This paper presents an approach for image cartoonization. By observing the cartoon painting behavior and consulting artists, we propose to separately identify three white-box representations from images: the surface representation that contains smooth surface of cartoon images, the structure representation that refers to the sparse color-blocks and flatten global content in the celluloid style workflow, and the texture representation that reflects high-frequency texture, contours and details in cartoon images. A Generative Adversarial Network (GAN) framework is used to learn the extracted representations and to cartoonize images. The learning objectives of our method are separately based on each extracted representations, making our framework controllable and adjustable. This enables our approach to meet artists' requirements in different styles and diverse use cases. Qualitative comparisons and quantitative analyses, as well as user studies, have been conducted to validate the effectiveness of this approach, and our method outperforms previous methods in all comparisons. Finally, the ablation study demonstrates the influence of each component in our framework.