A generalized clustering algorithm utilizing the geometrical shapes of clusters for segmentation of colored brain immunohistological images is presented. To simplify the computation, the dimension of vectors composed from the pixel RGB components is reduced from three to two by applying a de-correlation mapping with the orthogonal bases of the eigenvectors of the auto-covariance matrix. Since the brain immunohistochemical images have stretched clusters that appear long and narrow in geometrical shape, we use centroids of straight lines instead of single points to approximate the clusters. An iterative algorithm is developed to optimize the linear centroids by minimizing the approximation mean-squared error. The partitioning of the two-dimensional vector domain into three portions classifies each image pixel into one of the three classes: The microglial cell cytoplasm, the combined hematoxylin stained cell nuclei and the neuropil, and the pale background. Regions of the combined hematoxylin stained cell nuclei and the neuropil are to be separated based on the differences in their regional shapes. The segmentation results of real immunohistochemical images of brain microglia are provided and discussed.