Our image formation model approximates the production of the sensor images from an underlying true scene. It describes the graylevel intensities in the sensor images as locally affine transformations of the graylevel intensities arising from the scene. The model is given by
where,
indexes the sensors,
a is the sensor image,
s is the true scene,
is the sensor bias (captures effects of dysfunctional sensor elements,
is the sensor gain (which includes the effects of local polarity reversals), and
is the sensor noise
The model is defined at each location (i.e., hyperpixel) of a Laplacian pyramid. The Laplacian pyramid is a multiresolution and multiscale representation of an image. Defining the model in the pyramid domain allows one to capture the relationships between graylevel features in the sensor images and the scene existing at multiple scales.