In the QBIC project in particular efficient methods for retrieving images based on their colour content were developed. The method involved the construction of lower bounds on colour histogram distance measures for efficiency reasons. To this end a semi-positivity condition had to be imposed. In this note we prove a conjecture concerning this condition. Moreover we exhibit a more general construction for a suitable class of distance measures and establish a connection to certain abstract results on positive definite kernels. (orig.)SIGLEAvailable from TIB Hannover: RR 8166(95-06) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBayerische Forschungsstiftung, Muenchen (Germany)DEGerman