coding a new image model

Frean and I started coding up our generative image model. Since all that matters is histograms, we only need counts in regions of the image. Frean had a nice trick in which we pre-cumulate what you might call the "indicator" images, one per histogram bin, and then counts in bins become some very simple operations only on the corners of the region. Awesome and fast and very numpythonic.

We tested the method by swinging a patch over a SDSS image, and looking at the likelihood of a source-plus-background model as a function of source location. Obvious sources in the SDSS image stood out at huge confidence in this one-source likelihood map. And the model is just "the pixel histogram of a source is different from that of the background" plus a bit of "we know the background is close to flat" in quantile-based bins. Within the source and background regions there are no beliefs; that is, we treat the pixels within the regions as having been generated iid.

This model is very naive—it doesn't represent our complex beliefs about astronomical images. However, this will hurt us most when we think about compact sources, and least when we think about large, low surfae-brightness (intensity) sources, which was the original goal of the project. We decided that we are not interested in bright sources: They are easy! This is a project about finding subtle features (and subtle problems with the data).

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