6B-L1:DENSE FLOW: BRIGHTNESS CONSTRAINT

🧙 Motion Estimation: Optical flow

• Optical flow is the apparent motion of objects or surfaces

➕ 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.

💀 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)

➕ Combining These Two Equations: (1st and 2nd in the previous header's list)

Brightness constancy constraint equation:

📏 Gradient Component of Flow

⭕ Aperture Problem

🤔 Additional Flow Constraints

• Nearby pixels move together (Local)

• Motion must be consistent over the entire image (Global)

• Only consider distinct regions (such as corners)

🌠 Smooth Optical Flow