Segmentation is the act of partitioning an image into different regions by creating boundaries between regions. $k$-means image segmentation is the simplest prevalent approach. However, the segmentation quality is contingent on the initial parameters (the cluster centers and their number). In this paper, a convolution-based modified adaptive $k$-means (MAKM) approach is proposed and evaluated using images collected from different sources (MATLAB, Berkeley image database, VOC2012, BGH, MIAS, and MRI).The evaluation shows that the proposed algorithm is superior to $k$-means++, fuzzy $c$-means, histogram-based $k$-means, and subtractive $k$-means algorithms in terms of image segmentation quality ( $Q$-value), computational cost, and RMSE. The proposed algorithm was also compared to state-of-the-art learning-based methods in terms of IoU and MIoU; it achieved a higher MIoU value.