Lossy and Lossless Image Compression using Legendre Polynomials

Today is the digital era and the human being is surrounded by digital gadgets. Now a days, photography is a part of human being's daily life and digital images are widely used in computer applications. As the megapixels of the digital cameras are increasing, more storage memory is required and at the same time more bandwidth is needed for transmission of digital images. This results in need of image compression. This paper explains the use of Legendre polynomials for lossy and lossless image compression. Different approximations for image transformation have been evaluated as 1-D Legendre polynomials, 1-D adaptive Legendre polynomials, 2-D Legendre polynomials and 2-D adaptive Legendre polynomials. Moreover, the performance of different image scanning methods have been tested. Results have been compared in terms of peak signal-to-noise ratio (PSNR), nominal compression rate (NCR), mean structural similarity (MSSIM) and compression ratio in order to minimize the difference between the approximated polynomial output and the original pixel gray level.