Added mutual information matcher and tests

import numpy as np

def mi(t1, t2, **kwargs):

    """

    Computes the correlation coefficient between two images using a histogram

    comparison (Mutual information for joint histograms). The result coefficient

    will be between 0 and 4

    Parameters

    ----------

    t1 : ndarray

         First image to use in the histogram comparison

    t2 : ndarray

         Second image to use in the histogram comparison

    Returns

    -------

    : float

      Correlation coefficient computed between the two images being compared

      between 0 and 4

    """

    hgram, x_edges, y_edges = np.histogram2d(t1.ravel(),t2.ravel(), **kwargs)

    # Convert bins counts to probability values

    pxy = hgram / float(np.sum(hgram))

    px = np.sum(pxy, axis=1) # marginal for x over y

    py = np.sum(pxy, axis=0) # marginal for y over x

    px_py = px[:, None] * py[None, :] # Broadcast to multiply marginals

    # Now we can do the calculation using the pxy, px_py 2D arrays

    nzs = pxy > 0 # Only non-zero pxy values contribute to the sum

    return np.sum(pxy[nzs] * np.log(pxy[nzs] / px_py[nzs]))

def mutual_information(d_template, s_image, bins=100, func=mi):

    """

    Applys the mutual information matcher function over a search image using a

    defined template. Where the search area is 2x the size of the template image

    Parameters

    ----------

    template : ndarray

               The input search template used to 'query' the destination

               image

    image : ndarray

            The image or sub-image to be searched

    bins : int

           Number of bins to use when computing the histograms

    Returns

    -------

    x : float

        The x offset

    y : float

        The y offset

    max_corr : float

               The strength of the correlation in the range [-1, 1].

    corr_map : ndarray

               Map of corrilation coefficients when comparing the template to

               locations within the search area

    """

    image_size = s_image.shape

    template_size = d_template.shape

    y_diff = abs(template_size[0] - image_size[0])

    x_diff = abs(template_size[1] - image_size[1])

    max_corr = -np.inf

    corr_map = np.zeros((y_diff+1, x_diff+1))

    max_i = -1  # y

    max_j = -1  # x

    for i in range(y_diff+1):

        for j in range(x_diff+1):

            sub_image = s_image[i:i+template_size[1],  # y

                                j:j+template_size[0]]  # x

            corr = func(sub_image, d_template, bins=bins)

            if corr > max_corr:

                max_corr = corr

                max_i = i

                max_j = j

            corr_map[i, j] = corr

    # This is still operating at the pixel scale. Use the template_match_autoreg

    # logic to achieve submpixel weighting.

    x_offset = max_j - (template_size[1]/2)

    y_offset = max_i - (template_size[0]/2)

    return x_offset, y_offset, max_corr, corr_map

import math

import os

import sys

import unittest

from unittest.mock import patch

import pytest

import numpy as np

from .. import mutual_information

def test_good_mi():

    test_image1 = np.array([[i for i in range(50)] for j in range(50)])

    # test_image2 = np.ones((50, 50))

    corrilation = mutual_information.mi(test_image1, test_image1)

    assert corrilation == 2.3025850929940455

def test_bad_mi():

    test_image1 = np.array([[i for i in range(50)] for j in range(50)])

    test_image2 = np.ones((50, 50))

    corrilation = mutual_information.mi(test_image1, test_image2)

    assert corrilation == pytest.approx(0)

def test_mutual_information():

    d_template = np.array([[i for i in range(50, 100)] for j in range(50)])

    s_image = np.array([[150 - i for i in range(150)] for j in range(150)])

    x_offset, y_offset, max_corr, corr_map = mutual_information.mutual_information(d_template, s_image, bins=20)

    assert x_offset == -25

    assert y_offset == -25

    assert max_corr == 2.9755967600033015