How do you incorporate prior knowledge and constraints into your image registration model?

In my experience, the simpler the registration is, the more robust the final result will be. Simplification helps to minimize ambiguity and uncertainty of the registration problem.

The primary issue is the mutual registration of an image from one sensor to an image from another sensor. We presume that the images are of some real world domain which is captured in each image. Hence there is the problem of determining parts of the two images which corresponded to the shared sensed domain. Within this shared domain there may be fixed point features which will have corresponding points on each image. A regularization transformation between coordinates of corresponding in the two images may be fitted in various ways. It may be that the prior knowledge is fuzzy point data which need to be matched. More complex prior knowledge may take the form of boundaries. 2 images generalize to n.

With some practice, one can quickly assess the best registration strategy. For example, if you have two images of the same object with the same or similar modalities, if the images of the object are geometrically similar, using an area-based registration might be the first solution

I would consider the main means of incorporating prior information would be by identification of the types of corresponding features needed to be matched. The initial values of parameters of the registration transformation are largely immaterial, since movement away from arbitrary starting values to data-matching values would be expected to be very rapid. A simple co-registration transformation may have higher errors in some regions than in others, possibly near boundaries of the shared domain. This might suggest a partitioning of the domain into sub regions in which co-registration takes place.

One aspect of most images is that they are coloured. Each pixel in each image has intensity values in a number of spectral bands. For each colour band we have an intensity "topography" across the images. Matching these colour topographies can be done using correlational measures, attaining sub-pixel co-registration results. Combining results over all bands further improves whole-image pixel-based co-registration accuracy.

I agree, however standardization of color for image pixel type is problematic, do i use Microsoft crayons, Adobe, etc. A few years ago, I wanted to standardize a color schema based on tissue type, asked the FDA if anybody (pathologist) had tried, all I heard was the sound of crickets. Without a standard of some type correlation within data sets and outside for a compare and contrast delta is truly an AI project, my opinion

Simplicity of functional form of a co-registration transformation is not in itself a desirable feature in the registration process. Rather, appropriateness to the structure and complexity of the data is necessary. In fact, using a neural net involves a highly over-parametetized non-linear model, but recent experience use of reinforcement learning methods to impose constraints, corresponding to prior knowledge, seem to have been very successful in complex areas of analysis and understanding.

I'm Bayesian approaches to data analysis and interpretation a "prior distribution" of the parameters of a model is assumed known. This is then combined with the likelihood of the data, assuming some probability model, to produce a posterior distribution of theodel parameters, (after the data has been "used"). Clearly if the prior is merely conjectured or guessed then the posterior is really just a guess. Empirical priors allow us to stay data-based and minimize guessing.