Continuous-Line Image Stylization Based on Hilbert Curve

Horizontal and vertical lines hold significant aesthetic and psychological importance, providing a sense of order, stability, and security. This paper presents an image stylization method that quickly generates non-self-intersecting and regular continuous lines based on the Hilbert curve, a well-known space-filling curve consisting of only horizontal and vertical segments. We first calculate the grayscale threshold based on gray quantization for the original image and recursively subdivide the cells according to the density in each cell. To avoid generating new feature curves due to limited gray quantization, a recursive subdivision with probability is designed to smooth the density. Then, we utilize the rule of Hilbert curve to generate continuous lines connecting all the cells. Between different degrees of Hilbert curves, bridge curves composed of horizontal and vertical lines are constructed, which are also intersection-free, instead of a straight line linking them directly. There are two parameters provided for feasibly adjusting variate effects. The image stylization framework could be generalized to other space-filling curves like the Peano curve. Compared to existing methods, our approach can generate pleasing results quickly and is fully automated. Many results show our method is robust and effective.