normalized_cross_correlation.py

__author__ = "Hamideh Kerdegari"
__copyright__ = "Copyright 2023"
__credits__ = ["Hamideh Kerdegari"]
__license__ = "Hamideh Kerdegari"
__maintainer__ = "Hamideh Kerdegari"
__email__ = "hamideh.kerdegari@gmail.com"
__status__ = "R&D"

# This script is used for measuring cross correlation between two images.
import numpy as np
import matplotlib.pyplot as plt
#from aloe.plots import plot_image
from PIL import Image

def norm_dot(img1, img2):
    """
    return normalized dot product of the arrays img1, img2
    """
    # make 1D value lists
    v1 = np.ravel(img1)
    v2 = np.ravel(img2)

    # get the norms of the vectors
    norm1 = np.linalg.norm(v1)
    norm2 = np.linalg.norm(v2)
    #print('norms of NDP vectors: ', norm1, norm2)

    ndot = np.dot( v1/norm1, v2/norm2)
    return ndot

def norm_data(data):
    """
    normalize data to have mean=0 and standard_deviation=1
    """
    mean_data=np.mean(data)
    std_data=np.std(data, ddof=1)
    #return (data-mean_data)/(std_data*np.sqrt(data.size-1))
    return (data-mean_data)/(std_data)

def ncc(data0, data1):
    """
    normalized cross-correlation coefficient between two data sets

    Parameters
    ----------
    data0, data1 :  numpy arrays of same size
    """
    return (1.0/(data0.size-1)) * np.sum(norm_data(data0)*norm_data(data1))

def print_similarity_measures(img1, img2, nc0=None, nd0=None):
    nd = norm_dot(img1, img2)
    nc = ncc(img1, img2)
    print('NCC: ', nc, ' NDP: ', nd)
    if not ((nc0 is None) or (nd0 is None)):
        print('dNCC: ', nc-nc0, ' dNDP: ', nd-nd0)
    return