基于容积约束Power图的图像分片逼近

给出一种在容积约束Power图结构上的图像分片多项式逼近方法.将Power图的权重与图像颜色信息相关联，设计了一种带容积约束Power图的顶点位置与权值交替优化的图像逼近算法.该算法运用误差反馈机制以及图像显著性检测等方法生成密度函数图像，并根据原始图像的颜色信息和得到的密度函数图像分两次来指导初始化点集生成，通过构建最终的Power图来逼近目标图像.利用Power图对目标图像进行区域分割，定义了度量逼近误差的带容积约束的优化能量函数，分别计算能量函数关于位置和权重的梯度，将原问题分解为两个子问题分而治之，借助密度函数图像生成的高效初始化点分布，通过不断更新Power图的顶点位置和权值得到相对较优的Power图，最终拟合出逼近图像.实验结果表明，该算法能够较好地逼近彩色图像，并有效保持了图像显著区域的特征.

Image Approximation on Capacity-Constrained Power Diagram

This paper proposes a novel method for piecewise polynomial image approximation based on the capacity-constrained power diagram. By associating the weights of a power diagram with the image color information, an efficient image approximation algorithm is designed which alternately optimizes the positions and the weights of a capacity-constrained power diagram. This method defines the density function by using error feedbacks and the saliency information of the original image, which guides the generation of the initial point distributions in the optimization. It solves the color image approximation problem by constructing the optimal power diagram. A capacity-constrained energy function is defined to measure the approximate error based on power diagram, and the explicit formulas are given for computation of the gradients of the energy function. The optimization of the energy function is converted into two sub-problems, which are tackled by alternately moving the point positions and updating the weights of the points of the power diagram. Experimental results show the correctness and efficiency of the method above.