Semi-Invariant Algorithm for Color to Gray and Back

This paper proposes a reversible algorithm to convert color images to gray images with keeping chroma and spatial resolution. K. Braun and R. L. de Queiroz proposed a color-to-gray mapping algorithm. The method can almost recover the original color, but it had theoretical problems that both chroma and spatial resolution deteriorated. Our algorithm succeeded to solve those problems by devising a color embedding technique. By replacing a subband of a luminance component by quantized high-pass and chrominance signals, semi-invariant algorithm for chroma and spatial resolution can be realized. Experimental results show that the proposed method can recover vivid color images with keeping spatial resolution from textured gray images. Introduction Digital images can be classified roughly to 24bit color images and 8bit gray images. We have come to tend to treat colorful images by the development of various kinds of devices. However, there is still much demand to treat color images as gray images from the viewpoint of running cost, data quantity, etc. We can convert a color image into a gray image by linear combination of RGB color elements uniquely. Meanwhile, the inverse problem to find an RGB vector from a luminance value is an ill-posed problem. Therefore, it is impossible theoretically to completely restore a color image from a gray image. For this problem, recently, colorization techniques have been proposed [1][4]. Those methods can re-store a color image from a gray image by giving color hints. However, the color of the restored image strongly depends on the color hints given by a user as an initial condition subjectively. By the way, in 2005, K. Braun and R. L. de Queiroz proposed a sensational method to convert color images to gray images which can be later decoded and converted back to color. The method was based on wavelet transforms and on replacing bandpass subbands by chrominance signals. So, most of the high-frequency components of the luminance signal are lost, and the spatial resolution of the recovered image deteriorates. Furthermore, the gray image converted from the replaced subbands by the inverse wavelet can overflow the 8bit range. This causes a fall of chroma of color recovered image. Figures 1 and 2 show images with color recovery by Ref. [5]. The chroma and spatial resolution decrease. In this paper, we propose a color-to-gray mapping technique which can improve those problems, that is, our method can recover color images from color embedded gray images with having almost kept chroma and spatial resolution of original color images. In order to keep the spatial resolution of the original color image, we store the high-frequency subband signals in the low bit packet by compressing the range of data. In order to keep the chroma, we store the chrominance components in the high bit packet through β-transform which will be proposed in this paper. After describing a basic algorithm in Sec. 2, Sec. 3 presents the proposed algorithms to convert color-to-gray images and to recover color information from the textured gray image. Section 4 presents some experimental results. Finally Sec. 5 makes the conclusions of this paper. (a) Original (b) Gray image (c) Reconstructed image Figure 1 Image "Palette" with color recovery by Ref.[5]