4 Results

To evaluate our new selection method we first looked at performance using synthetic data. To construct the canonical gamut we took a subset of the surface reflectances of the Munsell chips [ 14 ], imaged under the most spectrally uniform of the Judd [ 3 ] daylight phases (D55). For our camera sensors we used three perfectly narrow band sensors: the red sensor was sensitive to light at 610nm (and no other wavelength) and the green and blue sensors were sensitive to 540 and 450nm light respectively. These narrow-band sensors have the advantage that they sample colour signals in a similar manner to the receptors found in the human eye[ 5 ]. Given narrow-band sensors the induced camera response of the k th sensor to a surface with reflectance function under the illuminant is calculated[ 13 ]:

The canonical gamut is then the convex hull of all sensor responses generated for all Munsells. To allow for the fact that in practice chromaticities outside the range of the Munsell chips may occur we expanded the canonical gamut by 10%.

A synthetic image was created by selecting between 1 and 11 surfaces from the set of Munsell chips with the test illuminant being either a yellowish or bluish Planckian black-body radiator[ 14 ] (these illuminants plus the canonical light are representative of typical illuminants). The sensor responses of the camera were calculated according to equation (11) and these values were used as input to the colour in perspective gamut mapping procedure which returned a set of feasible maps. To choose a single mapping from the feasible set we used each of the three selection methods: maximum[ 4 ] and mean[ 2 ] calculated in 2-d perspective and the mean in three dimensions that was discussed in section 3. As a measure of the accuracy of our chosen mapping we calculated the angle between our chosen mapping and the correct answer. Also, to give some idea of the worst case performance of each method we calculated the maximum angle possible between our chosen mapping and all the other mappings in the feasible set. To obtain a stable statistic we generated 500 scenes for each number of surfaces and unknown illuminant. Selection performance for is summarised in Figure 2 .

   
Figure 2: Results using synthetic data, for yellowish and bluish Planckian black-body radiators, are shown top and bottom. Left- and right-hand graphs show actual and worst-case error performances as a function of the number of colours in a scene

The graphs on the left hand side show average angular error against the number of surfaces in the image for each of the three selection methods. The right hand graphs show the worst case error for each of the three methods. In both the average and worst case it is clear that the 3-d mean selection procedure outperforms both the maximum area or 2-d mean selectors. For small numbers of surfaces (between 1 and 5) the 3-d mean estimate does between 100% and 50% better. This level of performance increase offers a clear practical advantages for scenes where the range of colours is small (for example images of forests typically contain shades of only two or three colours). As the number of surfaces are increased the difference in performance narrows. This is to be expected since increasing the number of colours in the image leads to a smaller feasible set.

To test the performance with real data we began by creating a measured canonical gamut. We imaged a Macbeth colour chart under whitish cloudy sky illumination and calculated the convex hull of the rgbs that were induced in a a SONY DXC-930 colour camera (which had linear response). An image of the Macbeth chart is shown in Figure 3 above.

   
Figure 3: The Macbeth Colour Chart

The Macbeth chart was then imaged under blue sky and yellow tungsten lights. For each illuminant we then generated random scenes by selecting between 1 and 11 of the 24 checker patches and used these as input to the gamut mapping algorithm.

Figure 4 shows the results using yellow tungsten, and blue daylight as the unknown illuminant (top and bottom respectively). We again show average (left) and worst case (right) performance for each of the three selection methods. The graphs show the same trend as for the synthetic data. These clearly show that the new selection method produces a significant improvement in performance over either of the two previously used selection methods.

   
Figure 4: Results using real data For unknown illuminants: yellowish tungsten (top), and bluish daylight (bottom).