To the Graduate Council: I am submitting herewith a dissertation ...

Chapter 2: Related Work 18To model the transformations aligning the images several approaches were used.Global parametric transformations, such as affine and projective warps, assume that asingle set of parameters will be valid for the whole image. More accurate localparametric mappings were employed for registration and image warping [Zitova03].Other methods while global in nature are capable of modeling local deformations,these include radial basis functions techniques, chief among which are Thin-plateSplines methods [Bookstein89]. While these above methods were mostly used in thecase feature correspondences are available, other techniques recover bothcorrespondences and transformations at the same time. For example another approachused in the case of images with complex and/or local deformation is elasticregistration, introduced by Bajcsy [Bajcsy89]. These techniques modeled the imagesas pieces of an elastic rubber sheet that are subject to external stretching forces andinternal smoothness and stiffness constraints that bring them into alignment withminimal amount of bending and stretching. The external forces are derived byoptimization of a similarity function defined on the intensity values or on the boundarystructures.In the case of very localized deformations registration can be addressed by the socalledfluid registration, where a viscous fluid model was used to model the flow ofone image in the process of aligning with the reference image [Woolny02]. Inaddition other non-rigid methods are commonly used including diffusion registration[Thirion98][Andersen01], and PDE-driven level sets [Hermosillo02]. For a thoroughrecent survey on image registration techniques we refer to Zitova and Flusser[Zitova03]. In this research the application of our new matching criterion to imageregistration was somewhat limited when compared to our work on 3D alignment;nonetheless we are convinced that our framework will be very useful for bothmultimodal and single-sensor image alignment under different non-rigidtransformation models.