def compute_variance_grayscale(self, clusters, centroids, gImage, k):
    # compute variance
    variance = 0

    for i in range(len(clusters)): #iterate over the available clusters
        cluster = clusters[i]
        sum = 0;
        centroid = centroids[i]
        for j in cluster: #for each data point in cluster j compute the sum
            sum += (gImage.getImageValueAt(j[0], j[1]) - centroid) ** 2

        variance += sum / (len(cluster) - k); #add the sum to the given variance

    return variance

        def compute_variance_rgb(self, clusters, centroids, cImage, k):
    # compute variance
    variance = 0
    for i in range(len(clusters)):
        cluster = clusters[i]
        sum = 0;
        centroid = centroids[i]
        for j in cluster:
            b,g,r = cImage.getImageValueAt(j[0], j[1])
            b_e = (b - centroid[0]) ** 2
            g_e = (g - centroid[1]) ** 2
            r_e = (r - centroid[2]) ** 2

            sum += (b_e + g_e + r_e)

        variance += sum / (len(cluster) - k);

    return variance

np.sum([n[i] * np.log(n[i]) -
               n[i] * np.log(N) -
             ((n[i] * d) / 2) * np.log(2*np.pi*cl_var) -
             ((n[i] - 1) * d/ 2) for i in range(m)]) - const_term