Automatic determination of number of clusters in K-means for colored image segmentation using PCA eigen vectors and weighted color channel variance

Determining the optimal number of clusters in k-means-based color image segmentation remains a fundamental challenge in color image segmentation, where segmentation quality is highly sensitive to the choice of K and centroid initialization. Existing techniques often rely on heuristic thresholds, domain-specific assumptions, or computationally heavy procedures. This paper presents a data-driven and computationally lightweight method that automatically estimates K by analyzing the variance structure of color channels through Principal Component Analysis (PCA). The method computes the significant principal components across the color channels in the RGB, HSV and Lab spaces and applies eigenvalue-based weighting to obtain a robust estimate of K , which is then supplied directly to standard k-means. Evaluation on the BSDS500 dataset demonstrates that the proposed PCA-derived cluster estimation produces segmentation results that are consistent with human annotations while remaining computationally efficient. RGB and HSV achieved the highest precision, whereas the Lab color space produced the strongest recall and F-measure. These findings indicate that the proposed framework provides a threshold-free and computationally lightweight approach for automatically estimating the number of color clusters for K-means image segmentation on the evaluated BSDS500 dataset.