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We present a new shape descriptor, the differential profile, for shape representation and recognition, which is derived from differential and geometric quantities evaluated at points on a shape. We model differential profiles from a class of shapes as a finite mixture of Gaussians, and use an expectation-maximization (EM) procedure for class-wise model learning. Experiments on handwritten digit and...
Regression or least squares fitting is an important problem in statistics, data mining and many other applications. In recent years, basis functions derived from the underlying geometry of data, primarily Laplacian eigenfunctions, have attracted much interest. In this paper, we present a new framework based on adaptive Laplacian eigenfunctions and show the benefit of using a time-varying basis in...
In this paper, we propose a new learning framework based on the mathematical concept of varifolds (Morgan, 2000), which are the measure-theoretic generalization of differentiable manifolds. We compare varifold learning with the popular manifold learning and demonstrate some of its specialties. Algorithmically, we derive a neighborhood refinement technique for hypergraph models, which is conceptually...
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