Compression of Image Block Means for Non-equal Size Partition Schemes Using Delaunay Triangulation and Prediction

An approach based on applying Delaunay triangulation to compression of mean values of image blocks that have non-identical shape and size is proposed. It can be useful for image compression methods that require the use of image partition schemes with non-equal block size like fractal and DCT-based image coding. The data about block mean values occupy a rather considerable part of total data saved for each block coding. For example, in fractal image compression this part requires about 30-35% of the total size of the coded image file. For DCT based coding the percentage is a little bit smaller, but, nevertheless, it is rather large for getting noticeable improvement of compression ratio in case of more efficient coding of block mean values. In case of identical image blocks (like for JPEG) the block mean value coding is a trivial task. However, for non-identical blocks, i.e. the blocks that do not have equal size and/or are characterized by various shapes, the task of block mean value compression becomes complicated. Several methods of block mean value coding are considered. In particular, the drawbacks of using quantization with further redundancy elimination by entropy coders are discussed. Another considered method is the forming of the block mean value image and its further compression by lossy coders. Finally, the motivations in favor of Delaunay triangulation application to block mean value image coding are presented. The proposed compression method based on Delaunay triangulation consists of the three basic stages. At the first stage, the coordinates of apexes that coincide with block centers in partition scheme are determined. The order of their adding to triangulation is also discussed. It is demonstrated that pseudo-random order of apex adding produces appropriately good results and is rather simple. At the second stage just the Delaunay triangulation and error prediction are carried out. At the third stage, the prediction errors are quantized, compressed by entropy coder and saved together with other data for the compressed image. The peculiarities of image decoding procedure are discussed and the corresponding block schemes are presented. For several test images the analysis of the proposed method is carried out and its performance is compared to some conventional methods. An improvement of image block mean compression due to application of Delaunay triangulation and prediction is demonstrated. Numerical simulation data confirming the fact of more effective coding the block mean values for different partition schemes are given.