Marbling图案的计算机仿真
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摘要
Marbling是一门在液体表面制作彩色流体状图案的传统手工艺术。对Marbling的仿真是计算机图形学领域中艺术模拟的一大组成部分。计算机仿真Marbling的研究对传播、继承和保护古老文明,弘扬传统艺术有着重要的理论意义和现实的应用价值。本文主要研究计算机仿真Marbling的若干关键技术,具体包括基于物理方法的Marbling仿真、基于图像及视频的Marbling风格化、基于数学函数方法的Marbling仿真、基于演化计算的Marbling图案设计。论文的主要研究成果包括：
1.提出了一个快速、精确的Marbling仿真方法。该方法基于二维流体动力学仿真。首先,在时间和空间上数值求解经典的Navier-Stokes流体方程获得流体的速度场。然后,对密度场进行对流得到可视的Marbling图案。我们采用三阶稳定的USCIP对流模式和简单有效的转换函数使生成的图案颜色鲜艳、图案清晰精美。本系统基于CUDA平台求解复杂的流体方程,为用户提供了一个设计Marbling图案的实时交互环境。
2.提出了一个实时自动的图像及视频Marbling风格化框架。首先,将输入图像从RGB颜色空间转换到CIE Lab颜色空间,对其中的亮度通道进行后续操作。然后,使用迭代双边滤波的方法逐渐构造出一个光滑、连贯的特征流场。最后,将获得的特征流场作为Navier-Stokes方程的力场,从而驱动图像进行流动并变形。由于图像沿着自身的特征流场进行流动,因此生成的图案不仅保持了Marbling图案的流体特征,而且也保持了图像中的物体形状。我们使用对流纹理坐标的方法避免图案出现模糊的现象。
3.提出了一个基于数学函数方法的Marbling仿真技术。该方法将Marbling工艺中常用的滴管、刷子、尖笔、梳子、漩涡等操作抽象成对应的数学解析表达式。这些公式满足不可压缩流的特点,并且均是可逆函数。正函数用于生成矢量的Marbling图形,逆函数用于生成像素的Marbling图像。此外,本文方法在三维场景装饰、三维模型高清细节绘制、图像编辑和交互式视频处理方面都有广泛应用。
4.将设计方法学和人工智能的遗传算法相结合,提出了一种计算机辅助Marbling纹理设计方法。借助于该方法,设计人员从繁琐的数学公式中释放出来,将精力放在对Marbling图案的评估和选择上,并引导生成符合设计师要求的图案。该方法生成的Marbling的图案满足纺织工业界矢量图形、无缝拼接、同一图案不同色彩搭配的需求。
Marbling is a traditional art of aqueous surface design to create intricate fluid-like patterns. The simulation of marbling is one of the popular techniques for modeling traditional artistic media in computer graphics. The simulation of marbling art plays important role in broadcasting, inheritance and protection of the ancient civilization and traditional art. Consequently, it has not only the important theoretical significance but also the realistic application value. The thesis mainly focuses on some key issues on the marbling simulation, including physically-based marbling simulation, mathematical marbling, image and video marbleization, and evolutionary design of marbling patterns. The results of the thesis consist of the followings.
1. We present a fast and accurate marbling simulation system, which is based on the physical model of the traditional marbling process. The method borrows some idea from the two-dimensional computer fluid dynamic simulation. We first numerically solve the Navier-Stokes fluid equations to get the velocity field. Then, we advect the density field to obtain the marbling patterns. To simulate the very sharp lines among different paints, a third-order accurate but fast Unsplit semi-Lagragian Constrained Interpolation Profile method and a simple yet effective transformation function are applied. The system is implemented on the GPU and allows artists to create marbling textures with real-time visual feedback.
2. We present a real-time image marbleization method that converts an image or video into a marble-like appearance automatically. Firstly, our method converts the input image from RGB color space to CIE-Lab color space. Then, it iteratively constructs a smooth and coherent edge tangent flow field by using a bilateral filter. Next, the obtained flow field is used as the external force in Navier-Stokes equation and the color advection of the input image results in a marbleized image. Since the image flows along its salient features, the resulted patterns not only possess the fluid-like characteristics, but also preserve the shape of the objects well in the images. We advect images'texture coordinates to avoid color mixture.
3. We proposed a mathematical approach with closed-form expressions to simulate marbling. The method abstracts the frequently used tools of marbling (i.e. eye dropper, brush, stylus, comb, and curl) as corresponding mathematical formulas. These tool functions are incompressible and invertible. A forward application is appropriate for creating vector-based marbling patterns, and an inverse application is appropriate for pixel-based ones. In addition, the method has wide applications include surface details rendering on3D objects, image editing, and interactive video processing.
4. By integrating design methodology theories with evolutionary computation, we developed a design system to evolve preferred designs on complex marbling patterns. The system is formulated in a way to assist the productive-deductive-inductive design reasoning process of the users. Therefore, complex mathematical functions do not cognitively overload the designers, who are released for the more critical tasks of aesthetic assessment and new design rules induction. In addition, the resulting patterns fulfill the textile industry requirements of seamless tiling, different colourways, and vector output.
1.提出了一个快速、精确的Marbling仿真方法。该方法基于二维流体动力学仿真。首先,在时间和空间上数值求解经典的Navier-Stokes流体方程获得流体的速度场。然后,对密度场进行对流得到可视的Marbling图案。我们采用三阶稳定的USCIP对流模式和简单有效的转换函数使生成的图案颜色鲜艳、图案清晰精美。本系统基于CUDA平台求解复杂的流体方程,为用户提供了一个设计Marbling图案的实时交互环境。
2.提出了一个实时自动的图像及视频Marbling风格化框架。首先,将输入图像从RGB颜色空间转换到CIE Lab颜色空间,对其中的亮度通道进行后续操作。然后,使用迭代双边滤波的方法逐渐构造出一个光滑、连贯的特征流场。最后,将获得的特征流场作为Navier-Stokes方程的力场,从而驱动图像进行流动并变形。由于图像沿着自身的特征流场进行流动,因此生成的图案不仅保持了Marbling图案的流体特征,而且也保持了图像中的物体形状。我们使用对流纹理坐标的方法避免图案出现模糊的现象。
3.提出了一个基于数学函数方法的Marbling仿真技术。该方法将Marbling工艺中常用的滴管、刷子、尖笔、梳子、漩涡等操作抽象成对应的数学解析表达式。这些公式满足不可压缩流的特点,并且均是可逆函数。正函数用于生成矢量的Marbling图形,逆函数用于生成像素的Marbling图像。此外,本文方法在三维场景装饰、三维模型高清细节绘制、图像编辑和交互式视频处理方面都有广泛应用。
4.将设计方法学和人工智能的遗传算法相结合,提出了一种计算机辅助Marbling纹理设计方法。借助于该方法,设计人员从繁琐的数学公式中释放出来,将精力放在对Marbling图案的评估和选择上,并引导生成符合设计师要求的图案。该方法生成的Marbling的图案满足纺织工业界矢量图形、无缝拼接、同一图案不同色彩搭配的需求。
Marbling is a traditional art of aqueous surface design to create intricate fluid-like patterns. The simulation of marbling is one of the popular techniques for modeling traditional artistic media in computer graphics. The simulation of marbling art plays important role in broadcasting, inheritance and protection of the ancient civilization and traditional art. Consequently, it has not only the important theoretical significance but also the realistic application value. The thesis mainly focuses on some key issues on the marbling simulation, including physically-based marbling simulation, mathematical marbling, image and video marbleization, and evolutionary design of marbling patterns. The results of the thesis consist of the followings.
1. We present a fast and accurate marbling simulation system, which is based on the physical model of the traditional marbling process. The method borrows some idea from the two-dimensional computer fluid dynamic simulation. We first numerically solve the Navier-Stokes fluid equations to get the velocity field. Then, we advect the density field to obtain the marbling patterns. To simulate the very sharp lines among different paints, a third-order accurate but fast Unsplit semi-Lagragian Constrained Interpolation Profile method and a simple yet effective transformation function are applied. The system is implemented on the GPU and allows artists to create marbling textures with real-time visual feedback.
2. We present a real-time image marbleization method that converts an image or video into a marble-like appearance automatically. Firstly, our method converts the input image from RGB color space to CIE-Lab color space. Then, it iteratively constructs a smooth and coherent edge tangent flow field by using a bilateral filter. Next, the obtained flow field is used as the external force in Navier-Stokes equation and the color advection of the input image results in a marbleized image. Since the image flows along its salient features, the resulted patterns not only possess the fluid-like characteristics, but also preserve the shape of the objects well in the images. We advect images'texture coordinates to avoid color mixture.
3. We proposed a mathematical approach with closed-form expressions to simulate marbling. The method abstracts the frequently used tools of marbling (i.e. eye dropper, brush, stylus, comb, and curl) as corresponding mathematical formulas. These tool functions are incompressible and invertible. A forward application is appropriate for creating vector-based marbling patterns, and an inverse application is appropriate for pixel-based ones. In addition, the method has wide applications include surface details rendering on3D objects, image editing, and interactive video processing.
4. By integrating design methodology theories with evolutionary computation, we developed a design system to evolve preferred designs on complex marbling patterns. The system is formulated in a way to assist the productive-deductive-inductive design reasoning process of the users. Therefore, complex mathematical functions do not cognitively overload the designers, who are released for the more critical tasks of aesthetic assessment and new design rules induction. In addition, the resulting patterns fulfill the textile industry requirements of seamless tiling, different colourways, and vector output.
引文
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