2nd/10_Wiki/Topics/Other/Lucas-Kanade-Method.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

id	title	category	status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	verification_status	tags	raw_sources	last_reinforced	github_commit	tech_stack
wiki-2026-0508-lucas-kanade-method	Lucas-Kanade Method	10_Wiki/Topics	verified	self	LK Optical Flow Lucas-Kanade Tracker KLT Tracker	none	A	0.95	applied	computer-vision optical-flow tracking classical-cv		2026-05-10	pending	language framework python opencv

Lucas-Kanade Method

매 한 줄

"매 small window, 매 brightness constancy, 매 linear least squares 의 motion vector". Lucas-Kanade (LK, 1981) 매 sparse optical flow estimation 매 classical method — 매 each tracked point 의 local 2D velocity 의 linear system 의 solve. 2026 매 deep methods (RAFT, GMA) 매 dominate dense flow, LK 매 still the go-to 매 sparse tracking + low-compute embedded systems.

매 핵심

매 Assumptions

1. Brightness constancy: I(x, y, t) ≈ I(x+dx, y+dy, t+dt).
2. Small motion: Taylor expand 매 first-order valid.
3. Spatial coherence: small window 매 same motion 의 share.

매 The equation

• 매 I_x · u + I_y · v + I_t = 0 (optical flow constraint, per pixel).
• 매 underdetermined (2 unknowns, 1 equation) → window aggregation.
• 매 N pixels in window → over-determined linear system A·d = b.
• 매 d = (Aᵀ A)⁻¹ Aᵀ b (least squares).

매 Failure modes

• Aperture problem: window 매 1D structure (edge) → A^T A singular.
• Large motion: Taylor first-order 매 break — 매 pyramid LK 의 fix.
• Illumination change: brightness constancy 매 violate.
• Occlusion: tracked point 매 disappear — 매 forward-backward check.

매 응용

1. Sparse feature tracking (KLT in SLAM).
2. Video stabilization (camera motion estimation).
3. Embedded vision (drone OF sensor).
4. Initial track for deep refinement.

💻 패턴

Pattern 1: OpenCV calcOpticalFlowPyrLK

import cv2
import numpy as np

cap = cv2.VideoCapture("video.mp4")
ret, prev = cap.read()
prev_gray = cv2.cvtColor(prev, cv2.COLOR_BGR2GRAY)
p0 = cv2.goodFeaturesToTrack(prev_gray, maxCorners=200, qualityLevel=0.01, minDistance=10)

while True:
    ret, frame = cap.read()
    if not ret:
        break
    gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
    p1, status, err = cv2.calcOpticalFlowPyrLK(
        prev_gray, gray, p0, None,
        winSize=(21, 21), maxLevel=3,
        criteria=(cv2.TERM_CRITERIA_EPS | cv2.TERM_CRITERIA_COUNT, 30, 0.01),
    )
    good = p1[status.flatten() == 1]
    prev_gray = gray
    p0 = good.reshape(-1, 1, 2)

Pattern 2: Vanilla LK (educational)

import numpy as np

def lucas_kanade(I1, I2, points, window=15):
    """매 each point 의 (u, v) flow vector 의 return."""
    half = window // 2
    Ix = np.gradient(I1, axis=1)
    Iy = np.gradient(I1, axis=0)
    It = I2.astype(float) - I1.astype(float)
    flow = np.zeros((len(points), 2))
    for i, (x, y) in enumerate(points):
        x, y = int(x), int(y)
        Ix_w = Ix[y-half:y+half+1, x-half:x+half+1].flatten()
        Iy_w = Iy[y-half:y+half+1, x-half:x+half+1].flatten()
        It_w = It[y-half:y+half+1, x-half:x+half+1].flatten()
        A = np.stack([Ix_w, Iy_w], axis=1)
        b = -It_w
        if np.linalg.matrix_rank(A.T @ A) < 2:
            continue  # aperture problem
        d, *_ = np.linalg.lstsq(A, b, rcond=None)
        flow[i] = d
    return flow

Pattern 3: Pyramid LK (large motion)

def pyramid_lk(I1, I2, points, levels=4, window=15):
    """매 coarse-to-fine — 매 large motion 의 handle."""
    pyr1 = [I1]
    pyr2 = [I2]
    for _ in range(levels - 1):
        pyr1.append(cv2.pyrDown(pyr1[-1]))
        pyr2.append(cv2.pyrDown(pyr2[-1]))
    flow = np.zeros((len(points), 2))
    pts = points / (2 ** (levels - 1))
    for level in reversed(range(levels)):
        d = lucas_kanade(pyr1[level], pyr2[level], pts, window)
        flow = flow * 2 + d
        if level > 0:
            pts = pts * 2 + d
    return flow

Pattern 4: Forward-backward consistency

def fb_consistency(I1, I2, points, threshold=1.0):
    """매 forward 의 track 매 backward 의 verify — 매 lost point 의 reject."""
    p1 = points
    p2, st_fwd, _ = cv2.calcOpticalFlowPyrLK(I1, I2, p1, None)
    p1_back, st_bwd, _ = cv2.calcOpticalFlowPyrLK(I2, I1, p2, None)
    err = np.linalg.norm(p1 - p1_back, axis=2).flatten()
    valid = (st_fwd.flatten() == 1) & (st_bwd.flatten() == 1) & (err < threshold)
    return p2[valid]

Pattern 5: KLT corner re-seeding

def klt_track_with_reseed(cap, max_corners=200, min_count=50):
    ret, prev = cap.read()
    prev_gray = cv2.cvtColor(prev, cv2.COLOR_BGR2GRAY)
    p0 = cv2.goodFeaturesToTrack(prev_gray, max_corners, 0.01, 10)
    while True:
        ret, frame = cap.read()
        if not ret:
            break
        gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
        p1, st, _ = cv2.calcOpticalFlowPyrLK(prev_gray, gray, p0, None)
        good = p1[st.flatten() == 1]
        if len(good) < min_count:
            new_pts = cv2.goodFeaturesToTrack(gray, max_corners, 0.01, 10)
            good = np.concatenate([good, new_pts.reshape(-1, 2)])
        p0 = good.reshape(-1, 1, 2).astype(np.float32)
        prev_gray = gray
        yield good

Pattern 6: LK 의 deep flow init (2026 hybrid)

# 매 deep model (RAFT) 매 dense flow 의 give — 매 LK 의 sub-pixel refine.
def hybrid_flow(I1, I2, raft_model, points):
    dense_flow = raft_model(I1, I2)  # H x W x 2
    coarse = dense_flow[points[:, 1].astype(int), points[:, 0].astype(int)]
    refined = lucas_kanade(I1, I2, points + coarse, window=7)
    return coarse + refined

매 결정 기준

상황	Approach
Sparse feature tracking	KLT (LK + good features).
Large motion	Pyramid LK.
Dense flow + GPU	RAFT / GMA (deep).
Embedded / ms latency	LK 의 stick.
Robust tracking	LK + forward-backward + RANSAC.

기본값: cv2.calcOpticalFlowPyrLK with window=21, maxLevel=3, FB consistency check, periodic re-seed.

🔗 Graph

• 부모: Computer Vision
• 응용: KLT-Tracker
• Adjacent: RAFT

🤖 LLM 활용

언제: Code generation for embedded vision, classical CV pipelines, baseline implementation before deep methods. 언제 X: Production dense flow at scale (use RAFT/GMA), occlusion-heavy scenes (use Cotracker).

❌ 안티패턴

• No pyramid for large motion: 매 LK 매 only handle ~1 pixel motion at single scale.
• Track forever without re-seed: 매 features 매 disappear → tracking dies.
• Ignore aperture problem: 매 edge-only window → spurious flow.
• No FB check: 매 lost points 매 silently track 매 noise.

🧪 검증 / 중복

• Verified: Lucas & Kanade (1981) "An iterative image registration technique", Bouguet (2000) pyramid LK, OpenCV docs.
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — full content with vanilla LK, pyramid LK, FB consistency, deep hybrid 2026