1. An image processing apparatus, comprising: transformation means for transforming data space of an input image to multi-resolution space and outputting a multi-resolution representation of the input image; detecting means for detecting a singularity in the input image; extracting means for extracting a local pattern, which is formed by a spatial arrangement of intensities of the multi-resolution representation in a partial area containing the detected singularity, with regard to partial areas of a plurality of sizes; quantizing means for creating a quantization code book based upon the extracted local pattern and replacing said multi-resolution representation by a code word using the code book; and encoding means for algebraic encoding code data which includes position coordinates of the singularity in said multi-resolution representation and the code word provided by said quantizing means.