A similarity measure is developed for comparing labelled images. The proposed measure is calculated based on binary relations of arbitrary pixels in the labelled images. Hence, the proposed measure can evaluate the difference between two images speedy by pixel-to-pixel calculation. The measure can be used for not only spatial labelled images by area-based labelling such as region segmentation, but also colour labelled images by pixel-based labelling such as colour clustering. A few actual applications are shown in order to explain the behaviour.