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The first thing I would do writing such a paper would be to test current compression algorithms by create a collage of the similar images and see how that compares to the size of the indiviual images.
Compressed length is already known to be a powerful metric for classification tasks, but requires polynomial time to do the classification. As much as I hate to admit it, you're better off using a neural network because they work in linear time, or figuring out how to apply the kernel trick to the metric outlined in this paper.
a formal paper on using compression length as a measure of similarity: https://arxiv.org/pdf/cs/0111054
a blog post on this topic, applied to image classification:
https://jakobs.dev/solving-mnist-with-gzip/
I was not talking about classification. What I was talking about was a simple probe at how well a collage of similar images compares in compressed size to the images individually. The hypothesis is that a compression codec would compress images with similar colordistribution in a spritesheet better than if it encode each image individually. I don't know, the savings might be neglible, but I'd assume that there was something to gain at least for some compression codecs. I doubt doing deduplication post compression has much to gain.
I think you're overthinking the classification task. These images are very similar and I think comparing the color distribution would be adequate. It would of course be interesting to compare the different methods :)
Yeah. I understand. But first you have to cluster your images so you know which ones are similar and can then do the deduplication. This would be a powerful way to do that. It's just expensive compared to other clustering algorithms.
My point in linking the paper is that "the probe" you suggested is a 20 year old metric that is well understood. Using normalized compression distance as a measure of Kolmogorov Complexity is what the linked paper is about. You don't need to spend time showing similar images will compress more than dissimilar ones. The compression length is itself a measure of similarity.