Enhancement of Curve-Fitting Image Compression Using Hyperbolic Function

Abstract

Image compression is one of the most interesting fields of image processing that is used to reduce image size. 2D curve-fitting is a method that converts the image data (pixel values) to a set of mathematical equations that are used to represent the image. These equations have a fixed form with a few coefficients estimated from the image which has been divided into several blocks. Since the number of coefficients is lower than the original block pixel size, it can be used as a tool for image compression. In this paper, a new curve-fitting model has been proposed to be derived from the symmetric function (hyperbolic tangent) with only three coefficients. The main disadvantages of previous approaches were the additional errors and degradation of edges of the reconstructed image, as well as the blocking effect. To overcome this deficiency, it is proposed that this symmetric hyperbolic tangent (tanh) function be used instead of the classical 1st- and 2nd-order curve-fitting functions which are asymmetric for reformulating the blocks of the image. Depending on the symmetric property of hyperbolic tangent function, this will reduce the reconstruction error and improve fine details and texture of the reconstructed image. The results of this work have been tested and compared with 1st-order curve-fitting, and standard image compression (JPEG) methods. The main advantages of the proposed approach are: strengthening the edges of the image, removing the blocking effect, improving the Structural SIMilarity (SSIM) index, and increasing the Peak Signal-to-Noise Ratio (PSNR) up to 20 dB. Simulation results show that the proposed method has a significant improvement on the objective and subjective quality of the reconstructed image.