A Hierarchical vector Quantization scheme is implemented and an optimal thresholding technique of quadtree segmentation for performing high quality low bit rate image compression is proposes. A mathematical model is constructed under the assumption that the standard deviations of sub-blocks are larger than or equal to the standard deviation of the upper level block which is generated by merging of sub-blocks. This thresholding technique based on the mathematical modeling allows producing about 1 dB improved performance in terms of PSNR at most ranges of bit rates over the quadtree coder, which is based on MSE for quadtree segmentation.