A new implementation of discrete multiscale filtering

In this paper, a conventional discrete implementation of the diffusion equation is analyzed. It is shown that when the evolution time step is less than 1/4 , the conventional discrete implementation satisfies the scale-space condition. As the evolution time increases, the image becomes smoother and smoother, thus making the evolution increasingly slow and the computing time lengthy. To solve this problem, a new discrete implementation is proposed. It is shown that the proposed implementation satisfies the scale-space condition when discrete time steps are arbitrarily large. The new discrete implementation of the diffusion equation not only preserves the scale-space condition but also effectively reduces the evolution time. The experiments in range image segmentation show that the proposed method has a similar segmentation effect as the conventional methods, but with much less computing time.