1. A multidimensional image compression and decompression system having a compression device which codes image data at least including a two-dimensional static image for transmission, and a decompression device which reproduces image data by decoding a coded image signal transmitted from said compression device: comprising luminance decision means provided at said compression device, for deciding how luminance data included in said image data is distributed in at least two dimensions on the basis of a reference value; address generation means provided at said compression device, for generating position data after determining at least two-dimensional positions of distribution of said luminance data determined by said luminance decision means; characteristic point decision means provided at said compression device, for determining a plurality of characteristic points which are local maximum points in a curvature of an equal luminance line of a luminance function at least in said two-dimensional static image on the basis of said luminance data decided by said luminance decision means, and said position data generated by said address generation means with respect to said at least two-dimensional static image; and luminance data decision means provided at said decompression device, for deciding luminance data of pixels except pixels corresponding to said characteristic points by using interpolational data which includes at least a plane for interpolation, which is determined by several adjacent points in said plurality of characteristic points in at least said two-dimensional static image reproduced by image data supplied from said compression device, thereby forming a multidimensional reproduced image using both said luminance data of said characteristic points and said luminance data of said pixels except said pixels corresponding to said characteristic points.