【摘要】 四面体网格在医学图像、可视化等领域有广泛的应用.现有的体素图像生成四面体网格算法通常需要进行去噪、分割、四面体化等多个步骤,从而导致误差的不断累积.这里提出了一种直接由带噪音的原始体素数据生成最终需要的四面体网格的算法.本算法的核心是针对体素图像四面体化的需求提出了一种基于全变分稀疏模型的优化方法,并通过交替方向乘子法等数值算法高效地优化该变分模型,直接从输入的原始体素图像中得到四面体网格,同时对网格的顶点位置、连接关系、四面体的属性信息都进行了优化.通过在模拟数据与真实数据上的实验表明,该算法在处理即使带有噪音的数据时也能很好地重建四面体网格,并能保持原始信号的尖锐特征.更多还原

【Abstract】 Tetrahedral meshes have been widely used in medicine and visualization. In general,to convert a volume image to a tetrahedral mesh,conventional methods first denoise the input volume image,then segment the image and finally construct a tetrahedral mesh. However, these methods make the error accumulate. Here an algorithm was presented to approximate a volume image directly by a tetrahedral mesh with each tetrahedron having a constant intensity/attribute value. The algorithm finds the vertex positions and connectivity of the mesh and the tetrahedral attribute values as a solution to a total variation(TV) problem. The objective function of the TV problem is composed of three specifically-designed terms accounting for fitting errors,denoising effects and mesh quality control,respectively. Alternating direction method of multipliers(ADMM) was proposed to solve the optimization problem. As a result,the algorithm can produce high quality tetrahedral meshes faithfully approximating the input image with good feature preservation,and meanwhile it has the ability of reliably handling noisy images automatically. These features have been demonstrated by our experiments on various volumetric datasets including synthetic data and real medical images.更多还原