Lossless compression of medical images using Hilbert space-filling curves

A Hilbert space-filling curve is a curve traversing the 2(n) x 2(n)two-dimensional space and it visits neighboring points consecutively without crossing itself. The application of Hilbert space-filling curves in image processing is to rearrange image pixels in order to enhance pixel locality. A computer program of the Hilbert space-filling curve ordering generated from a tensor product formula is used to rearrange pixels of medical images. We implement four lossless encoding schemes, run-length encoding, LZ77 coding, LZW coding, and Huffman coding, along with the Hilbert space-filling curve ordering. Combination of these encoding schemes are also implemented to study the effectiveness of various compression methods. In addition, differential encoding is employed to medical images to study different format of image representation to the above encoding schemes. In the paper, we report the testing results of compression ratio and performance evaluation. The experiments show that the pre-processing operation of differential encoding followed by the Hilbert space-filling curve ordering and the compression method of LZW coding followed by Huffman coding will give the best compression result.