp Shiny Blurry Shiny
Shininess Factor • : angle between V and R • : angle between L and N cosq = L.N = |L||N|cosq = cosq
Shininess Factor Diffuse = kd Id cosq cosq decrease I 85o 45o 0o brighter darker
Shape Shape = Normal at a surface (Nx, Ny, Nz) unit
Normal Equation of Plane
Normal Normal is different at every point
Light Direction L is the same at every point Contour of Constant Intensity
SFS: Data Constraint Data Constraint
SFS: Energy Function • Known : Ia, kd, (a,b,1), I(x,y) • Unknown : p,q
