There are many ways to compare images and the best feature representation and metric certainly depend on the domain and the task at hand.

In principle, you could probably start by using SIFT features and bag of visual words image representations. Other types of frequently used local image features include SURF, LESH, GLOH, ORB, HoG, Haar, etc. - there are many different feature types that capture texture information.

Additionally, if your images have color, you could also make some binned color histogram representations or, alternatively, color correlograms.

You can perform some normalization to represent the images as probability distributions of some sort... in that case you could either use the Manhattan and Euclidean distance or the symmetrized Kullback-Leibler divergence.

I would look at the topic on "Content-based image retrieval",

or in a first attempt may be try to reduce the dimension with principal components (PCA) and test some distance on it,

or obtain a cortoon-texture image and compare only the cartoon image. or a combination etc.

There are many ways to compare images and the best feature representation and metric certainly depend on the domain and the task at hand.

In principle, you could probably start by using SIFT features and bag of visual words image representations. Other types of frequently used local image features include SURF, LESH, GLOH, ORB, HoG, Haar, etc. - there are many different feature types that capture texture information.

Additionally, if your images have color, you could also make some binned color histogram representations or, alternatively, color correlograms.

You can perform some normalization to represent the images as probability distributions of some sort... in that case you could either use the Manhattan and Euclidean distance or the symmetrized Kullback-Leibler divergence.

You are talking here about a whole specific field of research which is the Image Retrieval, well it contains several steps starting by image preprocessing then image segmentation and the extraction of image features and the construction of the signature then finally the procedure of comparaison, as Jose Mejia said, try to look at "Content based image retrieval" topic and surveys

You extract certain features (local and global features) and then compute the Euclidian distance between the feature set. if the computed distance is minimum, more similar are the images and vice versa.

http://en.wikipedia.org/wiki/Structural_similarity

The structural similarity (SSIM) index is a method for measuring the similarity between two images. The SSIM index is a full reference metric, in other words, the measuring of image quality based on an initial uncompressed or distortion-free image as reference. SSIM is designed to improve on traditional methods like peak signal-to-noise ratio (PSNR) and mean squared error (MSE), which have proven to be inconsistent with human eye perception.

Some more ressources:

https://ece.uwaterloo.ca/~z70wang/research/ssim/

http://cadik.posvete.cz/iqm/

Computing the mutual information using joint histogram can be used to measure the similarity between the two images. if the mutual information is high this indicates images are much similar and vice versa

Firstly, You should extract features (mean, median or EigenValues of image),

apply feature reduction method, like svd,

choose best features with the aid of feature selection methods(sfs or any)

At last, teach your system and test your system.

As I said before, you are facing a problem of image retrieval by example or known as CBIR systems.

To know how equal are the images must first remove their characteristics in previous reply showed some algorithms that do, called descriptors. However, not all descriptors extract the same kind of characteristics, some are for shape, color or texture.

The most used and most common are the moments of Hu (shape), co-occurrence matrix (texture) and color histogram (color). Some more complex and better outcomes are those that include the MPEG-7 developed by the MPEG group.

u can find out the SSIM INDEX

Tiny procedure to check if two images are similar.

It returns a 192 Bit checksum which can be compared to other checksums.

In contrast to a "normal" checksum(hash) this procedure will return a similar checksum if the two images are similar.

The two images can have different sizes,quality, brightness, contrast, saturation, tinit, noise and will be still considered as the same or similar (only a few bits change).

1)Check dimensions. If different => images are not the same.

2)Check formats. If the same => Perform precise comparison, pixel by pixel.

3) If different formats do this:

*Do not compare RGB (red,green,blue). Compare Brightness as half the weight and compare color/hue as the other half (or 2/3rds vs 1/3rd). Calculate the difference in values and depending on 'tolerance' value they are the same or they are not.

*JPEG heavily compresses the color information but tries not to ruin the liminance values.

findimagedupes #

is pretty good. You can run "findimagedupes -v fingerprint images" to let it print "perceptive hash", for example.

Exact Comparison #

The quickest way to determine if two images have exactly the same contents is to get the difference between the two images, and then calculate the bounding box of the non-zero regions in this image. If the images are identical, all pixels in the difference image are zero, and the bounding box function returns None.

**** import ImageChops

def equal(im1, im2):

return ImageChops.difference(im1, im2).getbbox() is None

Root-Mean-Square Difference #

To get a measure of how similar two images are, you can calculate the root-mean-square (RMS) value of the difference between the images. If the images are exactly identical, this value is zero. The following function uses the difference function, and then calculates the RMS value from the histogram of the resulting image.

# Example: File: imagediff.py

import ImageChops

import math, operator

def rmsdiff(im1, im2):

"Calculate the root-mean-square difference between two images"

h = ImageChops.difference(im1, im2).histogram()

# calculate rms

return math.sqrt(reduce(operator.add,

map(lambda h, i: h*(i**2), h, range(256))

) / (float(im1.size[0]) * im1.size[1]))

Some Links

http://stackoverflow.com/questions/11173816/compare-2-16x16-pixel-images-similarity

http://stackoverflow.com/questions/23931/what-algorithm-to-compare-two-images

http://stackoverflow.com/questions/827680/where-can-i-find-code-for-comparing-two-images-and-determining-how-similar-they?lq=1

http://stackoverflow.com/questions/189943/how-can-i-quantify-difference-between-two-images

http://stackoverflow.com/questions/25977/how-can-i-measure-the-similarity-between-two-images

The simplest solution is to use an image substraction, you can introduce a range in order to consider some "acceptable" differences.

If there are geometric differences between the images, things become a bit more complicated, and computing image difference (or SSIM, which is a better choice) is not enough.

You first have to compute the geometric transform. If you know exactly what model the transform should follow (translation, rotation, Euclidean, affine, etc.), then a good technique is to extract scale-invariant and rotation-invariant features, such as SIFT or SURF, match them, and then compute the transform using RANSAC or one of its derived methods (there is code for all of this in OpenCV).

If it's a free-from geometric transform, then I would advise looking into medical image registration methods, which have been adressing this issue for years.

One you have computed the transform, you can map one image to the other and use image difference or SSIM.

You can calculate the Mean Square Error (MSE) which compares two images on a pixel-by-pixel basis, Thus, two images that are exactly the same will produce an infinite PSNR value.

I have a non-programming answer, but it may help send you the right direction in thinking about how to deal with your problem. Indeed, you could code for this once you break down what is actually happening :-).

As a visual/graphic designer I often employ a simple, elegant technique in graphic software to align identical image layers for perfect alignment (Adobe Photoshop, but anything similar and cheaper will do). It is quick and if there are any differences between the two image layers you can see actual differences very, very easily.

Overlap two similar images in layers. By inverting the top layer (ie make negative) and setting opacity to 50% has a very useful side-effect: As you move the top layer, where pixels perfectly match the lower layer it becomes a perfect solid mid-grey and conversely where it doesn't match it appears coloured and detailed.

Attached is an example Photoshop .PSD file. Trying moving the top identical layer around x/y axes and you will quickly see what I describe.

Please take a look at SSIM method. This method is the most familiar similarity measure between two signal and the most similar method to the human vision system.Other simple method like MSE and PSNR are exist,but they sensitive to noise and some other problems.You can find more information about it in the following link:

https://ece.uwaterloo.ca/~z70wang/research/ssim/

I have enclosed Matlab implementation of this method.

@ehsan mirsadeghi

thanks for the answer

There are many ways to achieve the goal. I have used following techniques.

1) Histogram Matching

2) Image Subtraction

3) Use IrfanView to compare both images together

You  can use this simple code to  compute the Euclidean minimum distance 

function [recognizedindex] = ED(testingdata, trainingdata)

% Function to compute the Euclidean minimum distance

% between the the testingdata, trainingdata

% the inputs:

%

% testingdata: M x F matrix containing the esing data

%

% trainingdata: N x F matrix containing the training data,

% where N is the number of samples

% and F is the number of features.

%

%

% The output:

% recognizedindex: 1 x F sized vector of Euclidean minimum

% distance indices for all the testing data

%

n=size(testingdata,1);

recognizedindex=[ ];

for k=1:n

euclide_dist = [ ];

for i=1 : size(trainingdata,1)

temp = (norm(testingdata(k,:)-trainingdata(i,:)))^2;

euclide_dist = [euclide_dist temp];

end

[euclide_dist_min recognized_index] = min(euclide_dist);

recognizedindex=[ recognizedindex;recognized_index];

end

recognizedindex=recognizedindex';

Dear Rakesh

two dimensional correlation is  the simplest and the most applicable for your aim. however,systematic approach is the image Registration. if  you want use the algorithm in an application, following reference can be usefull :

[1] Zitova, Barbara, and Jan Flusser. "Image registration methods: a survey." Image and vision computing 21.11 (2003): 977-1000.

I'm so appreciated if I can help more.

Regards

Hello Rakesh,

For finding of image similar or not, you can use joint histogram, if your joint histogram gets diagonal line then two images are exact same, otherwise both images are not same.

You can also use SIFT/SURF features for finding of similar features points.

you can use euclidean distance between images

http://www.mathworks.com/matlabcentral/answers/24399-how-to-find-euclidean-distance-for-an-image

or

http://stackoverflow.com/questions/26543880/how-to-find-euclidean-distance-between-keypoints-of-a-single-image-in-opencv

Think big, develop your own algorithm...

Found some useful blogs for you - http://mathminers.com/2016/05/27/image-analysis-using-tensor-flow/

http://mathminers.com/2016/05/18/face-recognition-analysis-using-python/

It is late to answer , but I choose to say something as this task has something to do with recent research topic called person re-identification, - simply put , it focus on checking similarity between image of pedestrian taken from different camera. As I relate the question to this specific application , the focus now grow to not only distance , but also robust feature followed by suitable distance. Assuming the two images to be compared shows difference in the way they were capture , i.e illumination , orientation and occlusion, different alignment. feature and distance ,in this case, are to be used based on the aforementioned challenges . Convolution neural net based features gotten immense popularity in getting complex features - The priniciple is learn the feature , not crafting it once and use it all time as in the so called hand-crafted features ... After all , it all depends on the task at hand as mentioned earlier .. some examples of distance measure and their python implementation are given here

http://dataaspirant.com/2015/04/11/five-most-popular-similarity-measures-implementation-in-python/

Pixel by pixel comparison can be a solution. However, it is not a usual process. Usually, in the research, measurement of PSNR, MSE, UIQI, SSIM values or performing a histogram comparison are the famous processes which are used to measure the degree of similarities of two images.

Dear Rakesh

I suggest you using a suitable feature analysis.

I offer you this paper:

"Article Texture analysis and classification dealing with rotation an...

Your q is understandable . IMHO the following different situations arise wrt "similarity"(not exhaustive) .

1. Are the images say passport photos to be checked?

2. Is it a scene in a movie frame one frame to another.

3. Is it a particular object being tracked in optic flow.

3 Are they bobs of some cell in a microscopic image

4. Are they stars in the sky?(maybe radio images)

5. Same image from different angles , time and different cameras.

Possible approach:

A1.Identify the domain of investigtion to reduce the problem

including whether an object inside an image is being considerd or

the whole image.

A2 Ideally and intuitively start with "Identical cocept"then each pixel of both images must be same. This would not be very practical. Still we can apply the geometric notion of "similarity" e.g.a simple scaling makes the images identical. Now we can extend these concepts into different domains e.g. matrix norms,

PSD, Statistical parameters, Probability etc . we may have to choose from these.

A3. If it is a perioidc phenomena statistical approach of correlation and PSD may yield good results.

A4 If it is a classification problem Naive Bayesian approach

may be suitable.

...and so on..

Hope it helps.

Good Luck in your research.

Cheers