Abstract
Surface registration is the process of determining the rigid body transformation that relocates a set of three-dimensional Cartesian coordinates as close as possible to a corresponding surface model. This procedure is used in free-form surface inspection, computer vision, and a wide variety of other applications. Newton methods for non-linear numerical minimization are rarely applied to this problem because of the high cost of computing the first and second derivatives through finite difference methods. This paper presents an approach to reduce this cost by providing analytic formulas for the derivatives. The resulting Newton methods are more efficient and accurate than those implemented in past research and have distinct advantages compared to the registration methods most widely used today. In this first part, the formulation of the analytic derivatives is presented along with a discussion of their application in various Newton methods.
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