On translation planes of orderq 3 that admit a collineation group of orderq 3

Let II be a translation plane of orderq ³, with kernel GF(q) forq a prime power, that admits a collineation groupG of orderq ³ in the linear translation complement. Moreover, assume thatG fixes a point at infinity, acts transitively on the remaining points at infinity andG/E is an abelian group of orderq ², whereE is the elation group ofG.In this article, we determined all such translation planes. They are (i) elusive planes of type I or II or (ii) desirable planes.Furthermore, we completely determined the translation planes of orderp ³, forp a prime, admitting a collineation groupG of orderp ³ in the translation complement such thatG fixes a point at infinity and acts transitively on the remaining points at infinity. They are (i) semifield planes of orderp ³ or (ii) the Sherk plane of order 27.     

A family of translation planes of order q 2m+1 with two orbits of length 2 and q 2m+1−1 on l ∞

A class of translation planes of order q ^2m+1, where q is an odd prime power and m1, is constructed. If m=1, then this class is contained in the class of order q ³ constructed by Hiramine [5]. These planes of order q ^2m+1 are of dimension 2m+1 over their kernels. If q ^2m+13³, then the linear translation complements of these planes have two orbits of length 2 and q ^2m+1–1 on l and this class contains many planes which are not generalized André planes. If q ^2m+1= 3³, then each plane of this class is isomorphic to the Hering plane of order 27.Dedicated to Professor Tuyosi Oyama on his 60th birthday     

Color removal method considering perceived lightness

Optical Review - A novel color removal method for digital color images is proposed. In this method, differences of colors in an input color image are reflected effectively, and the perceived...     

Fast image enlargement using predefined codebook and eigenspace backprojection for lost pixel

In this paper, a new image enlargement method applying the backprojection for lost pixel (BPLP) to the predefined codebook-based method is proposed. BPLP is a method for image restoration. In BPLP, the eigenspace reflecting the characteristics of an input image is generated from the remained pixels and is used to restore the missing pixels. In the proposed method, the eigenspace is replaced by one generated from the predefined codebook (PDC). PDC represents edge-blurring properties in a small image patch and consists of pairs of low- and high-frequency image patches on various edge patterns. By replacing the PDC-based estimation of lost high-frequency components with BPLP, a fast image enlargement method retaining its performance can be developed. Through some experiments, the effectiveness of the proposed method was demonstrated. Especially, it was confirmed that the processing time of the proposed method was shortened to about 1/50 that of the PDC-based method.     

The nonexistence of projective planes of order 12 with a collineation group of order 8

In this article, we prove that there does not exist a symmetric transversal design which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We use an orbit theorem for symmetric transversal designs to prove our result. As a corollary of the result, we prove that there is no projective plane of order 12 admitting a collineation group of order 8. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 411–430, 2008     

Hue-preserving image enhancement in CIELAB color space considering color gamut

Optical Review - In this paper, we propose a color image enhancement method that uses the CIELAB color space to improve the quality of degraded images for human visual perception. In our method,...     

Gradient-norm-based histogram equalization taking account of HSV color space distribution

In the present paper, we propose an image contrast enhancement method that can enhance the contrast of a color image naturally by taking account of a color space shape. The proposed method realizes the natural enhancement based on two kinds of intensity histograms: a gradient-norm-based histogram and an ideal histogram derived from the shape of a color space. The former histogram is used to suppress over-enhancement in the flat regions of an image and the latter histogram is used to prevent the whole image from being darken. Concretely, the aforementioned intensity histograms are appropriately mixed into a histogram with a weight based on the average intensity of the input image. The contrast enhancement of the input image is realized using the cumulative histogram of the mixed histogram as an intensity transform function. To verify the validity of the proposed method, in experiments, the proposed method is applied to a variety of images and experimental results are evaluated qualitatively and quantitatively.     

The Existence of a Symmetric Transversal Design STD 7[21; 3]

In this note we construct a symmetric transversal design STD₇[21; 3]. Therefore there exists an orthogonal array OA(63, 21, 3, 2). Communicated by: J.D. Key     

Image enhancement with lightness correction and image sharpening based on characteristics of vision for elderly persons

Optical Review - In general, as people age the functions of their sensory organs deteriorate. For example, in the eye of an elderly person, the visual field becomes dark owing to a decrease in the...