In this paper, we propose a digital image enlargement method based on a fuzzy technique that improves half-pixel generation, especially for convex and concave signals. The proposed method is a modified version of the image enlargement scheme previously proposed by the authors, which achieves accurate half-pixel interpolation and enlarges the original image by convolution with the Lanczos function. However, the method causes impulse-like artifacts in the enlarged image. In this paper, therefore, we introduce a fuzzy set and fuzzy rule for generating half-pixels to improve the interpolation of convex and concave signals. Experimental results demonstrate that, in terms of image quality, the proposed method shows superior performance compared to bicubic interpolation and our previous method.

A simple depth-key-based image composition is proposed, which uses two still images with depth information, background and foreground object. The proposed method can place the object at various locations in the background considering the depth in the 3D world coordinate system. The main feature is that a simple algorithm is provided, which enables us to achieve the depthward movement within the camera plane, without being aware of the 3D world coordinate system. Two algorithms are proposed (P-OMDD and O-OMDD), which are based on the pin-hole camera model. As an advantage, camera calibration is not required before applying the algorithm in these methods. Since a single image is used for the object representation, each of the proposed methods has its limitations in terms of fidelity of the composite image. P-OMDD faithfully reproduces the angle at which the object is seen, but the pixels of the hidden surface are missing. On the contrary, O-OMDD can avoid the hidden surface problem, but the angle of the object is fixed, wherever it moves. It is verified through several experiments that, when using O-OMDD, subjectively natural composite images can be obtained under any object movement, in terms of size and position in the camera plane. Future tasks include improving the change in illumination due to positional changes and the partial loss of objects due to noise in depth images.

Gaussian integer has a potential to enhance the safety of elliptic curve cryptography (ECC) on system under the condition fixing bit length of integral and floating point types, in viewpoint of the order of a finite field. However, there seems to have been no algorithm which makes Gaussian integer ECC safer under the condition. We present the algorithm to enhance the safety of ECC under the condition. Then, we confirm our Gaussian integer ECC is safer in viewpoint of the order of finite field than rational integer ECC or Gaussian integer ECC of naive methods under the condition.