Abstract: Concerning the poor matching performance of two-dimensional gray-scale transformation in Fisher classification algorithm, an improved space mapping gray-scale transformation method was proposed. It put position and brightness into the gray-scale transformation at the same time, and formatted linear mapping between three-dimensional curved surfaces. The method quantified the scaling coefficient firstly, then calculated and quantified the other coefficients of improved gray-scale transformation to improve the possibility of successful range-domain matching. The experimental results show that this method reduces the number of coding blocks, improves the compression ratio and shortens the encoding time, while the quality of decoded image does not get much influenced.

Key words: fractal image compression, Fisher classification, gray-scale transformation, inner product space mapping, scaling coefficient, quadtree partition

摘要： 针对Fisher分类分形图像压缩算法中二维灰度变换匹配性能较差的问题，提出了改进的空间映射灰度变换方法。该方法将位置与亮度同时纳入到灰度变换中，形成三维空间上曲面模式之间的线性映射，并预先量化空间映射压缩因子，再计算和量化空间映射灰度变换的其他系数，提高range块和domain块成功匹配的可能性。实验证明，该方法在不降低重构图像质量的前提下，减少了编码块数，提高了图像的压缩比，大幅缩短了编码时间。

关键词: 分形图像压缩, Fisher分类, 灰度变换, 内积空间映射, 压缩因子, 四叉树分割