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## Enter Image Analysis

• First define your problem: if are the two gel images, written as functions on the plane, then they are related by    (1)
where , which is a function of position , is unknown and the difference or residual error is the difference between the `aligned gels'.
• So all we have to do is estimate and split into two components: interesting stuff and artefacts:  (2)
• Easy? Well...it's just a tad ill-posed, like all the interesting problems in image analysis. After all, we could set , the identity, then would just be the difference between the raw images - or we could set to be a constant translation to be added to every point in the image, ie  (3)
or...well just about anything you care to choose really. Each one gives a .
• In other words, we must use prior knowledge to solve this one. And about the only thing we can be sure about is that the is a smooth function of .
• Ideally, we would like a Maximum a Posteriori (MAP) estimate of , along the lines of  (4)
where E denotes expectation and the sample mean of .

Next: Geometry Correction Up: So What's the Problem? Previous: So What's the Problem?

Roland Wilson
5/31/2000