Biharmonic diffusion curve images from boundary elements
Biharmonic diffusion curve images from boundary elements
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DOI：
10.1145/2508363.2508426
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
Peter W. M. Ilbery;Luke Kendall;C. Concolato;Michael McCosker
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文献类型：
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作者：
Peter W. M. Ilbery;Luke Kendall;C. Concolato;Michael McCosker
目前对图形图像的自由形式、基于曲线的创作有很大的兴趣。具体地说，通过允许图像设计者通过绘制曲线并沿这些曲线的任一侧设置颜色值来指定自然主义图像，“扩散曲线”促进了图形图像的创建。最近，已经提出了基于双调和方程的扩散曲线的扩展，它通过指定的颜色值提供平滑内插，并允许图像设计者指定曲线上的颜色梯度约束。提出了一种边界元方法(BEM)，用于绘制具有光滑内插和梯度约束的扩散曲线图像，该方法生成求解的边界元素图像表示。可以使用一种新颖而有效的逐行方法从求解的表示中评估扩散曲线图像。我们还描述了“曲线感知”上采样，在这种上采样中，可以使用公式求值或曲线附近的校正从较低分辨率的图像上采样全分辨率扩散曲线图像。边界元解的图像表示是紧凑的。因此，在将求解的图像表示传输到设备以进行渲染并且由于时间或处理限制而不希望在设备处进行PDE求解的情况下，它提供了优势。
There is currently significant interest in freeform, curve-based authoring of graphic images. In particular, "diffusion curves" facilitate graphic image creation by allowing an image designer to specify naturalistic images by drawing curves and setting colour values along either side of those curves. Recently, extensions to diffusion curves based on the biharmonic equation have been proposed which provide smooth interpolation through specified colour values and allow image designers to specify colour gradient constraints at curves. We present a Boundary Element Method (BEM) for rendering diffusion curve images with smooth interpolation and gradient constraints, which generates a solved boundary element image representation. The diffusion curve image can be evaluated from the solved representation using a novel and efficient line-by-line approach. We also describe "curve-aware" upsampling, in which a full resolution diffusion curve image can be upsampled from a lower resolution image using formula evaluated orrections near curves. The BEM solved image representation is compact. It therefore offers advantages in scenarios where solved image representations are transmitted to devices for rendering and where PDE solving at the device is undesirable due to time or processing constraints.