A method and apparatus for perfectly lossless and minimal-loss interconversion of digital color data between spectral color spaces (RGB) and perceptually based luma-chroma color spaces (Y′CBCR) is disclosed. In particular, the present invention provides a process for converting digital pixels from R′G′B′ space to Y′CBCR space and back, or from Y′CBCR space to R′G′B′ space and back, with zero error, or, in constant-precision implementations, with guaranteed minimal error. This invention permits digital video editing and image editing systems to repeatedly interconvert between color spaces without accumulating errors. In image codecs, this invention can improve the quality of lossy image compressors independently of their core algorithms, and enables lossless image compressors to operate in a different color space than the source data without thereby becoming lossy. The present invention uses fixed-point arithmetic with signed and unsigned rounding normalization at key points in the process to maintain reversibility.