Optical Flow

Module: Computer Vision | Difficulty: Intermediate

Optical Flow Constraints

Brightness Constancy

First-order Taylor expansion gives the optical flow constraint:

Lucas-Kanade Method

Assume constant flow in a local window :

where

Horn-Schunck Regularization

End-Point Error (EPE)

import cv2
import numpy as np

def lucas_kanade_flow(prev_gray, curr_gray, features):
    lk_params = dict(
        winSize=(15, 15), maxLevel=2,
        criteria=(cv2.TERM_CRITERIA_EPS \| cv2.TERM_CRITERIA_COUNT, 10, 0.03)
    )
    next_pts, status, err = cv2.calcOpticalFlowPyrLK(
        prev_gray, curr_gray, features, None, **lk_params
    )
    return next_pts, status, err

def dense_flow(prev_gray, curr_gray):
    flow = cv2.calcOpticalFlowFarneback(
        prev_gray, curr_gray, None,
        pyr_scale=0.5, levels=3, winsize=15,
        iterations=3, poly_n=5, poly_sigma=1.2, flags=0
    )
    return flow

Key Takeaways

• Optical flow estimates per-pixel motion between frames
• Lucas-Kanade is sparse and fast; Horn-Schunck is dense and smooth
• Deep flow networks (FlowNet, RAFT) achieve superior accuracy