Experiment - Output Uniformity

[sambux1]

We need to test how uniform, or "random looking," the output is of various hash functions. I'm assigning to @ahmedh409 as a good starting point.

We need to write a function that takes as input a perceptual or perceptographic hash function (should work for both since they have similar interfaces) and returns some metrics that evaluate the uniformity of the output.

For all experiments, it is probably useful to normalize the hash values by interpreting them as integers and scaling them to the range [0, 1]. This might require an extra helper function.

The metrics we will want include (but feel free to add more here):

• average hash value of the entire dataset
• average hash value of each of the categories
• some way of measuring similarity (not sure exactly how this will work)
• the min and max similarities among the categories

In terms of measuring uniformity, this means that the average hash value should be 0.5 normalized (or very close).

I expect (based on intuition and some published results) that standard perceptual hash functions will not achieve very good uniformity. We should confirm this and hopefully show that the perceptographic constructions do better.