study Diffusion Curves: A Vector Representation for Smooth-Shaded Images

Diffusion Curves: A Vector Representation for Smooth-Shaded ImageAlexandrina OrzanAdrienBousseauHolgerWinnem¨ollerPascal BarlaJo¨elleThollotDavid Salesin3SIGGRAPH08

AbstractDiffusion curve represent smooth shaded image

Manual, assisted or automatic extraction for the diffusion curve

GPU-based multi-grid gradient solutionOutlineIntroductionRelative WorkDiffusion CurvesCreating Diffusion CurvesResultsDiscussion & Future Work

IntroductionBenefits of vector-based primitives More compact representation, resolution-independence, geometric editability,easity animated, more readily stylized Limited to represent complex color gradientsOnly support linear or radial gradientsFail in soft shadows, defocus blur, diffuse shading, glossy reflection …

Introduction – cont.Gradient mesh(Adobe Illustrator and Corel CorelDraw)A lattice with colors at each vertex that are linearly interpolated across the meshDifficult to create meshesOptimized gradient mesh[Sun et al.,SIGGRAPH07]A semi-automatic method for optimizing a manually initialized mesh

Diffusion CurveA curve that diffuses colors on both sidesSupport traditional freehand drawingArtists sketch lines first as color boundariesMost color variations can be assumed to caused by edgesEdges constitute a near-complete and natural primitive for encoding and editing images [Carlsson 88; Elder 99; Elder and Goldberg 01]

ContributionA prototype allowing manual creation and editing of diffusion curvesA full automatic conversion from a bitmap to diffusion curves

Gradient ToolsOptimized Gradient Meshes[Sun el al. SIGGRAPH07]A manually initialized meshSample and estimate color of control points on Ferguson patchesOptimize the reconstruct image with constrains – smooth, vector line guided and boundary constrainedInitial meshOptimized meshreconstructedphotographic

Gradient ToolsGradient Brush[McCann & Pollard, SIGGRAPH08]Interactive edge-focused drawing tools on gradient domain G Brush, edge copy, clone I = GSolve as Poisson Eq. with GPU-based multigridmethod  I = ‧GGradient brushEdge brushClone brush

GPU-Based Multigrid Method for Gradient-DomainMulti-grid methodUse a coarse version of the domain to efficiently solve for the low frequency components of the solution, Use a fine version of the domain to refine the high frequency components. GPU-based multigrid method[Kazhdan and Hoppe, SIGGRAPH08][Goodnight et al.,03][Briggs et al.,00]

Standard Multigrid V-cycleu= F Figure 1 of “Streaming Multigrid for Gradient-Domain Operations on Large Images”, SIGGRAPH 08

Diffusion CurvesDiffusion curveFinal image

RenderingDiffusion curveFinal image Color source (CL, CR)2.DiffuseSharp color image 1. Rasterize sources3. ReblurWyWxBlur sourcesBlur map (B)Smoothness of the transition between Left and Right

1. Rasterize sourcesDiffusion curve(similar to edge-based representation [Elder 99])PBezier splineCRCLColor source - interpolationΣBlur source - interpolation

Gradient FieldCompute the gradient of RGB 3 channels on the edgeswx,y = (CL – CR) NP0 0 0 …0 ..….….0 ..0 0 0 ..CRCLN

2. DiffusionICSharp color image Compute I from gradient w with color source C as constrainApply GPU-based multigrid methodUse Jocobi relaxation to solve each level of multigridLimit the number of relaxation iteration, ex: 512x512 image5i Jacobi iteration per multigrid leveli is the level no. (fine  coarse)w = (wx, wy)Solve Poisson equation with color constrain C I =‧wI(x,y) = C(x,y) where pixel (x,y) store color value

3. ReblurringDiffuse the Blur map [Elder 99] to define blur kernel size with multigrid methodBlur each pixel with the blur kernel defined in blur mapFinal image Sharp color image B = 0B(x,y) = σ(x,y) if pixel (x,y) is on a curveσB

Panning and ZoomingRequire to solve a global eq. How to pan&zoom without a full Poisson solution at a higher resolution ?Compute a low-resolution diffusion on the un-zoomed image domainUse the obtained solution to define Dirichlet boundary conditions around the zooming window I =‧wI(x,y) = C(x,y)Curves outside the current viewport still influence the viewport’s content !

Creating Diffusion CurvesManualartists can create an image with our tool by sketching the lines of the drawing and then filling in the colorAssistedartists can trace manually over parts of an image and we recover the colors of the underlying contentAutomaticartists can automatically convert an image into our representation and possibly post-edit it

Assisted Extracting color control points along a drawn curveIdentify color outliersSample colors along the curve at distance d in NMeasure σ of the neighborhoodeach sample. Identify outliers where if it deviates too much from meanFit a polyline to the color points usingDouglasPeucker algorithmStart from the first and the last pt.Repeatedly subdivide the line into smaller segments until the max diff < єThe end points of the final polyline yield the color controls pointsNdworking on L*a*b channels

Original imageStylistic tracing using color sampling (drawing time < 1 min.)Original imageActive contours and color sampling (drawing time 90 min.)

Automatic ExtractionOriginal bitmapAutomatic reconstruction

study Diffusion Curves: A Vector Representation for Smooth-Shaded Images

1. Data ExtractionStructure-preserving manipulation[Orzan et al.,07]Extract edge locations and blur values for edge pixels after scale space analysisExtract colors at both side of edge

1. Data ExtractionStructure-preserving manipulation[Orzan et al.,07]Extract edge locations and blur values for edge pixels after scale space analysisExtract colors at both edgeConnect pixel-chains from the edge map and proceed to sample colors in the original image on both sides of edgeHard to detect the color on blur edges – pick the colors at 3σ

2. Conversion to Diffusion CurveOpen source Portraces.w. [Selinger 03]Approximate a pixel chain with a polyline that has a min. number of segmentsLeast approximation errorTransform the polyline into a smooth curve made from end-to-end connected Bezier curveLeast square Bezier fitting based on a max. user-specified fitting error and degree of smoothness

ResultNvidiaGeForce 8800Realtime performance512 x 512 gridSeveral thousands curveswebsite

study Diffusion Curves: A Vector Representation for Smooth-Shaded Images

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study Diffusion Curves: A Vector Representation for Smooth-Shaded Images