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All-sky imaging systems are currently very popular. They are used in ground-based meteorological stations and as a crucial part of the weather monitors for autonomous robotic telescopes. Data from all-sky imaging cameras provide important information for controlling meteorological stations and telescopes, and they have specific characteristics different from widely-used imaging systems. A particularly promising and useful application of all-sky cameras is for remote sensing of cloud cover. Post-processing of the image data obtained from all-sky imaging cameras for automatic cloud detection and for cloud classification is a very demanding task. Accurate and rapid cloud detection can provide a good way to forecast weather events such as torrential rainfalls. However, the algorithms that are used must be specifically calibrated on data from the all-sky camera in order to set up an automatic cloud detection system. This paper presents an assessment of a modified k-means++ color-based segmentation algorithm specifically adjusted to the WILLIAM (WIde-field aLL-sky Image Analyzing Monitoring system) ground-based remote all-sky imaging system for cloud detection. The segmentation method is assessed in two different color-spaces (L*a*b and XYZ). Moreover, the proposed algorithm is tested on our public WMD database (WILLIAM Meteo Database) of annotated all-sky image data, which was created specifically for testing purposes. The WMD database is available for public use. In this paper, we present a comparison of selected color-spaces and assess their suitability for the cloud color segmentation based on all-sky images. In addition, we investigate the distribution of the segmented cloud phenomena present on the all-sky images based on the color-spaces channels. In the last part of this work, we propose and discuss the possible exploitation of the color-based k-means++ segmentation method as a preprocessing step towards cloud classification in all-sky images. Full article