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

Chapter 1: Introduction 4To achieve our goals we started by devising a robust feature descriptor for generalunorganized and noisy point-sets. Several local and global descriptors were proposedfor surface-based registration, using mostly differential properties. Given that we workwith the most general case of point-sets we will employ a recently developed andpowerful tool for feature inference namely tensor voting. The philosophical reasonbehind this choice, as well as behind the choice of the point-sets representation, is thatcurrent 3D digitization devices actually provide point-sets sampled from the surfaces.Surface topology and differential properties are currently just inferred from thesesamples. In the registration task the goal is precisely to reconstruct these surfaces fromthe combination of several datasets. The redundancy of information will allow for theaccurate recovery of shapes. Hence it is more suitable, when possible, to register theraw point-sets without any processing so that we don’t loose irrecoverable shapeinformation. The efficient Tensor Voting framework [Medioni00] will help us indesigning a local feature descriptor which will measure the visual importance of points,also known as saliency. This descriptor will prove robust to noise and information rich.It will allow the implicit embedding of salient feature information and confidence in aconvenient format suitable for our registration algorithm. It will also have the advantageof being computationally efficient.Having a good local descriptor such as our point saliency measure will helpsignificantly with the correspondence task, which is the main challenge for registration.In the work that will be described in this dissertation we depart from the ICP criterionand designing a new energy function that quantifies registration. In this we are guidedby the limitations of ICP methods. Our development starts with a simple combinatorialmatching criterion that is consistent with a rigorous definition of the registration task. Acontinuously differentiable energy function is obtained from this criterion by themethod known as mollification, which is simply a smoothing by convolution with aGaussian kernel. We will interpret this criterion physically in terms of Gaussian forcefields that are exerted by one of the point-sets on the other. The strength of this field