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The aim of image compression is to reduce the required bytes efficiently that effectively affected the stored and/or communicated data, based on exploiting the redundancy(s). The techniques classified according either the redundancy removal that impels the lossless and lossy scheme or the way of removing redundancy that impels spatial, transform and hybrid coding. Images are over-burdened with redundancies, where for grayscale images the spatial (interpixel) redundancy embedded between image pixels, while for color images the spectral redundancy between color bands and along the band itself of spatial redundancy base, in addition to coding and psycho-visual redundancies that existed in both types. Today, various acceptable standard image compression techniques available, such as the graphics interchange format (GIF), joint photographic experts group (JPEG), or JPG2 (JPEG-2000), with always need to new compression schemes of high performance. Polynomial coding of the spatial efficient modern image compression techniques still under development where the core involves predictions and differentiation (residual) of modelling base, this paper reviews the main efforts related to compress grayscale and color images using the polynomial coding techniques. [ABSTRACT FROM AUTHOR]