Coherent Line Drawing

1. Coherent Line Drawing 논문 세미나 그래픽스 연구실 윤종철 2008.5.22

2. 목차 Abstract 1. Introduction 1.1 Related work 1.2 Contribution and Overview 2. Flow construction 2.1 Edge Tangent Flow 3. Line construction 3.1 Flow-based Difference-of-Gaussians 3.2 Iterative FDoG filtering 4. Results 5. Discussion and Future work

3. Abstract

4. Abstract • Image로부터 automaticallyLine을 drawing하는 NPR technique 제안 • Coherent, smooth, stylistic line에 초점 • Noise는 억제하고, highly coherent line을 찾는 flow-guided anisotropic filtering 소개 • 간단하고 구현이 쉬운 method

5. 1. Introduction

6. 1. Introduction • Line drawing은 prehistoric ages로부터 visual communication의 the simplest, oldest임이 틀림없다. • Line drawing은 minimal amount of data를 사용하고, object shape을 효율적으로 나타낼 수 있음

7. 1. Introduction • Object surface의 tonal information이 아닌 shape을 그리는 Black-and-white line drawing에초점 • Image로부터 line을 그리는 Automatic technique • Clean, smooth, coherent, stylistic line

8. 1. Introduction • Flow-driven anisotropic filtering framework가 main contribution • Edge detection filter를 변형하여 flow에 의해 정의된 anisotropic kernel에 적용 • Noise 억제

9. 1.1 Related work • NPR community에서, 3D model의 line을 그리는 methods Suggestive Contours for Conveying Shape [DeCarlo et al. 2003] Coherent Stylized Silhouetees [Kalnins et al. 2003] A Few Good Lines: Suggestive Drawing of 3D Models Sousa and Prusinkiewicz 2003]

10. 1.1 Related work • 순수한 line drawing보다 부분적으로 사용 ex) color, tone, material etc. Interactive pen-and-ink illustration [Salisbury et al. 1994] Processing images and video for an impressionist effect [Litwinowicz 1997]

11. 1.1 Related work • Photograph tooning같은 NPR style은 explicit display of line을 요구 Stylization and Abstraction of Photographs [DeCarlo and Santella 2002]

12. 1.1 Related work Real-time video abstraction [Winnemoller et al. 2006]

13. 1.2 contribution and Overview • 기술적인 contribution2가지 • feature-preserving local edge flow(edge tangent flow라고 불리는), Kernel-based nonlinear vector smoothing technique 개발 • Line illustration을 그리는 Flow-based anisotropic DoG filtering technique 제안

14. 1.2 contribution and Overview • Advantages • Line coherence: • kernel size 조정으로 isolated edge point의 set으로부터 line drawing 가능 • Robustness: • noise 억제 spurious line 줄임 • Quality: good • Simplicity: 구현 쉬움 • Generality: • flow-based filtering framework가 general. Featurepreservation term에서 다른 filter 사용가능

15. 2. Flow construction

16. 2.1 Edge Tangent Flow • High-quality line drawing을 위해 vector field는 다음요구를 만족해야 • Vectorflowmust describe the salient edge tangent direction in the neighborhood • Neighboring vectors must be smoothly aligned except at sharp corners • Important edges must retain their original directions

17. 2.1 Edge Tangent Flow

18. 2.1 Edge Tangent Flow • 각 pixel-centered kernel에서, nonlinear vector smoothing을 실행 • 두드러진 edgedirection은 보존, 약한 edge는 이웃의 지배적인 direction을 따르게. • Sharp corners 보존하고원하지 않는 swirling artifact를 피하기 위해 similar orientation의 edge에 smoothing을 장려. • 강하지만 관계없는 vector에 영향을 받는 약한 vector를 예방

19. 2.1 Edge Tangent Flow • X : (x, y) image pixel • I(x) : input image • : Neighborhood of x • k : vector normalizing term • t(x) : edge tangent: a vector perpendicular to the image gradient

20. 2.1 Edge Tangent Flow • For the spatial weight function Ws, radially-symmetric box filter of radius r, where r is the radius of the kernel :

21. 2.1 Edge Tangent Flow • The other two weight functions, Wm and Wd, play the key role in feature preserving. • Wm : magnitude weight function • denotes the normalized gradient magnitude at z, and controls the fall-off rate • Wd : direction weight function

22. 2.1 Edge Tangent Flow • denotes the ‘current’ normalized tangent vector at y • Sign function • This induces tighter alignment of vectors while avoiding swirling flows

23. 2.1 Edge Tangent Flow • t(x)는 initialgradient map of the input image I 로부터 perpendicular vector를 구해서 얻음 • t(x)는 normalize된 후 사용 • Initial gradient map은 Sobel operator(appendix 참고)로 계산 • Ourfilter는 ETF를 update하기 위해 iteratively 제공할 수 있음: • g(x)도 따라서 update됨(gradient magnitude 는변하지 않음) • 본 논문에서는 2~3번 update 했음

24. Appendix : Sobel operator • Mathematically, the operator uses two 3×3 kernels which are convolved with the original image to calculate approximations of the derivatives - one for horizontal changes, and one for vertical. If we define A as the source image, and Gx and Gy are two images which at each point contain the horizontal and vertical derivative approximations, the computations are as follow:

25. 2.2 Discussion

26. 3. Line construction

27. 3.1 Flow-based Difference-of-Gaussians • 방정식 1에 의해 만들어진 local flow에 의해 모양이 정의된 커널을 사용하는 flow-guided anisotropic DoG filter를 제공 • t(x)는 local edge 방향을 나타내고 이것은 gradient의 수직방향에서 highest contrast를 가질 가능성이 높을 것이라는 것을 의미 • 이 idea는 edge flow를 따라서 이 gradient direction에 linear DoG filter를 제공하는 것 • flow를 따라 filter의 반응을 누적

28. 3.1 Flow-based Difference-of-Gaussians

29. 3.1 Flow-based Difference-of-Gaussians

30. 3.1 Flow-based Difference-of-Gaussians

31. 3.1 Flow-based Difference-of-Gaussians

32. 3.1 Flow-based Difference-of-Gaussians

33. 3.2 Iterative FDoG filtering • FDoG에서 파라미터 변경하는 것보다 iterative FDoG filtering은 line coherence를 향상에종종 더 효과 • 원본 이미지에 (10)에서 얻은 이미지 중첩시키고 다시 FDoG filter 사용 • 만족할 때까지 반복 • FDoG filter 사용 전에 Gaussian-blur 쓰면 더 smooth해짐 • 초기에 disconnected component는 connect 됨

34. 4. Results

35. 4. Results

36. 4. Results

37. 4. Results(Bonus)

38. 5. Discussion and Future work • DoG filter 기반인 우리의 FDoG filter는 몇몇 limitation 공유 • high-contrast background일 때, 비록 이 area가 지각에 의해 중요하지 않아도 line의 빽빽한 집합으로 채워짐 • well-defined strokes보다는 line이 픽셀 집합처럼 형성 • isolated edge segments에 FDoG filter 유용, but여전히 local kernel상에서 작동하기 때문에 global scale subjective contour는 찾기 어려움 • future work • 가속

39. END