Qualitative Image Compression Algorithm Relying on Quadtree

Abstract This paper presents an image compression algorithm that has the ability to divide the original grey level image into unoverlapped blocks depending on a threshold value. The proposed algorithm is based on quadtree. It can compress and decompress the image in easy way using two stacks instead of tree. In the compression process, the proposed technique stores the information of all blocks, for instance the upper left coordinate, size, minimum, and difference values in a stack, and the divided blocks are numbered in effective way. This information will be used to decompress the image again. It was found that the algorithm provides a high compression ratio ranged between 0.12 and 0.68. Keywords: quadtree, image compression, image processing . 1. Introduction A compression algorithm finds redundancy in data and removes detail too minute to be detected by the human eye. For example, in an uncompressed image file, a shade slightly different, unnoticeable by the human eye, is numerically significant, and extra storage is allocated for this unnoticeable feature [1]. The internet, digital library, multimedia publishing service, geographical information system, computer-aided design and medical image archiving systems, image processing are widely used. However, since image data takes enormous storage space, how to store and retrieve an image, both economically and effectively, has a high priority in current research efforts [2]. Therefore, the necessity of efficient data compression is increasing. A compression algorithm finds redundancy in data and removes detail too minute to be detected by the human eye. For example, in an uncompressed image file, a shade slightly different, unnoticeable by the human eye, is numerically significant, and extra storage is allocated for this unnoticeable feature [1]. Data compression provides two advantages: reducing storage space and transmission time by finding the humanly imperceptible differences [3]. Data-compression techniques may be applied to digital image data. Compressed files are stored more efficiently and transmitted more quickly. The degree of data compaction is expressed as the compression ratio; that is, a ratio of the original digital file size to the new compressed file size. Many techniques for data compression have been developed. For any individual compression technique applied to a given image, a fixed compression ratio may be achieved without loss of data (lossless compression). Higher compression ratios may be obtained when data loss is permitted (lossy compression). Greater levels of lossy compression generally imply inferior image quality. A major advantage of the quadtree technique for data compression is the simplicity of its approach. Unlike many other compression techniques, a quadtnee algorithm can compress images relatively quickly on a personal computer. We were particularly interested in the potential identification of a threshold compression ratio at which there would be no significant loss of diagnostic accuracy [4]. The most widely used multimedia data are two-dimensional images; hence we focus on these data. There are many compression techniques in use today; these techniques include those that use mathematical transforms such as Discrete Cosine Transform (DCT) transform [5-8], wavelet transform [9-12], fractal [13-16], and quadtree techniques [17-19]. Most of the aforementioned techniques tend to be mathematically complex, except for the quadtree algorithm. The quadtrees are powerful and simple data structures for representing compressing digital images. It is possible to find applications of quadtree decomposition in many different contexts, such as the compression of sub-band coefficients in wavelet decomposition and coding of the sub-blocks data in EBCOT algorithm. The quadtree decomposition is an important tool for fractal image compression where many suitable smart variants of quadtrees are used and applied [20]. The quadtree algorithms are based on simple averages and comparisons. A quadtree is a tree-like data structure where each node either terminates on a leaf containing useful information, or branches into four sub-level quadtrees [21].