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.