Abstract: Abstracting images into geometric representations is an important topic in the field of image processing. To improve the ability of polygonal meshes in capturing curved features of images and further enhance the quality of reconstructed images, this paper proposes a variational generation framework for polygonal meshes, which sets the distance between piecewise approximating functions defined on the mesh and the input image as an energy function, and minimizes it to generate image-adaptive polygonal meshes. Quadratic Bézier curves are introduced to bend each mesh edge, thereby enhancing the mesh’s capability to capture image features. To efficiently optimize the mesh, explicit gradient formulas of the energy function with respect to mesh vertices and Bézier control points are derived, and an alternating optimization strategy is employed to iteratively update these two items after mesh initialization using superpixels. Compared with existing approaches such as curved triangular meshes or ordinary polygonal meshes, the results of our method demonstrate remarkable improvements in both image approximation quality and visual effects, the root mean square error between the reconstructed images and the original images is generally reduced by 3.57% to 6.97% compared to curved triangular meshes, and by 39.81% to 56.94% compared to ordinary polygon meshes.