A halftoning technique that uses a simple GA has proven to be very effective to generate high quality halftone images. Recently, the two major drawbacks of this conventional halftoning technique with GAs, i.e. it uses a substantial amount of computer memory and processing time, have been overcome by using an improved GA (GA-SRM) that applies genetic operators in parallel putting them in a cooperative-competitive stand with each other. The halftoning problem is a true multiobjective optimization problem. However, so far, the GA based halftoning techniques have treated the problem as a single objective optimization problem. In this work, the improved GA-SRM is extended to a multiobjective optimization GA to simultaneously generate halftone images with various combinations of gray level precision and spatial resolution. Simulation results verify that the proposed scheme can effectively generate several high quality images simultaneously in a single run reducing even further the overall processing time.

Let q and f(x) be an odd characteristic and an irreducible polynomial of degree m over Fq, respectively. Then, suppose that F(x)=xmf(x+x-1) becomes irreducible over Fq. This paper shows that the conjugate zeros of F(x) with respect to Fq form a normal basis in Fq2m if and only if those of f(x) form a normal basis in Fqm and the compart of conjugates given as follows are linearly independent over Fq, {γ-γ-1,(γ-γ-1)q, …,(γ-γ-1)qm-1} where γ is a zero of F(x) and thus a proper element in Fq2m. In addition, from the viewpoint of q-polynomial, this paper proposes an efficient method for checking whether or not the conjugate zeros of F(x) satisfy the condition.

This paper presents a new data hiding scheme under fractal image generation via Fourier filtering method for Computer Graphics (CG) applications. The data hiding operations are achieved in the frequency domain and a method similar to QAM used in digital communication is introduced for efficient embedding in order to explore both phase and amplitude components simultaneously. Consequently, this scheme enables us not only to generate a natural terrain surface without loss of fractalness analogous to the conventional scheme, but also to embed larger amounts of data into an image depending on the fractal dimension. This scheme ensures the correct decoding of the embedded data under lossy data compression such as JPEG by controlling the quantization exponent used in the embedding process.

This paper presents an accelerated image halftoning technique using an improved genetic algorithm with tiny populations. The algorithm is based on a new cooperative model for genetic operators in GA. Two kinds of operators are used in parallel to produce offspring: (i) SRM (Self-Reproduction with Mutation) to introduce diversity by means of Adaptive Dynamic-Block (ADB) mutation inducing the appearance of beneficial mutations. (ii) CM (Crossover and Mutation) to promote the increase of beneficial mutations in the population. SRM applies qualitative mutation only to the bits inside a mutation block and controls the required exploration-exploitation balance through its adaptive mechanism. An extinctive selection mechanism subjects SRM's and CM's offspring to compete for survival. The simulation results show that our scheme impressively reduces computer memory and processing time required to obtain high quality halftone images. For example, compared to the conventional image halftoning technique with GA, the proposed algorithm using only a 2% population size required about 15% evaluations to generate high quality images. The results make our scheme appealing for practical implementations of the image halftoning technique using GA.

This paper presents a new data hiding scheme via steganographic image transformation, which is different from conventional data hiding techniques. The transformation is achieved in the frequency domain and the concept of Fourier filtering method is used. An input image is transformed into a fractal image, which can be used in Computer Graphic (CG) applications. One of the main advantages of this scheme is the amount of data to be hidden (embedded) is equal to that of the host signal (generated fractal image) while it is in general limited in the conventional data hiding schemes. Also both the opened fractal image and the hidden original one can be properly used depending on the situation. Unauthorized users will not notice the "secret" original image behind the fractal image, but even if they know that there is a hidden image it will be difficult for them to estimate the original image from the transformed image. Only authorized users who know the proper keys can regenerate the original image. The proposed method is applicable not only as a security tool for multimedia contents on web pages but also as a steganographic secret communication method through fractal images.