A discrete image flux conduction equation which is completely new in this field is proposed. The new approach starts with formulating a discrete image flux conduction equation based on the concept of heat conduction theory. Based on this discrete equation, the status change at a time point can be directly computed from its spatial neighborhood. To more accurately estimate an image flux, we have used an orthogonal wavelet basis to approximate the gradient of the intensity at each point. Since the proposed approach is discrete by nature, it is not necessary to formulate a continuous PDE to fit the discrete image data set. Furthermore, introduction of different numerical methods to solve the PDE can also be avoided. Since the proposed approach does not require that a PDE be solved, it is therefore more efficient and accurate than the conventional methods. Experimental results obtained using both synthetic signals and real images have demonstrated that the proposed model could effectively handle the selective image smoothing problem.

We proposed a new dyadic wavelet-based conduction approach to take the place of the nonlinear diffusion equation for selective image smoothing. We also proved that the proposed iterated system always satisfies the so-called maximum-minimum principle no matter what kind of wavelet basis is used. Since the proposed approach does not require one to solve a partial differential equation (PDE), it is therefore more efficient and accurate than the conventional nonlinear diffusion/conduction-based methods. Experimental results using 1-D synthetic data and a real image demonstrated that the proposed method can efficiently remove noise and preserve real data.

A novel image protection scheme called "cocktail watermarking" is proposed in this paper. We analyze and point out the inadequacy of the modulation techniques commonly used in ordinary spread spectrum watermarking methods and the visual model-based ones. To resolve the inadequacy, two watermarks which play complementary roles are simultaneously embedded into a host image. We also conduct a statistical analysis to derive the lower bound of the worst likelihood that the better watermark (out of the two) can be extracted. With this "high" lower bound, it is ensured that a "better" extracted watermark is always obtained. From extensive experiments, results indicate that our cocktail watermarking scheme is remarkably effective in resisting various attacks, including combined ones.