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# 6B-L1:DENSE FLOW: BRIGHTNESS CONSTRAINT
## :mage: Motion Estimation: Optical flow
* Optical flow is the apparent motion of objects or surfaces
## :heavy\_plus\_sign: Problem Definition Optical Flow
* How to estimate pixel motion from image I(x, y, t) to I(x, y, t+1)
* Two key assumptions:
* **color constancy**: A point in I(x, y, t) looks the same in I(x', y', t+1). For gray scale images, this is brightness constancy
* **small motion: points do not move very far.**
## :skull: Optical flow constraints (grayscale images)
1. Brightness constancy constraint (equation)
1. I(x, y, t) = I(x+v, y+u, t+1)
2. Small motion (u and v are less than 1 pixel, or smooth) (Taylor serious expansion)
## :heavy\_plus\_sign: Combining These Two Equations: (1st and 2nd in the previous header's list)
Brightness constancy constraint equation:
## :straight\_ruler: Gradient Component of Flow
## :o: Aperture Problem
## :thinking: Additional Flow Constraints
* [x] Nearby pixels move together (Local)
* [x] Motion must be consistent over the entire image (Global)
* [x] Only consider distinct regions (such as corners)
## :stars: Smooth Optical Flow
