Coherent Line Drawing

Coherent Line Drawing 2008.5.221Abstract1. Introduction1.1 Related work1.2 Contribution and Overview2. Flow construction2.1 Edge Tangent Flow3. Line construction3.1 Flow-based Difference-of-Gaussians3.2 Iterative FDoG filtering4. Results5. Discussion and Future work2Abstract3

AbstractImage automatically Line drawing NPR technique Coherent, smooth, stylistic line Noise , highly coherent line flow-guided anisotropic filtering method41. Introduction51. IntroductionLine drawing prehistoric ages visual communication the simplest, oldest .Line drawing minimal amount of data , object shape

61. IntroductionObject surface tonal information shape Black-and-white line drawing Image line Automatic techniqueClean, smooth, coherent, stylistic line

71. IntroductionFlow-driven anisotropic filtering framework main contributionEdge detection filter flow anisotropic kernel Noise

81.1 Related workNPR community, 3D model line methods9

Coherent Stylized Silhouetees [Kalnins et al. 2003]

Suggestive Contours for Conveying Shape [DeCarlo et al. 2003]

A Few Good Lines: Suggestive Drawing of 3D ModelsSousa and Prusinkiewicz 2003]

1.1 Related work line drawing ex) color, tone, material etc.10Interactive pen-and-ink illustration [Salisbury et al. 1994]Processing images and video for an impressionist effect [Litwinowicz 1997]1.1 Related workPhotograph tooning NPR style explicit display of line 11

Stylization and Abstraction of Photographs [DeCarlo and Santella 2002]1.1 Related work12

Real-time video abstraction [Winnemoller et al. 2006]1.2 contribution and Overview contribution 2feature-preserving local edge flow(edge tangent flow ), Kernel-based nonlinear vector smoothing technique Line illustration Flow-based anisotropic DoG filtering technique 13

1.2 contribution and OverviewAdvantagesLine coherence: kernel size isolated edge point set line drawing Robustness: noise spurious line Quality: goodSimplicity: Generality: flow-based filtering framework general. Feature preservation term filter

142. Flow construction152.1 Edge Tangent FlowHigh-quality line drawing vector field Vector flow must describe the salient edge tangent direction in the neighborhoodNeighboring vectors must be smoothly aligned except at sharp cornersImportant edges must retain their original directions162.1 Edge Tangent Flow17

2.1 Edge Tangent Flow pixel-centered kernel, nonlinear vector smoothing edge direction , edge direction .Sharp corners swirling artifact similar orientation edge smoothing . vector vector

182.1 Edge Tangent FlowX : (x, y) image pixelI(x) : input image : Neighborhood of xk : vector normalizing termt(x) : edge tangent: a vector perpendicular to the image gradient

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

2.1 Edge Tangent FlowThe 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

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Wm weight function , center x gradient magnitude neighboring pixel y weight . . value 7 dominant vector .

tcur(z) z current normalized tangent vector . weight function , .21

2.1 Edge Tangent Flow denotes the current normalized tangent vector at y

Sign functionThis induces tighter alignment of vectors while avoiding swirling flows22

0 vector , swirling . 222.1 Edge Tangent Flowt(x) initial gradient map of the input image I perpendicular vector t(x) normalize Initial gradient map Sobel operator(appendix ) Our filter ETF update iteratively :g(x) update(gradient magnitude ) 2~3 update 23

23Appendix : Sobel operatorMathematically, the operator uses two 33 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:24

Edge detection 242.2 Discussion25

263. Line construction 1 ETF, t(x), local flow flow-guided anisotropic DoG filter . t(x) local edge . gradient highest contrast . idea edge flow gradient direction linear DoG filter . flow filter . edge filter , edge output . edge coherence , noise .

263.1 Flow-based Difference-of-Gaussians 1 local flow flow-guided anisotropic DoG filter t(x) local edge gradient highest contrast idea edge flow gradient direction linear DoG filter flow filter

27 edge filter , edge output . edge coherence , noise .

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3.1 Flow-based Difference-of-Gaussians283.1 Flow-based Difference-of-Gaussians29

Cx(s) x integal curve , s arc-length parameter positive, negative value . x curve center Cx(0)=x. filtering framework . Cx , 1 filter f t(Cx(s)) line ls . (6) ls(t) parameter t line ls . t arc-length parameter, ls Cx(s) . ls(0)=Cx(s). ls gradient vector g(Cx(s)) . I(ls(t)) ls(t) input image I .

f, difference-of-Gaussians(DoG) : (7) Gsigma variance sigma 1 gaussian function . (8) sigma_c sigma_s center surrounding section. sigma_s=1.6sigma_c setting. sigma_c . sigma_s T . line width . rho noise detected level .293.1 Flow-based Difference-of-Gaussians30

F(s) Cx : (9) F s weight . sigma_m S . sigma_m flow kernel , line coherence degree .

(9) H , binary thresholding black-and-white image convert. (10) tau 0~1. binary line illustration . 303.1 Flow-based Difference-of-Gaussians31

6 FDoG filter parameter . default setting sigma_m=3.0, sigma_c=1.0, rho=0.99 313.1 Flow-based Difference-of-Gaussians32

7 edge detector . 8 FDoG noise robustness . threshold line coherence noise FDoG threshold

323.2 Iterative FDoG filteringFDoG iterative FDoG filtering line coherence (10) FDoG filter FDoG filter Gaussian-blur smooth33 disconnected component connect

FDoG filter filter response iteratively . FDoG iterative FDoG filtering line coherence . FDoG application , (10) output filter input reinitialize. FDoG filter . line connectivity . 2~3. FDoG filter optionally gaussian-blur . 9 disconnected component connect .

334. Results34

4. Results35

4. Results36

method popular line extraction technique 512 by 512 4~6

364. Results(Bonus)37

5. Discussion and Future workDoG filter FDoG filter limitation high-contrast background , area line well-defined strokes line isolated edge segments FDoG filter , but local kernel global scale subjective contour future work 38line drawing NPR , NPR . flow-based anisotropic filtering framework general, filter , filter . DoG filter FDoG filter limitation . , high-contrast background line . area . well-defined strokes DoG, line . isolated edge segments FDoG filter , local kernal global scale subjective contour .future work . 38END39