Lossy Compression Using Adaptive Polynomial Image Encoding

In this paper, an efficient lossy compression approach using adaptive-block polynomial curve-fitting encoding is proposed. The main idea of polynomial curve fitting is to reduce the number of data elements in an image block to a few coefficients. The proposed approach consists of two processes: encoding and decoding. In the encoding process, the coefficient matrix is created by representing each block of the image with a first- or second-order two-dimensional polynomial. The encoded block size of the image is variable. The polynomial order and the encoded block size are determined dynamically depending on the value of a threshold. A prefix code of two bits is used to differentiate the encoding states. Uniform quantization is applied to the coefficient matrix to store these coefficients effectively. In the decoding process, the reconstructed (decompressed) image is built from the quantized coefficient matrix. The fitting variables are two-dimensional (x, y). The encoding and decoding processes require a single image scan without the need to transfer the matrix to another domain. Experimentally, a high compression ratio is achieved at an acceptable quality for both gray and color images. The results are comparable to those of most recent studies.