Hard versus fuzzy c-means clustering for color quantization

Color quantization is an important operation with many applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms. Recent studies have demonstrated the effectiveness of hard c-means (k-means) clustering algorithm in this domain. Other studies reported similar findings pertaining to the fuzzy c-means algorithm. Interestingly, none of these studies directly compared the two types of c-means algorithms. In this study, we implement fast and exact variants of the hard and fuzzy c-means algorithms with several initialization schemes and then compare the resulting quantizers on a diverse set of images. The results demonstrate that fuzzy c-means is significantly slower than hard c-means, and that with respect to output quality, the former algorithm is neither objectively nor subjectively superior to the latter.