I am looking to compare a new image to a database of images, and then output the higher "similarity". The images I want to compare are similar, but the problem is though because they're not pixel by pixel equal. I've tried to use BoW (Bag Of Words) model already (I implemented it in Matlab, but I'm willing to learn openCV), as per recommendation, I tried various implementations without success, the best correct rate I got was 30%, which is something really low.
Let me show you what I am talking about: imgur gallery with 5 example images. I want to detect that the four initial images are equal, and the fifth one is different. I wouldn't mind only detecting that the ones with the same angle orientation are equal, though. (In my example 2, 3 and 4)
So, that being said, are there any better methods than BoW for that? Or perhaps BoW should be enough if I implemented in a different way?
Thanks in advance.
I would try some keypoint based approach using randomized trees. Has the advantage that point extraction is local and adapts to many sort of transformations (Like the ones your pictures show). The advantage of being local is that they are more robust against changes in illumination across the scene, occlusions, and so on.
Also, take a look at the SURF algorithm.
I 'm trying to find an efficient way of acceptable complexity to
detect an object in an image so I can isolate it from its surroundings
segment that object to its sub-parts and label them so I can then fetch them at will
It's been 3 weeks since I entered the image processing world and I've read about so many algorithms (sift, snakes, more snakes, fourier-related, etc.), and heuristics that I don't know where to start and which one is "best" for what I'm trying to achieve. Having in mind that the image dataset in interest is a pretty large one, I don't even know if I should use some algorithm implemented in OpenCV or if I should implement one my own.
Summarize:
Which methodology should I focus on? Why?
Should I use OpenCV for that kind of stuff or is there some other 'better' alternative?
Thank you in advance.
EDIT -- More info regarding the datasets
Each dataset consists of 80K images of products sharing the same
concept e.g. t-shirts, watches, shoes
size
orientation (90% of them)
background (95% of them)
All pictures in each datasets look almost identical apart from the product itself, apparently. To make things a little more clear, let's consider only the 'watch dataset':
All the pictures in the set look almost exactly like this:
(again, apart form the watch itself). I want to extract the strap and the dial. The thing is that there are lots of different watch styles and therefore shapes. From what I've read so far, I think I need a template algorithm that allows bending and stretching so as to be able to match straps and dials of different styles.
Instead of creating three distinct templates (upper part of strap, lower part of strap, dial), it would be reasonable to create only one and segment it into 3 parts. That way, I would be confident enough that each part was detected with respect to each other as intended to e.g. the dial would not be detected below the lower part of the strap.
From all the algorithms/methodologies I've encountered, active shape|appearance model seem to be the most promising ones. Unfortunately, I haven't managed to find a descent implementation and I'm not confident enough that that's the best approach so as to go ahead and write one myself.
If anyone could point out what I should be really looking for (algorithm/heuristic/library/etc.), I would be more than grateful. If again you think my description was a bit vague, feel free to ask for a more detailed one.
From what you've said, here are a few things that pop up at first glance:
Simplest thing to do it binarize the image and do Connected Components using OpenCV or CvBlob library. For simple images with non-complex background this usually yeilds objects
HOwever, looking at your sample image, texture-based segmentation techniques may work better - the watch dial, the straps and the background are wisely variant in texture/roughness, and this could be an ideal way to separate them.
The roughness of a portion can be easily found by the Eigen transform (explained a bit on SO, check the link to the research paper provided there), then the Mean Shift filter can be applied on the output of the Eigen transform. This will give regions clearly separated according to texture. Both the pyramidal Mean Shift and finding eigenvalues by SVD are implemented in OpenCV, so unless you can optimize your own code its better (and easier) to use inbuilt functions (if present) as far as speed and efficiency is concerned.
I think I would turn the problem around. Instead of hunting for the dial, I would use a set of robust features from the watch to 'stitch' the target image onto a template. The first watch has a set of squares in the dial that are white, the second watch has a number of white circles. I would per type of watch:
Segment out the squares or circles in the dial. Segmentation steps can be tricky as they are usually both scale and light dependent
Estimate the centers or corners of the above found feature areas. These are the new feature points.
Use the Hungarian algorithm to match features between the template watch and the target watch. Alternatively, one can take the surroundings of each feature point in the original image and match these using cross correlation
Use matching features between the template and the target to estimate scaling, rotation and translation
Stitch the image
As the image is now in a known form, one can extract the regions simply via pre set coordinates
So I'm trying to run a comparison of different images and was wondering if anyone could point me in the right direction for some basic metrics I can take for the group of images.
Assuming I have two images, A and B, I pretty much want as much data as possible about each so I can later programmatically compare them. Things like "general color", "general shape", etc. would be great.
If you can help me find specific properties and algorithms to compute them that would be great!
Thanks!
EDIT: The end goal here is to be able to have a computer tell me how "similar" too pictures are. If two images are the same but in one someone blurred out a face; they should register as fairly similar. If two pictures are completely different, the computer should be able to tell.
What you are talking about is way much general and non-specific.
Image information is formalised as Entropy.
What you seem to be looking for is basically feature extraction and then comparing these features. There are tons of features that can be extracted but a lot of them could be irrelevant depending on the differences in the pictures.
There are space domain and frequency domain descriptors of the image which each can be useful here. I can probably name more than 100 descriptors but in your case, only one could be sufficient or none could be useful.
Pre-processing is also important, perhaps you could turn your images to grey-scale and then compare them.
This field is so immensely diverse, so you need to be a bit more specific.
(Update)
What you are looking for is a topic of hundreds if not thousands of scientific articles. But well, perhaps a simplistic approach can work.
So assuming that the question here is not identifying objects and there is no transform, translation, scale or rotation involved and we are only dealing with the two images which are the same but one could have more noise added upon it:
1) Image domain (space domain): Compare the pixels one by one and add up the square of the differences. Normalise this value by the width*height - just divide by the number of pixels. This could be a useful measure of similarity.
2) Frequency domain: Convert the image to frequency domain image (using FTT in an image processing tool such as OpenCV) which will be 2D as well. Do the same above squared diff as above, but perhaps you want to limit the frequencies. Then normalise by the number of pixels. This fares better on noise and translation and on a small rotation but not on scale.
SURF is a good candidate algorithm for comparing images
Wikipedia Article
A practical example (in Mathematica), identifying corresponding points in two images of the moon (rotated, colorized and blurred) :
You can also calculate sum of differences between histogram bins of those two images. But it is also not a silver bullet...
I recommend taking a look at OpenCV. The package offers most (if not all) of the techniques mentioned above.
Sometimes two image files may be different on a file level, but a human would consider them perceptively identical. Given that, now suppose you have a huge database of images, and you wish to know if a human would think some image X is present in the database or not. If all images had a perceptive hash / fingerprint, then one could hash image X and it would be a simple matter to see if it is in the database or not.
I know there is research around this issue, and some algorithms exist, but is there any tool, like a UNIX command line tool or a library I could use to compute such a hash without implementing some algorithm from scratch?
edit: relevant code from findimagedupes, using ImageMagick
try $image->Sample("160x160!");
try $image->Modulate(saturation=>-100);
try $image->Blur(radius=>3,sigma=>99);
try $image->Normalize();
try $image->Equalize();
try $image->Sample("16x16");
try $image->Threshold();
try $image->Set(magick=>'mono');
($blob) = $image->ImageToBlob();
edit: Warning! ImageMagick $image object seems to contain information about the creation time of an image file that was read in. This means that the blob you get will be different even for the same image, if it was retrieved at a different time. To make sure the fingerprint stays the same, use $image->getImageSignature() as the last step.
findimagedupes is pretty good. You can run "findimagedupes -v fingerprint images" to let it print "perceptive hash", for example.
Cross-correlation or phase correlation will tell you if the images are the same, even with noise, degradation, and horizontal or vertical offsets. Using the FFT-based methods will make it much faster than the algorithm described in the question.
The usual algorithm doesn't work for images that are not the same scale or rotation, though. You could pre-rotate or pre-scale them, but that's really processor intensive. Apparently you can also do the correlation in a log-polar space and it will be invariant to rotation, translation, and scale, but I don't know the details well enough to explain that.
MATLAB example: Registering an Image Using Normalized Cross-Correlation
Wikipedia calls this "phase correlation" and also describes making it scale- and rotation-invariant:
The method can be extended to determine rotation and scaling differences between two images by first converting the images to log-polar coordinates. Due to properties of the Fourier transform, the rotation and scaling parameters can be determined in a manner invariant to translation.
Colour histogram is good for the same image that has been resized, resampled etc.
If you want to match different people's photos of the same landmark it's trickier - look at haar classifiers. Opencv is a great free library for image processing.
I don't know the algorithm behind it, but Microsoft Live Image Search just added this capability. Picasa also has the ability to identify faces in images, and groups faces that look similar. Most of the time, it's the same person.
Some machine learning technology like a support vector machine, neural network, naive Bayes classifier or Bayesian network would be best at this type of problem. I've written one each of the first three to classify handwritten digits, which is essentially image pattern recognition.
resize the image to a 1x1 pixle... if they are exact, there is a small probability they are the same picture...
now resize it to a 2x2 pixle image, if all 4 pixles are exact, there is a larger probability they are exact...
then 3x3, if all 9 pixles are exact... good chance etc.
then 4x4, if all 16 pixles are exact,... better chance.
etc...
doing it this way, you can make efficiency improvments... if the 1x1 pixel grid is off by a lot, why bother checking 2x2 grid? etc.
If you have lots of images, a color histogram could be used to get rough closeness of images before doing a full image comparison of each image against each other one (i.e. O(n^2)).
There is DPEG, "The" Duplicate Media Manager, but its code is not open. It's a very old tool - I remember using it in 2003.
You could use diff to see if they are REALLY different.. I guess it will remove lots of useless comparison. Then, for the algorithm, I would use a probabilistic approach.. what are the chances that they look the same.. I'd based that on the amount of rgb in each pixel. You could also find some other metrics such as luminosity and stuff like that.
Given two different image files (in whatever format I choose), I need to write a program to predict the chance if one being the illegal copy of another. The author of the copy may do stuff like rotating, making negative, or adding trivial details (as well as changing the dimension of the image).
Do you know any algorithm to do this kind of job?
These are simply ideas I've had thinking about the problem, never tried it but I like thinking about problems like this!
Before you begin
Consider normalising the pictures, if one is a higher resolution than the other, consider the option that one of them is a compressed version of the other, therefore scaling the resolution down might provide more accurate results.
Consider scanning various prospective areas of the image that could represent zoomed portions of the image and various positions and rotations. It starts getting tricky if one of the images are a skewed version of another, these are the sort of limitations you should identify and compromise on.
Matlab is an excellent tool for testing and evaluating images.
Testing the algorithms
You should test (at the minimum) a large human analysed set of test data where matches are known beforehand. If for example in your test data you have 1,000 images where 5% of them match, you now have a reasonably reliable benchmark. An algorithm that finds 10% positives is not as good as one that finds 4% of positives in our test data. However, one algorithm may find all the matches, but also have a large 20% false positive rate, so there are several ways to rate your algorithms.
The test data should attempt to be designed to cover as many types of dynamics as possible that you would expect to find in the real world.
It is important to note that each algorithm to be useful must perform better than random guessing, otherwise it is useless to us!
You can then apply your software into the real world in a controlled way and start to analyse the results it produces. This is the sort of software project which can go on for infinitum, there are always tweaks and improvements you can make, it is important to bear that in mind when designing it as it is easy to fall into the trap of the never ending project.
Colour Buckets
With two pictures, scan each pixel and count the colours. For example you might have the 'buckets':
white
red
blue
green
black
(Obviously you would have a higher resolution of counters). Every time you find a 'red' pixel, you increment the red counter. Each bucket can be representative of spectrum of colours, the higher resolution the more accurate but you should experiment with an acceptable difference rate.
Once you have your totals, compare it to the totals for a second image. You might find that each image has a fairly unique footprint, enough to identify matches.
Edge detection
How about using Edge Detection.
(source: wikimedia.org)
With two similar pictures edge detection should provide you with a usable and fairly reliable unique footprint.
Take both pictures, and apply edge detection. Maybe measure the average thickness of the edges and then calculate the probability the image could be scaled, and rescale if necessary. Below is an example of an applied Gabor Filter (a type of edge detection) in various rotations.
Compare the pictures pixel for pixel, count the matches and the non matches. If they are within a certain threshold of error, you have a match. Otherwise, you could try reducing the resolution up to a certain point and see if the probability of a match improves.
Regions of Interest
Some images may have distinctive segments/regions of interest. These regions probably contrast highly with the rest of the image, and are a good item to search for in your other images to find matches. Take this image for example:
(source: meetthegimp.org)
The construction worker in blue is a region of interest and can be used as a search object. There are probably several ways you could extract properties/data from this region of interest and use them to search your data set.
If you have more than 2 regions of interest, you can measure the distances between them. Take this simplified example:
(source: per2000.eu)
We have 3 clear regions of interest. The distance between region 1 and 2 may be 200 pixels, between 1 and 3 400 pixels, and 2 and 3 200 pixels.
Search other images for similar regions of interest, normalise the distance values and see if you have potential matches. This technique could work well for rotated and scaled images. The more regions of interest you have, the probability of a match increases as each distance measurement matches.
It is important to think about the context of your data set. If for example your data set is modern art, then regions of interest would work quite well, as regions of interest were probably designed to be a fundamental part of the final image. If however you are dealing with images of construction sites, regions of interest may be interpreted by the illegal copier as ugly and may be cropped/edited out liberally. Keep in mind common features of your dataset, and attempt to exploit that knowledge.
Morphing
Morphing two images is the process of turning one image into the other through a set of steps:
Note, this is different to fading one image into another!
There are many software packages that can morph images. It's traditionaly used as a transitional effect, two images don't morph into something halfway usually, one extreme morphs into the other extreme as the final result.
Why could this be useful? Dependant on the morphing algorithm you use, there may be a relationship between similarity of images, and some parameters of the morphing algorithm.
In a grossly over simplified example, one algorithm might execute faster when there are less changes to be made. We then know there is a higher probability that these two images share properties with each other.
This technique could work well for rotated, distorted, skewed, zoomed, all types of copied images. Again this is just an idea I have had, it's not based on any researched academia as far as I am aware (I haven't look hard though), so it may be a lot of work for you with limited/no results.
Zipping
Ow's answer in this question is excellent, I remember reading about these sort of techniques studying AI. It is quite effective at comparing corpus lexicons.
One interesting optimisation when comparing corpuses is that you can remove words considered to be too common, for example 'The', 'A', 'And' etc. These words dilute our result, we want to work out how different the two corpus are so these can be removed before processing. Perhaps there are similar common signals in images that could be stripped before compression? It might be worth looking into.
Compression ratio is a very quick and reasonably effective way of determining how similar two sets of data are. Reading up about how compression works will give you a good idea why this could be so effective. For a fast to release algorithm this would probably be a good starting point.
Transparency
Again I am unsure how transparency data is stored for certain image types, gif png etc, but this will be extractable and would serve as an effective simplified cut out to compare with your data sets transparency.
Inverting Signals
An image is just a signal. If you play a noise from a speaker, and you play the opposite noise in another speaker in perfect sync at the exact same volume, they cancel each other out.
(source: themotorreport.com.au)
Invert on of the images, and add it onto your other image. Scale it/loop positions repetitively until you find a resulting image where enough of the pixels are white (or black? I'll refer to it as a neutral canvas) to provide you with a positive match, or partial match.
However, consider two images that are equal, except one of them has a brighten effect applied to it:
(source: mcburrz.com)
Inverting one of them, then adding it to the other will not result in a neutral canvas which is what we are aiming for. However, when comparing the pixels from both original images, we can definatly see a clear relationship between the two.
I haven't studied colour for some years now, and am unsure if the colour spectrum is on a linear scale, but if you determined the average factor of colour difference between both pictures, you can use this value to normalise the data before processing with this technique.
Tree Data structures
At first these don't seem to fit for the problem, but I think they could work.
You could think about extracting certain properties of an image (for example colour bins) and generate a huffman tree or similar data structure. You might be able to compare two trees for similarity. This wouldn't work well for photographic data for example with a large spectrum of colour, but cartoons or other reduced colour set images this might work.
This probably wouldn't work, but it's an idea. The trie datastructure is great at storing lexicons, for example a dictionarty. It's a prefix tree. Perhaps it's possible to build an image equivalent of a lexicon, (again I can only think of colours) to construct a trie. If you reduced say a 300x300 image into 5x5 squares, then decompose each 5x5 square into a sequence of colours you could construct a trie from the resulting data. If a 2x2 square contains:
FFFFFF|000000|FDFD44|FFFFFF
We have a fairly unique trie code that extends 24 levels, increasing/decreasing the levels (IE reducing/increasing the size of our sub square) may yield more accurate results.
Comparing trie trees should be reasonably easy, and could possible provide effective results.
More ideas
I stumbled accross an interesting paper breif about classification of satellite imagery, it outlines:
Texture measures considered are: cooccurrence matrices, gray-level differences, texture-tone analysis, features derived from the Fourier spectrum, and Gabor filters. Some Fourier features and some Gabor filters were found to be good choices, in particular when a single frequency band was used for classification.
It may be worth investigating those measurements in more detail, although some of them may not be relevant to your data set.
Other things to consider
There are probably a lot of papers on this sort of thing, so reading some of them should help although they can be very technical. It is an extremely difficult area in computing, with many fruitless hours of work spent by many people attempting to do similar things. Keeping it simple and building upon those ideas would be the best way to go. It should be a reasonably difficult challenge to create an algorithm with a better than random match rate, and to start improving on that really does start to get quite hard to achieve.
Each method would probably need to be tested and tweaked thoroughly, if you have any information about the type of picture you will be checking as well, this would be useful. For example advertisements, many of them would have text in them, so doing text recognition would be an easy and probably very reliable way of finding matches especially when combined with other solutions. As mentioned earlier, attempt to exploit common properties of your data set.
Combining alternative measurements and techniques each that can have a weighted vote (dependant on their effectiveness) would be one way you could create a system that generates more accurate results.
If employing multiple algorithms, as mentioned at the begining of this answer, one may find all the positives but have a false positive rate of 20%, it would be of interest to study the properties/strengths/weaknesses of other algorithms as another algorithm may be effective in eliminating false positives returned from another.
Be careful to not fall into attempting to complete the never ending project, good luck!
Read the paper: Porikli, Fatih, Oncel Tuzel, and Peter Meer. “Covariance Tracking Using Model Update Based
on Means on Riemannian Manifolds”. (2006) IEEE Computer Vision and Pattern Recognition.
I was successfully able to detect overlapping regions in images captured from adjacent webcams using the technique presented in this paper. My covariance matrix was composed of Sobel, canny and SUSAN aspect/edge detection outputs, as well as the original greyscale pixels.
An idea:
use keypoint detectors to find scale- and transform- invariant descriptors of some points in the image (e.g. SIFT, SURF, GLOH, or LESH).
try to align keypoints with similar descriptors from both images (like in panorama stitching), allow for some image transforms if necessary (e.g. scale & rotate, or elastic stretching).
if many keypoints align well (exists such a transform, that keypoint alignment error is low; or transformation "energy" is low, etc.), you likely have similar images.
Step 2 is not trivial. In particular, you may need to use a smart algorithm to find the most similar keypoint on the other image. Point descriptors are usually very high-dimensional (like a hundred parameters), and there are many points to look through. kd-trees may be useful here, hash lookups don't work well.
Variants:
Detect edges or other features instead of points.
It is indeed much less simple than it seems :-) Nick's suggestion is a good one.
To get started, keep in mind that any worthwhile comparison method will essentially work by converting the images into a different form -- a form which makes it easier to pick similar features out. Usually, this stuff doesn't make for very light reading ...
One of the simplest examples I can think of is simply using the color space of each image. If two images have highly similar color distributions, then you can be reasonably sure that they show the same thing. At least, you can have enough certainty to flag it, or do more testing. Comparing images in color space will also resist things such as rotation, scaling, and some cropping. It won't, of course, resist heavy modification of the image or heavy recoloring (and even a simple hue shift will be somewhat tricky).
http://en.wikipedia.org/wiki/RGB_color_space
http://upvector.com/index.php?section=tutorials&subsection=tutorials/colorspace
Another example involves something called the Hough Transform. This transform essentially decomposes an image into a set of lines. You can then take some of the 'strongest' lines in each image and see if they line up. You can do some extra work to try and compensate for rotation and scaling too -- and in this case, since comparing a few lines is MUCH less computational work than doing the same to entire images -- it won't be so bad.
http://homepages.inf.ed.ac.uk/amos/hough.html
http://rkb.home.cern.ch/rkb/AN16pp/node122.html
http://en.wikipedia.org/wiki/Hough_transform
In the form described by you, the problem is tough. Do you consider copy, paste of part of the image into another larger image as a copy ? etc.
What we loosely refer to as duplicates can be difficult for algorithms to discern.
Your duplicates can be either:
Exact Duplicates
Near-exact Duplicates. (minor edits of image etc)
perceptual Duplicates (same content, but different view, camera etc)
No1 & 2 are easier to solve. No 3. is very subjective and still a research topic.
I can offer a solution for No1 & 2.
Both solutions use the excellent image hash- hashing library: https://github.com/JohannesBuchner/imagehash
Exact duplicates
Exact duplicates can be found using a perceptual hashing measure.
The phash library is quite good at this. I routinely use it to clean
training data.
Usage (from github site) is as simple as:
from PIL import Image
import imagehash
# image_fns : List of training image files
img_hashes = {}
for img_fn in sorted(image_fns):
hash = imagehash.average_hash(Image.open(image_fn))
if hash in img_hashes:
print( '{} duplicate of {}'.format(image_fn, img_hashes[hash]) )
else:
img_hashes[hash] = image_fn
Near-Exact Duplicates
In this case you will have to set a threshold and compare the hash values for their distance from each
other. This has to be done by trial-and-error for your image content.
from PIL import Image
import imagehash
# image_fns : List of training image files
img_hashes = {}
epsilon = 50
for img_fn1, img_fn2 in zip(image_fns, image_fns[::-1]):
if image_fn1 == image_fn2:
continue
hash1 = imagehash.average_hash(Image.open(image_fn1))
hash2 = imagehash.average_hash(Image.open(image_fn2))
if hash1 - hash2 < epsilon:
print( '{} is near duplicate of {}'.format(image_fn1, image_fn2) )
If you take a step-back, this is easier to solve if you watermark the master images.
You will need to use a watermarking scheme to embed a code into the image. To take a step back, as opposed to some of the low-level approaches (edge detection etc) suggested by some folks, a watermarking method is superior because:
It is resistant to Signal processing attacks
► Signal enhancement – sharpening, contrast, etc.
► Filtering – median, low pass, high pass, etc.
► Additive noise – Gaussian, uniform, etc.
► Lossy compression – JPEG, MPEG, etc.
It is resistant to Geometric attacks
► Affine transforms
► Data reduction – cropping, clipping, etc.
► Random local distortions
► Warping
Do some research on watermarking algorithms and you will be on the right path to solving your problem. (
Note: You can benchmark you method using the STIRMARK dataset. It is an accepted standard for this type of application.
This is just a suggestion, it might not work and I'm prepared to be called on this.
This will generate false positives, but hopefully not false negatives.
Resize both of the images so that they are the same size (I assume that the ratios of widths to lengths are the same in both images).
Compress a bitmap of both images with a lossless compression algorithm (e.g. gzip).
Find pairs of files that have similar file sizes. For instance, you could just sort every pair of files you have by how similar the file sizes are and retrieve the top X.
As I said, this will definitely generate false positives, but hopefully not false negatives. You can implement this in five minutes, whereas the Porikil et. al. would probably require extensive work.
I believe if you're willing to apply the approach to every possible orientation and to negative versions, a good start to image recognition (with good reliability) is to use eigenfaces: http://en.wikipedia.org/wiki/Eigenface
Another idea would be to transform both images into vectors of their components. A good way to do this is to create a vector that operates in x*y dimensions (x being the width of your image and y being the height), with the value for each dimension applying to the (x,y) pixel value. Then run a variant of K-Nearest Neighbours with two categories: match and no match. If it's sufficiently close to the original image it will fit in the match category, if not then it won't.
K Nearest Neighbours(KNN) can be found here, there are other good explanations of it on the web too: http://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm
The benefits of KNN is that the more variants you're comparing to the original image, the more accurate the algorithm becomes. The downside is you need a catalogue of images to train the system first.
If you're willing to consider a different approach altogether to detecting illegal copies of your images, you could consider watermarking. (from 1.4)
...inserts copyright information into the digital object without the loss of quality. Whenever the copyright of a digital object is in question, this information is extracted to identify the rightful owner. It is also possible to encode the identity of the original buyer along with the identity of the copyright holder, which allows tracing of any unauthorized copies.
While it's also a complex field, there are techniques that allow the watermark information to persist through gross image alteration: (from 1.9)
... any signal transform of reasonable strength cannot remove the watermark. Hence a pirate willing to remove the watermark will not succeed unless they debase the document too much to be of commercial interest.
of course, the faq calls implementing this approach: "...very challenging" but if you succeed with it, you get a high confidence of whether the image is a copy or not, rather than a percentage likelihood.
If you're running Linux I would suggest two tools:
align_image_stack from package hugin-tools - is a commandline program that can automatically correct rotation, scaling, and other distortions (it's mostly intended for compositing HDR photography, but works for video frames and other documents too). More information: http://hugin.sourceforge.net/docs/manual/Align_image_stack.html
compare from package imagemagick - a program that can find and count the amount of different pixels in two images. Here's a neat tutorial: http://www.imagemagick.org/Usage/compare/ uising the -fuzz N% you can increase the error tolerance. The higher the N the higher the error tolerance to still count two pixels as the same.
align_image_stack should correct any offset so the compare command will actually have a chance of detecting same pixels.