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.
Highlights
Image processing has been considered to be one of the most important applications of computer engineering in recent decades
During the last two decades, image compression methods in the spatial domain have been developed using 2D curve-fitting, which essentially transforms the image from random values to simple mathematical equations [2]. 2D curve-fitting depends on dividing the image into blocks of pixels, which are converted into a set of equations
Optimum edge detection of the image can be considered to be an important factor for defining subjective image quality, ; in this manuscript, edge detection test will be considered as another measurement for image compression quality
Summary
Image processing has been considered to be one of the most important applications of computer engineering in recent decades. 2D curve-fitting depends on dividing the image into blocks of pixels, which are converted into a set of equations It can reduce the size of the storage space and save only a few coefficients of the equation that represent the blocks of image. Liu and Peng proposed a rotating mapping curve-fitting algorithm for image compression; this method depends on the correlation of the DC component and the rotation angle between adjacent blocks. This paper aims to improve the results that depend only on curve-fitting approach without applying any smoothing filter [23], segmentation algorithms [14], defining some polygon vertices [11,12,13], or without applying coding technique to the parameters [12,21,22] It uses a non-linear function which is more flexible than previous proposed curve-fitting or interpolation functions, which incorporates better edge and texture description. These four corners were used in the decoder to find the coefficients of (dxy + ax + by + c) [25,28]
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