Efficient transform using canonical signed digit in reversible color transforms

Color transforms are important methods in the analysis and processing of images. Image color transform and its inverse transform should be reversible for lossless image processing applications. However, color conversions are not reversible due to finite precision of the conversion coefficients. To overcome this limitation, reversible color transforms have been developed. Color integer transform requires multiplications of coefficients, which are implemented with shift and add operations in most cases. We propose to use canonical signed digit (CSD) representation of reversible color transform coefficients and exploitation of their common subexpressions to reduce the complexity of the hardware implementation significantly. We demonstrate roughly 50% reduction in computation with the proposed method.