Image Compression Based on Low-Pass Wavelet Transform and Multi-Scale Edge Compensation, Part I: MSEC Model

Xiaohui Xue Dept. of Computer Science, Harbin Institute of Technology, Harbin, Heilongjiang, P.R.China [email protected] The mainstream of image compression research has been based on the Shannon Information Theory for years. In image data, there exist statistical redundancy, knowledge redundancy and psychophysiological redundancy, and the latter two cannot be handled by Shannon theory. This paper presents the idea of multi-scale edge compensation, and puts forward the image compression method (MSEC) based on low-pass wavelet transform and multi-scale edge compensation, where low-pass wavelet transform is put forward to perform multi-scale transformation. MSEC attempts to give up the traditional compression framework based on statistics and establish a new scheme by taking a further step in the direction of using more knowledge redundancy and psychophysiological redundancy besides statistical redundancy. The idea is to decompose the image into the sum of roof edges and step edges at consecutively increasing scales and the final smooth background. Under certain conditions, the representation is orthogonal and thus extremely efficient. The encoder performs edge detection, edge compensation at every scale from fine to coarse, outputs the model information and the final background. The decoder synthesizes the image according to the recorded information of the multi-scale edge model and the background. Experimental results are considerably encouraging. For bits 24 512 512 × × Lena, when compressed by 159 times, the PSNR values for Y, U and V components are 28.2dB, 34.6dB and 34.5dB respectively. For a large class of images, compression as high as about 500 times is achieved, and the image quality remains acceptable. As a matter of fact, the performance of current MSEC system can be greatly improved in the future since MSEC technique involves many aspects of image processing including both image analysis and realistic image generation. Besides, we think the idea of multiscale edge compensation (MSEC) as interesting in much broader areas of computer vision apart from compression. The theory of MSEC model consists of two components. One is the models and processing methods for edges of MSEC. Scalability and recognition ability of edge detection are essential to MSEC. MSEC recognizes and processes two different kinds of edges: roof edge and step edge. The scalability of edge is associated with the algebraic precision of low-pass wavelet. The compensation models of edge profile and edge shape are also new concepts of MSEC. The other is the low-pass wavelet transform of MSEC, which studies the properties of low-pass wavelet transform in detail and explains why we use low-pass wavelet as our tool of muti-scale transform. The concept of algebraic precision of low-pass wavelet transform is crucial. Frequency response of low-pass wavelet is also inspected.