2,723 research outputs found
Learning from Distributions via Support Measure Machines
This paper presents a kernel-based discriminative learning framework on
probability measures. Rather than relying on large collections of vectorial
training examples, our framework learns using a collection of probability
distributions that have been constructed to meaningfully represent training
data. By representing these probability distributions as mean embeddings in the
reproducing kernel Hilbert space (RKHS), we are able to apply many standard
kernel-based learning techniques in straightforward fashion. To accomplish
this, we construct a generalization of the support vector machine (SVM) called
a support measure machine (SMM). Our analyses of SMMs provides several insights
into their relationship to traditional SVMs. Based on such insights, we propose
a flexible SVM (Flex-SVM) that places different kernel functions on each
training example. Experimental results on both synthetic and real-world data
demonstrate the effectiveness of our proposed framework.Comment: Advances in Neural Information Processing Systems 2
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TVL<sub>1</sub>shape approximation from scattered 3D data
With the emergence in 3D sensors such as laser scanners and 3D reconstruction from cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, contain only a limited degree of information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In addition, issues like sparse data measurements, noise, missing samples due to occlusion, and the inherently huge datasets involved in such representations makes this task extremely challenging. This paper addresses these issues by presenting a new 3D shape modelling framework for samples acquired from 3D sensor. Motivated by the success of nonlinear kernel-based approximation techniques in the statistics domain, existing methods using radial basis functions are applied to 3D object shape approximation. The task is framed as an optimization problem and is extended using non-smooth L1 total variation regularization. Appropriate convex energy functionals are constructed and solved by applying the Alternating Direction Method of Multipliers approach, which is then extended using Gauss-Seidel iterations. This significantly lowers the computational complexity involved in generating 3D shape from 3D samples, while both numerical and qualitative analysis confirms the superior shape modelling performance of this new framework compared with existing 3D shape reconstruction techniques
Surface Reconstruction from Scattered Point via RBF Interpolation on GPU
In this paper we describe a parallel implicit method based on radial basis
functions (RBF) for surface reconstruction. The applicability of RBF methods is
hindered by its computational demand, that requires the solution of linear
systems of size equal to the number of data points. Our reconstruction
implementation relies on parallel scientific libraries and is supported for
massively multi-core architectures, namely Graphic Processor Units (GPUs). The
performance of the proposed method in terms of accuracy of the reconstruction
and computing time shows that the RBF interpolant can be very effective for
such problem.Comment: arXiv admin note: text overlap with arXiv:0909.5413 by other author
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