This article talks about the SDHash package, which is a Python library for computing hashes of images which ignore perceptual differences.

As humans, it’s very easy to spot if two images are “the same”. Unfortunately, the same thing can’t be said of computers. A simple approach such as comparing two images pixel by pixel will fail in all but the most simple of cases. Even a more sophisticated method such as computing an $$\mathcal{L}_1$$ or $$\mathcal{L}_2$$ mean distance between the images and taking a small value to imply similarity is not much better.

For example, given an original image A, the following should produce equivalent images:

• Scaling with the same aspect ratio.
• Scaling with a very similar aspect ratio.
• Small blurring / high pass filtering.
• Lossy compression and reconstruction.

The previous set of transformations can be said to be natural, that is, they will most certainly occur in any systen, as images get moved around, edited etc . However, there’s an even bigger class of transformations which are adversarial, that is, somebody is trying to trick the system to believe one image is original when it is in fact not. User generated content sites face this problem, regardless of the mode of the content (text, image, audio, video).

The following adverserial transformations should produce equivalent images, as well:

• Removing a small area from the borders.
• $$90$$, $$180$$, $$270$$ degrees rotation.
• Horizontal or vertical flipping.
• Adding or removing a watermark.
• Alteration of color planes, but not of the luminance one.
• Grayscale conversion.
• Large-scale editing restricted to a small area (replacing some text with another, for example)

SDHash tries to solve the problem of whether two images are identical or not, modulo all the transformations in the first group, and some (removing of borders and color plane lterations) from the second.

The API it exposes is simple. The test_duplicate method receives two PIL images as input and returns either True or False depending on whether it considers the images as equivalent or not. The hash_image method returns a base64 encoded md5 hash of “stable” image contents. The test_duplicate method is essentially a test of whether the hashes of the arguments are equal. For more advanced usage, the second method is the tool of choice.

For example, a database table of the hashes can be used, with the result of hash_image as a primary key. Whenever new image needs to be added it can be checked first against the table and only if it is not found already, inserted. This allows $$O(1)$$ comparisons to be performed for each insertion, instead of $$O(n)$$. Similarly, a MapReduce job can compute the hashes of images in the map stage, which will result in all identical images being grouped together with the same key in the reduce stage. This allows an $$O(n)$$ algorithm for deuplicating a large dataset.

As a bonus, SDHash works with GIF animations. It treats them as a sequence of frames. Only the first, fifth, tenth etc. frames are considered. The same basic approach is used, but all the frames are considered at once.

# Algorithm

The core algorithm is straightforward:

• The input image is converted to a single plane of high-precision grayscale.
• This plane is resized to a standard width, while maintaing the aspect ratio.
• The DCT is computed on the plane.
• An MD5 hash is computed from a stream which starts with the width and height of the image, and continues with the top-left most significant DCT coefficients, in row major order, clamped to an interval and precision.

All details of the process can be controlled via arguments to the hasher object constructor, although their effect is somewhat esoteric. Good defaults have been provided.

# Installation

The main dependencies are on the Python image library and NumPy/SciPy etc. As such, depending on SDHash brings along a lot of baggage. Ideally and since it only depends on a very small piece of functionality, the library would just include the DCT code directly. Feel free to contribute a well tested implementation.

Installation is simple, via pip: