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• W2508957333 abstract "Object modeling plays a fundamental role in computer vision. Models are useful in many different applications including recognition, motion analysis and data reduction. This dissertation studies hyperquadric models and their applications to computer vision. A hyperquadric model in 3D describes a volumetric shape whose geometric bound is an arbitrary convex polytope. Hyperquadrics can model a wide range of complex shapes that cannot be obtained from other models such as superquadrics. While the modeling power of hyperquadrics is attractive, a number of problems must be overcome in order to use hyperquadrics for computer vision applications. The first and foremost of these is the problem of fitting hyperquadrics to range data. The difficulty is due to the existence of an infinite number of global minima (with zero error) that do not correspond to any meaningful shape. This dissertation presents a robust technique for fitting hyperquadric models to 2D and 3D data. The algorithm exhibits good convergence behavior and is largely insensitive to initialization.Hyperquadrics can model a wide range of shapes and hence they appear very attractive for recognition. However there is a fundamental problem with hyperquadrics that has to solved before hyperquadrics can be used for recognition. The problem lies with the non-uniqueness of the hyperquadric parameters. A given geometric shape (representable by a hyperquadric) can have more than one hyperquadric equation describing it, even when the coordinate system is fixed. This means that there is a one-to-many relationship between hyperquadric shapes and sets of hyperquadric parameters. Indexing into a database, however, requires a one-to-one correspondence between shapes and their descriptions. An important contribution of this dissertation is the reduction of the above one-to-many relationship to a one-to-one relationship. This dissertation explores the non-uniqueness of the hyperquadric parameters and proposes a method for arriving at a unique set of parameters for a given hyperquadric shape.This dissertation also presents a model based algorithm for the volumetric decomposition of range data into parts. A given hyperquadric model with a certain number of terms can be split into two separate models (or parts) by the introduction of an additional term. This additional term can be viewed as a dividing plane that divides the parent model. We use such a splitting scheme to subdivide a given object recursively into its constitute parts.Finally, this research proposes a model based approach for the estimation of global nonrigid motion. We show that the affine transformation between the parameters of two models is the same as the global affine transformation between the corresponding datasets. We also extend the discussion to include global polynomial transformations. The most attractive feature of this method is that it does not require point correspondences. The usefulness of our algorithm, is two-fold. First, it paves the way for viewing nonrigid motion hierarchically in terms of global and local motion. Second, it can be used as a front end to other motion-analysis techniques that assume small motion. When the motion between two datasets is large, our algorithm can be used to estimate an affine or polynomial transformation between the two datasets which can then be used to warp the first dataset closer to the second so as to satisfy the small motion assumption." @default.
• W2508957333 created "2016-09-16" @default.
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• W2508957333 date "1996-10-03" @default.
• W2508957333 modified "2023-09-26" @default.
• W2508957333 title "Hyperquadric models and applications" @default.
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