AbstractThe monochromatic static image can be represented as a scalar‐valued functionf(u,v), for the brightness or density at point (u,v) on the two‐dimensional coordinate space T. For the color image, the image is represented by a vector‐valued function composed of such signal components as red, green, blue or luminance, chrominance and saturation. The sampling of an image can be considered as derivation of a sequence {fi} of spatially discrete sampled values by dividing the coordinate space T. Denoting the partitioning of the coordinate space by {Si}, the sampled valuefiis a scalar or vector value, which is determined uniquely by the subimage {f(u,v) |(u,v) ϵSi}.This paper proposes a new variable rate sampling method which partitions the multidimensional coordinate space efficiently based on the vector quantization method. A high‐speed region partitioning algorithm is also shown which is based on the successive approximation vector quantization. The usefulness of the proposed method is demonstrated by simulation. Using those results, the sampling process is reformulated as the vector quantization in the coordinate space. Thus, a new development is made for the variable rate samplin