Calculate mean and var values for all images in the folder by combining mean and var of individual images

running_block_mean_and_std

# variance calculation algorithm for two datasets of different lengths is taken from
# Chan, Tony F.; Golub, Gene H.; LeVeque, Randall J. (1979), "Updating Formulae and a Pairwise Algorithm for Computing Sample Variances." (PDF), Technical Report STAN-CS-79-773, Department of Computer Science, Stanford University.
# http://i.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf
import os, sys
import numpy as np
import tifffile as tiff # pip install tifffile

TIF_FOLDER = 'img'
EXT = '.tiff'


def load_tiff(filename):
    image = tiff.imread(filename)
    imin, imax, imean, imed, istd, n = np.min(image), np.max(image), np.mean(image), np.median(image), np.std(image), image.size
    return imin, imax, imean, imed, istd, n

def calculate_block_mean_and_var(MEANS,VARS,NS):
    TS = np.multiply(MEANS,NS)
    SS = np.multiply(VARS,NS)
    TA = TS[0]
    NA = NS[0]
    SA = SS[0]
    for i in range(1,len(SS),1):
        NB  = NS[i]
        TB  = TS[i]
        SB  = SS[i]
        TAB = TA + TB
        SAB = SA + SB + NA/(NB*(NA+NB)) * (NB/NA*TA-TB)**2
        NA  = NA + NB
        TA  = TAB
        SA  = SAB
    MAB = TAB/np.sum(NS)
    VAB = SAB/np.sum(NS)
    return MAB,VAB

FLIST = []
for root, folders, files in os.walk(TIF_FOLDER):
    for f in files:
        if(f.endswith(EXT)):
            FLIST.append(f)

# flattened true version
FL = np.array([],dtype=np.float64)
FL_SIZE = 0
IMGS = []
for f in FLIST:
#    print(f)
    img = tiff.imread(os.path.join(TIF_FOLDER,f))
    IMGS.append(img)
    fl  = img.flatten().astype(np.float64)
    FL_SIZE += fl.size
    FL  = np.concatenate([FL,fl])

MA_TRUE = np.mean(FL)
VA_TRUE = np.var(FL)
print('TRUE MEAN = {}'.format(MA_TRUE))
print('TRUE VAR  = {}'.format(VA_TRUE))

NS     = []
IMEANS = []
IVARS  = []  

for img in IMGS:
    imean, ivar, n =  np.mean(img), np.var(img), img.size
    NS.append(n)
    IMEANS.append(imean)
    IVARS.append(ivar)

MAB,VAB = calculate_block_mean_and_var(IMEANS,IVARS,NS)

print('BLOCK MEAN = {} delta = {}'.format(MAB,MAB-MA_TRUE))
print('BLOCK VAR  = {} delta = {}'.format(VAB,VAB-VA_TRUE))    

print('WRONG MEAN = {}'.format(np.mean(IMEANS)))
print('WRONG VAR  = {}'.format(np.mean(IVARS)))