Optical flow

Sparse: Lucas–Kanade + pyramid

import cv2
import numpy as np

cap = cv2.VideoCapture("clip.mp4")
ret, old = cap.read()
old_gray = cv2.cvtColor(old, cv2.COLOR_BGR2GRAY)
pts = cv2.goodFeaturesToTrack(old_gray, maxCorners=200, qualityLevel=0.01, minDistance=7, blockSize=7)

lk_params = dict(
    winSize=(21, 21),
    maxLevel=3,
    criteria=(cv2.TERM_CRITERIA_EPS | cv2.TERM_CRITERIA_COUNT, 30, 0.01),
)

while True:
    ret, frame = cap.read()
    if not ret:
        break
    gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
    new_pts, st, err = cv2.calcOpticalFlowPyrLK(old_gray, gray, pts, None, **lk_params)
    good_new = new_pts[st == 1]
    good_old = pts[st == 1]
    # draw line from old to new for visualization
    old_gray = gray.copy()
    pts = good_new.reshape(-1, 1, 2)

cap.release()

Re-seed goodFeaturesToTrack periodically if tracks drift or disappear.

Dense: Farneback

flow = cv2.calcOpticalFlowFarneback(
    prev_gray, next_gray, None,
    pyr_scale=0.5, levels=3, winsize=15, iterations=3,
    poly_n=5, poly_sigma=1.2, flags=0,
)
# flow shape (H, W, 2): flow[...,0] = dx, flow[...,1] = dy

Visualize flow as HSV

mag, ang = cv2.cartToPolar(flow[..., 0], flow[..., 1])
hsv = np.zeros((*flow.shape[:2], 3), dtype=np.uint8)
hsv[..., 0] = ang * 180 / np.pi / 2
hsv[..., 1] = 255
hsv[..., 2] = cv2.normalize(mag, None, 0, 255, cv2.NORM_MINMAX)
bgr = cv2.cvtColor(hsv, cv2.COLOR_HSV2BGR)

Horn–Schunck (idea)

Minimizes ∫ (I_x u + I_y v + I_t)² + λ(|∇u|² + |∇v|²) dx for smooth, dense flow. Classic global method; not in core OpenCV Python as a single call—implement via iterative schemes or use specialized libraries.