HSI (hue, saturation, intensity) color space is widespread used in image processing community. H, S and I components corresponds the way human perceives color and they make possible to separate chromatic (hue and saturation) and achromatic (intensity) information. Cylindrical distance is measure of color difference that takes into account angular differences and it is suitable for color spaces defined in cylindrical coordinate system ( HSI, HSV etc.). Because of hue and saturation instability computation of this distance requires discrimination of chromatic and achromatic pixels. For this purpose discrete model based on threshold is used for cylindrical distance. In this paper we propose new modified cylindrical distance that uses continuous model instead of discrete model for differencing chromatic and achromatic pixels. In continuous model we define transition functions that determines importance (weight) of hue and saturation component, which better model gradual transition from scotopic to photopic vision. Proposed formulation is compared with original formulation of cylindrical distance using human judgment of color difference. Results show that proposed formulation better corresponds to human perception for colors on transition between achromatic and chromatic area.