What algorithm could be used to identify if images are the "same" or similar, regardless of size?
TinEye, the "reverse image search engine", allows you to upload/link to an image and it is able to search through the billion images it has crawled and it will return links to images it has found that are the same image.
However, it isn't a naive checksum or anything related to that. It is often able to find both images of a higher resolution and lower resolution and larger and smaller size than the original image you supply. This is a good use for the service because I often find an image and want the highest resolution version of it possible.
Not only that, but I've had it find images of the same image set, where the people in the image are in a different position but the background largely stays the same.
What type of algorithm could TinEye be using that would allow it to compare an image with others of various sizes and compression ratios and yet still accurately figure out that they are the "same" image or set?
Answer
These algorithms are usually fingerprint-based. Fingerprint is a reasonably small data structure, something like a long hash code. However, the goals of fingerprint function are opposite to the goals of hash function. A good hash function should generate very different codes for very similar (but not equal) objects. The fingerprint function should, on contrary, generate the same fingerprint for similar images.
Just to give you an example, this is a (not particularly good) fingerprint function: resize the picture to 32x32 square, normalize and and quantize the colors, reducing the number of colors to something like 256. Then, you have 1024-byte fingerprint for the image. Just keep a table of fingerprint => [list of image URLs]. When you need to look images similar to a given image, just calculate its fingerprint value and find the corresponding image list. Easy.
What is not easy - to be useful in practice, the fingerprint function needs to be robust against crops, affine transforms, contrast changes, etc. Construction of good fingerprint functions is a separate research topic. Quite often they are hand-tuned and uses a lot of heuristics (i.e. use the knowledge about typical photo contents, about image format / additional data in EXIF, etc.)
Another variation is to use more than one fingerprint function, try to apply each of them and combine the results. Actually, it's similar to finding similar texts. Just instead of "bag of words" the image similarity search uses a "bag of fingerprints" and finds how many elements from one bag are the same as elements from another bag. How to make this search efficient is another topic.
Now, regarding the articles/papers. I couldn't find a good article that would give an overview of different methods. Most of the public articles I know discuss specific improvement to specific methods. I could recommend to check these:
"Content Fingerprinting Using Wavelets". This article is about audio fingerprinting using wavelets, but the same method can be adapted for image fingerprinting.
PERMUTATION GROUPING: INTELLIGENT HASH FUNCTION DESIGN FOR AUDIO & IMAGE RETRIEVAL. Info on Locality-Sensitive Hashes.
Bundling Features for Large Scale Partial-Duplicate Web Image Search. A very good article, talks about SIFT and bundling features for efficiency. It also has a nice bibliography at the end