refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조
에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Antigravity Agent
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---
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id: wiki-2026-0508-lucas-kanade-method
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title: Lucas-Kanade Method
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [LK Optical Flow, Lucas-Kanade Tracker, KLT Tracker]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.95
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verification_status: applied
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tags: [computer-vision, optical-flow, tracking, classical-cv]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: python
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framework: opencv
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---
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# Lucas-Kanade Method
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## 매 한 줄
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> **"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.
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## 매 핵심
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### 매 Assumptions
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1. **Brightness constancy**: I(x, y, t) ≈ I(x+dx, y+dy, t+dt).
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2. **Small motion**: Taylor expand 매 first-order valid.
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3. **Spatial coherence**: small window 매 same motion 의 share.
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### 매 The equation
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- 매 I_x · u + I_y · v + I_t = 0 (optical flow constraint, per pixel).
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- 매 underdetermined (2 unknowns, 1 equation) → window aggregation.
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- 매 N pixels in window → over-determined linear system A·d = b.
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- 매 d = (Aᵀ A)⁻¹ Aᵀ b (least squares).
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### 매 Failure modes
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- **Aperture problem**: window 매 1D structure (edge) → A^T A singular.
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- **Large motion**: Taylor first-order 매 break — 매 pyramid LK 의 fix.
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- **Illumination change**: brightness constancy 매 violate.
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- **Occlusion**: tracked point 매 disappear — 매 forward-backward check.
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### 매 응용
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1. Sparse feature tracking (KLT in SLAM).
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2. Video stabilization (camera motion estimation).
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3. Embedded vision (drone OF sensor).
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4. Initial track for deep refinement.
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## 💻 패턴
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### Pattern 1: OpenCV calcOpticalFlowPyrLK
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```python
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import cv2
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import numpy as np
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cap = cv2.VideoCapture("video.mp4")
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ret, prev = cap.read()
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prev_gray = cv2.cvtColor(prev, cv2.COLOR_BGR2GRAY)
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p0 = cv2.goodFeaturesToTrack(prev_gray, maxCorners=200, qualityLevel=0.01, minDistance=10)
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while True:
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ret, frame = cap.read()
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if not ret:
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break
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gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
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p1, status, err = cv2.calcOpticalFlowPyrLK(
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prev_gray, gray, p0, None,
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winSize=(21, 21), maxLevel=3,
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criteria=(cv2.TERM_CRITERIA_EPS | cv2.TERM_CRITERIA_COUNT, 30, 0.01),
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)
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good = p1[status.flatten() == 1]
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prev_gray = gray
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p0 = good.reshape(-1, 1, 2)
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```
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### Pattern 2: Vanilla LK (educational)
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```python
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import numpy as np
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def lucas_kanade(I1, I2, points, window=15):
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"""매 each point 의 (u, v) flow vector 의 return."""
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half = window // 2
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Ix = np.gradient(I1, axis=1)
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Iy = np.gradient(I1, axis=0)
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It = I2.astype(float) - I1.astype(float)
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flow = np.zeros((len(points), 2))
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for i, (x, y) in enumerate(points):
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x, y = int(x), int(y)
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Ix_w = Ix[y-half:y+half+1, x-half:x+half+1].flatten()
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Iy_w = Iy[y-half:y+half+1, x-half:x+half+1].flatten()
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It_w = It[y-half:y+half+1, x-half:x+half+1].flatten()
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A = np.stack([Ix_w, Iy_w], axis=1)
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b = -It_w
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if np.linalg.matrix_rank(A.T @ A) < 2:
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continue # aperture problem
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d, *_ = np.linalg.lstsq(A, b, rcond=None)
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flow[i] = d
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return flow
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```
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### Pattern 3: Pyramid LK (large motion)
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```python
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def pyramid_lk(I1, I2, points, levels=4, window=15):
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"""매 coarse-to-fine — 매 large motion 의 handle."""
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pyr1 = [I1]
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pyr2 = [I2]
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for _ in range(levels - 1):
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pyr1.append(cv2.pyrDown(pyr1[-1]))
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pyr2.append(cv2.pyrDown(pyr2[-1]))
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flow = np.zeros((len(points), 2))
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pts = points / (2 ** (levels - 1))
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for level in reversed(range(levels)):
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d = lucas_kanade(pyr1[level], pyr2[level], pts, window)
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flow = flow * 2 + d
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if level > 0:
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pts = pts * 2 + d
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return flow
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```
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### Pattern 4: Forward-backward consistency
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```python
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def fb_consistency(I1, I2, points, threshold=1.0):
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"""매 forward 의 track 매 backward 의 verify — 매 lost point 의 reject."""
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p1 = points
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p2, st_fwd, _ = cv2.calcOpticalFlowPyrLK(I1, I2, p1, None)
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p1_back, st_bwd, _ = cv2.calcOpticalFlowPyrLK(I2, I1, p2, None)
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err = np.linalg.norm(p1 - p1_back, axis=2).flatten()
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valid = (st_fwd.flatten() == 1) & (st_bwd.flatten() == 1) & (err < threshold)
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return p2[valid]
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```
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### Pattern 5: KLT corner re-seeding
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```python
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def klt_track_with_reseed(cap, max_corners=200, min_count=50):
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ret, prev = cap.read()
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prev_gray = cv2.cvtColor(prev, cv2.COLOR_BGR2GRAY)
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p0 = cv2.goodFeaturesToTrack(prev_gray, max_corners, 0.01, 10)
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while True:
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ret, frame = cap.read()
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if not ret:
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break
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gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
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p1, st, _ = cv2.calcOpticalFlowPyrLK(prev_gray, gray, p0, None)
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good = p1[st.flatten() == 1]
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if len(good) < min_count:
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new_pts = cv2.goodFeaturesToTrack(gray, max_corners, 0.01, 10)
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good = np.concatenate([good, new_pts.reshape(-1, 2)])
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p0 = good.reshape(-1, 1, 2).astype(np.float32)
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prev_gray = gray
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yield good
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```
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### Pattern 6: LK 의 deep flow init (2026 hybrid)
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```python
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# 매 deep model (RAFT) 매 dense flow 의 give — 매 LK 의 sub-pixel refine.
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def hybrid_flow(I1, I2, raft_model, points):
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dense_flow = raft_model(I1, I2) # H x W x 2
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coarse = dense_flow[points[:, 1].astype(int), points[:, 0].astype(int)]
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refined = lucas_kanade(I1, I2, points + coarse, window=7)
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return coarse + refined
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```
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## 매 결정 기준
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| 상황 | Approach |
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| Sparse feature tracking | KLT (LK + good features). |
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| Large motion | Pyramid LK. |
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| Dense flow + GPU | RAFT / GMA (deep). |
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| Embedded / ms latency | LK 의 stick. |
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| Robust tracking | LK + forward-backward + RANSAC. |
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**기본값**: `cv2.calcOpticalFlowPyrLK` with window=21, maxLevel=3, FB consistency check, periodic re-seed.
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## 🔗 Graph
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- 부모: [[Computer Vision|Computer-Vision]]
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- 응용: [[KLT-Tracker]]
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- Adjacent: [[RAFT]]
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## 🤖 LLM 활용
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**언제**: Code generation for embedded vision, classical CV pipelines, baseline implementation before deep methods.
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**언제 X**: Production dense flow at scale (use RAFT/GMA), occlusion-heavy scenes (use Cotracker).
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## ❌ 안티패턴
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- **No pyramid for large motion**: 매 LK 매 only handle ~1 pixel motion at single scale.
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- **Track forever without re-seed**: 매 features 매 disappear → tracking dies.
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- **Ignore aperture problem**: 매 edge-only window → spurious flow.
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- **No FB check**: 매 lost points 매 silently track 매 noise.
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## 🧪 검증 / 중복
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- Verified: Lucas & Kanade (1981) "An iterative image registration technique", Bouguet (2000) pyramid LK, OpenCV docs.
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — full content with vanilla LK, pyramid LK, FB consistency, deep hybrid 2026 |
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