As the number of spectral channels significantly affects the system complexity, data load, time resolution, and spatial resolution of images, a multispectral color imaging system that aims to accurately reproduce the visible spectrum reflectance of object surfaces is preferred using a limited number of spectral channels. However, seldom literature has been explained statistically for the determination of numbers of spectral channels. The heuristic or even arbitrary number of spectral channel configurations challenges the purpose of multispectral color imaging for accurate spectral reconstruction and color reproduction. It is even more crucial with the emergence of various modalities of color imaging sensors, such as those of with liquid crystal tunable filters (LCTFs) and multispectral filter arrays (MSFAs) and recently developed nanostructure color filters. Previous evidence shows that the spectral transmittance of the optimal filter set for multispectral color cameras is Gaussian curves. We build upon the previously proposed multi-objective optimization method for filter selection with specific channels and systematically explore the way to determine the optimal number of spectral channels for typical multispectral color imaging systems with filters modeled by Gaussian functions.

The workflow for optimizing the number of spectral channels in the multispectral color imaging system studied in this research is illustrated in Fig. 1. Firstly, we provide a systematic theoretical presentation of the spectral sensitivity optimization by filter selection for the broadband multispectral imaging and the method for the channel numbers optimization, which could scarcely be found in the literature published so far to the best of our knowledge. The highlight of the proposed method is built upon the previously proposed multi-objective optimization method for filter selection, and we systematically explore the way to determine the optimal number of spectral channels for typical multispectral color imaging systems. Then, we investigate the optimal number of channels experimentally. Using the Munsell spectral reflectance dataset to construct the spectral imaging targets, imaging simulations and reflectance reconstruction under 10 noise levels are conducted by the spectral sensitivity of an actual CCD image sensor, the spectral distribution of the D65 illuminate, and the transmittance curves of the filters generated by Gaussian filter model. it involves 29 virtual multispectral cameras, or in other words, the channel numbers are 3-31, respectively.

1) Determination of the optimal number of channels. The optimal filters' serial numbers and the corresponding accumulative scores under different channel numbers are presented in Table 1. Figure 3 illustrates the concentration index of multi-objective functions (CMFs) under different channel numbers. Moreover, Fig. 4 depicts the performance of the best filter sets in terms of CIEDE2000 and MSE, respectively, under different channel numbers. Additionally, Fig. 5 displays the accumulative scores of the best filter sets' performance within the 29 numbers of channels.

2) Characterization of the filter set with the optimal channel number. The optimal number of channels for a multispectral color imaging system is 5 (Fig. 6) when the maximum number of channels is not greater than 8. Figure 7 presents the transmittance curves of the optimal Gaussian filter sets with five and nine channels, respectively. Table 3 presents the characteristics of the optimal Gaussian filter sets with five channels under two different illuminates. Table 4 compares the performance indices of the optimal Gaussian filter sets with five channels under different illuminates.

From the results, the following six items could be concluded: 1) For broadband multispectral color imaging, increasing the number of channels does not always lead to an improvement in spectral reconstruction accuracy. It is observed that a smaller number of spectral channels has the potential to simultaneously satisfy the requirements of color difference reproduction and spectral reconstruction error accuracy; 2) By employing the multi-objective optimization method within the optimal filter range for each channel, that is to say, extending the concept of CMF, a unique optimal number of channels can be obtained; 3) In general, a higher noise level (i. e., a lower signal-to-noise ratio) often indicates worse performance indicators, but the specific performance indicators may exhibit varying nonlinear characteristics with the noise; 4) CIEDE2000 is more sensitive to noise when compared to the relevant indicators, MSE and PSNR, as indicated in Fig. 7, and the latter two are more discrete; 5) Based on the principles of multi-objective optimization in this study, the optimal number of spectral channels for Gaussian filters with less than eight channels is 5 under the illuminant D65. Moreover, compared with illuminant A, D65 enhances the performance of the Gaussian filters with five channels in terms of spectral reconstruction and color reproduction; 6) Optimal filters with the same number of channels may differ under different spectral distribution light sources. Differences can be observed in terms of the geometric characteristics of transmittance curves, primarily the varying bandwidths. Furthermore, significant differences can be observed in performance, including color reproduction and spectral reconstruction.

Briefly, the spectral transmittance of the optimal color filter set can be described by a series of Gaussian curves, and the number of spectral channels significantly impacts its performance and complexity. We systematically explore the way to determine the optimal number of spectral channels for typical multispectral color imaging systems. It would be of great theoretical and practical significance to model the spectral channel of color imaging systems with different physical modalities as Gaussian spectral channels and then explore the necessary color filter channels to optimize multi-spectral color imaging systems.