Compare image similarity in Python using Structural Similarity, Pixel Comparisons, Wasserstein Distance (Earth Mover's Distance), and SIFT

measure_img_similarity.py

import warnings
from skimage.measure import compare_ssim
from skimage.transform import resize
from scipy.stats import wasserstein_distance
from scipy.misc import imsave
from scipy.ndimage import imread
import numpy as np
import cv2

##
# Globals
##

warnings.filterwarnings('ignore')

# specify resized image sizes
height = 2**10
width = 2**10

##
# Functions
##

def get_img(path, norm_size=True, norm_exposure=False):
  '''
  Prepare an image for image processing tasks
  '''
  # flatten returns a 2d grayscale array
  img = imread(path, flatten=True).astype(int)
  # resizing returns float vals 0:255; convert to ints for downstream tasks
  if norm_size:
    img = resize(img, (height, width), anti_aliasing=True, preserve_range=True)
  if norm_exposure:
    img = normalize_exposure(img)
  return img


def get_histogram(img):
  '''
  Get the histogram of an image. For an 8-bit, grayscale image, the
  histogram will be a 256 unit vector in which the nth value indicates
  the percent of the pixels in the image with the given darkness level.
  The histogram's values sum to 1.
  '''
  h, w = img.shape
  hist = [0.0] * 256
  for i in range(h):
    for j in range(w):
      hist[img[i, j]] += 1
  return np.array(hist) / (h * w) 


def normalize_exposure(img):
  '''
  Normalize the exposure of an image.
  '''
  img = img.astype(int)
  hist = get_histogram(img)
  # get the sum of vals accumulated by each position in hist
  cdf = np.array([sum(hist[:i+1]) for i in range(len(hist))])
  # determine the normalization values for each unit of the cdf
  sk = np.uint8(255 * cdf)
  # normalize each position in the output image
  height, width = img.shape
  normalized = np.zeros_like(img)
  for i in range(0, height):
    for j in range(0, width):
      normalized[i, j] = sk[img[i, j]]
  return normalized.astype(int)


def earth_movers_distance(path_a, path_b):
  '''
  Measure the Earth Mover's distance between two images
  @args:
    {str} path_a: the path to an image file
    {str} path_b: the path to an image file
  @returns:
    TODO
  '''
  img_a = get_img(path_a, norm_exposure=True)
  img_b = get_img(path_b, norm_exposure=True)
  hist_a = get_histogram(img_a)
  hist_b = get_histogram(img_b)
  return wasserstein_distance(hist_a, hist_b)


def structural_sim(path_a, path_b):
  '''
  Measure the structural similarity between two images
  @args:
    {str} path_a: the path to an image file
    {str} path_b: the path to an image file
  @returns:
    {float} a float {-1:1} that measures structural similarity
      between the input images
  '''
  img_a = get_img(path_a)
  img_b = get_img(path_b)
  sim, diff = compare_ssim(img_a, img_b, full=True)
  return sim


def pixel_sim(path_a, path_b):
  '''
  Measure the pixel-level similarity between two images
  @args:
    {str} path_a: the path to an image file
    {str} path_b: the path to an image file
  @returns:
    {float} a float {-1:1} that measures structural similarity
      between the input images
  '''
  img_a = get_img(path_a, norm_exposure=True)
  img_b = get_img(path_b, norm_exposure=True)
  return np.sum(np.absolute(img_a - img_b)) / (height*width) / 255


def sift_sim(path_a, path_b):
  '''
  Use SIFT features to measure image similarity
  @args:
    {str} path_a: the path to an image file
    {str} path_b: the path to an image file
  @returns:
    TODO
  '''
  # initialize the sift feature detector
  orb = cv2.ORB_create()

  # get the images
  img_a = cv2.imread(path_a)
  img_b = cv2.imread(path_b)

  # find the keypoints and descriptors with SIFT
  kp_a, desc_a = orb.detectAndCompute(img_a, None)
  kp_b, desc_b = orb.detectAndCompute(img_b, None)

  # initialize the bruteforce matcher
  bf = cv2.BFMatcher(cv2.NORM_HAMMING, crossCheck=True)

  # match.distance is a float between {0:100} - lower means more similar
  matches = bf.match(desc_a, desc_b)
  similar_regions = [i for i in matches if i.distance < 70]
  if len(matches) == 0:
    return 0
  return len(similar_regions) / len(matches)


if __name__ == '__main__':
  img_a = 'a.jpg'
  img_b = 'b.jpg'
  # get the similarity values
  structural_sim = structural_sim(img_a, img_b)
  pixel_sim = pixel_sim(img_a, img_b)
  sift_sim = sift_sim(img_a, img_b)
  emd = earth_movers_distance(img_a, img_b)
  print(structural_sim, pixel_sim, sift_sim, emd)

Thanks for the code! Out of curiosity, why do you normalize the exposure for earth mover and pixel similarity, but not the structural similarity?

Hi duhaime,

Can u please tell me which paper u referred, or if it is ur own, please provide link for material where i can get detailed explanation

Thanks in advance

did a bit of digging on the algo used here myself and just to share what I found:

• Structural Similarity Index
• The use of image histogram for Image Comparsion
• Earth Mover's Distance/ Wasserstein Metric
  • intro here and here
  • in the context of image histogram comparsion here's the paper
• For SIFT, SURF, and ORB, OpenCV has a pretty good documentation

hopefully this helps

Thanks for this research, ohjho--these are great references!

I would also encourage you to check out more modern image similarity techniques, like using pretrained neural networks (e.g. Inception) or training your own Autoencoder to measure image similarity.

These latter techniques can capture much more flexible notions of image similarity than the older methods shown above!

https://gist.github.com/duhaime/211365edaddf7ff89c0a36d9f3f7956c#file-measure_img_similarity-py-L129

You are using ORB feature detection not SIFT.

Can you updated from "scipy.ndimage import imread"?

You can replace this import scipy.ndimage import imread by from imageio import imread

Then replace get_img() by:

from imageio import imread

def get_img(path, norm_size=True, norm_exposure=False):
  '''
  Prepare an image for image processing tasks
  '''
  # flatten returns a 2d grayscale array
  img = imread(path, as_gray=True).astype(int)

  # resizing returns float vals 0:255; convert to ints for downstream tasks
  if norm_size:
    img = resize(img, (height, width), anti_aliasing=True, preserve_range=True)
  if norm_exposure:
    img = normalize_exposure(img)
  return img

Thank you very much for the code. I would like to use it to compare across formats (ie TIFFs with JPGs so that i can see if the files are versions of each other). I seem to run into an issue when working with tiffs and I wanted to know if there was a way around it:

~/env/lib/python3.7/site-packages/imageio/plugins/tifffile.py in _open(self, **kwargs)
    224                 self._f = None
    225                 f = self.request.get_file()
--> 226             self._tf = _tifffile.TiffFile(f, **kwargs)
    227 
    228             # metadata is the same for all images

~/env/lib/python3.7/site-packages/tifffile/tifffile.py in __init__(self, arg, name, offset, size, multifile, _useframes, _master, **kwargs)
   2189                         setattr(self, key, bool(value))
   2190                 else:
-> 2191                     raise TypeError(f'unexpected keyword argument: {key}')
   2192 
   2193         fh = FileHandle(arg, mode='rb', name=name, offset=offset, size=size)

TypeError: unexpected keyword argument: as_gray

Many thanks

@mufticsanjin I'd try an earlier scipy version, maybe 1.0.0 or so