Marchant and Onyango (J. Opt. Soc. Am. A 17, 1952, 2000) and Finlayson and Hordley (J. Opt. Soc. Am. A 18, 253, 2001) proposed the definition of an invariant parameter that can be applied to each pixel of a colored image in such a way that this image can be changed into a grey-scale one, in which color constancy is obtained with complete precision whenever the illuminant is Planckian-type and the three sensors which capture the image have Dirac's delta spectral sensitivities. In this work we look more closely at one of the points touched upon in the above-mentioned papers, which still needs to be studied in more detail: the optimal position of their spectral sensitivity maximums when we have real daylight illumination. We used an exhaustive search method, finding the best behaviour for the sets of spectral maximums: (645, 675 and 595 nm) and (550, 610 and 400 nm). Next, we extend our study to more realistic sensors considering for them a gaussian-type spectral sensitivity with 30nm half-bandwidth and maximum sensitivity at the wavelength of the two above mentioned triads. We compared the results obtained with these sensors with those obtained for real sensors, like commercial CCD cameras sensors. The performance of our sensors improves that obtained for the rest of sensors, also those employed by other authors. We have applied these results to natural scenes with the aim of classifying different kinds of vegetation.