Geometric model fitting is a fundamental task in computer graphics and computer vision. However, most geometric model fitting methods are unable to fit an arbitrary geometric model (e.g. a surface with holes) to incomplete data, due to that the similarity metrics used in these methods are unable to measure the rigid partial similarity between arbitrary models. This paper hence proposes a novel rigid geometric similarity metric, which is able to measure both the full similarity and the partial similarity between arbitrary geometric models. The proposed metric enables us to perform partial procedural geometric model fitting (PPGMF). The task of PPGMF is to search a procedural geometric model space for the model rigidly similar to a query of non-complete point set. Models in the procedural model space are generated according to a set of parametric modeling rules. A typical query is a point cloud. PPGMF is very useful as it can be used to fit arbitrary geometric models to non-complete (incomplete, over-complete or hybrid-complete) point cloud data. For example, most laser scanning data is non-complete due to occlusion. Our PPGMF method uses Markov chain Monte Carlo technique to optimize the proposed similarity metric over the model space. To accelerate the optimization process, the method also employs a novel coarse-to-fine model dividing strategy to reject dissimilar models in advance. Our method has been demonstrated on a variety of geometric models and non-complete data. Experimental results show that the PPGMF method based on the proposed metric is able to fit non-complete data, while the method based on other metrics is unable. It is also shown that our method can be accelerated by several times via early rejection.
Most GIPM methods take either a particular type of geometric model or geometric data as input. BGMF methods such as @cite_28 @cite_34 work on basic geometric models. @cite_15 @cite_25 rely on image information to achieve IPM while our work does not rely on images. @cite_29 assumes the number of model parameters is fixed. @cite_0 takes symmetry as an assumption. @cite_19 is limited to facade point clouds and split grammar. @cite_14 takes Manhattan-World as an assumption. @cite_3 is limited to constrained attribute grammar. @cite_1 @cite_38 @cite_31 work well on airborne laser scanning data, however, it is hard to extend them to other types of data. @cite_27 works on tree models. @cite_9 relys on semi-automatic segmentation operations. Our method is full-automatic and makes no assumption about the type of input geometric model and geometric data. Consequently, similar to @cite_20 @cite_35 , our method can be used for general-purpose GIPM.
@cite_38 @cite_31 @cite_14 @cite_35 @cite_28 @cite_29 @cite_9 @cite_1 @cite_3 @cite_0 @cite_19 @cite_27 @cite_15 @cite_34 @cite_25 @cite_20
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This paper proposes a novel 3D scene interpretation approach for robots in mobile manipulation scenarios using a set of 3D point features (Fast Point Feature Histograms) and probabilistic graphical methods (Conditional Random Fields). Our system uses real time stereo with textured light to obtain dense depth maps in the robot's manipulators working space. For the purposes of manipulation, we want to interpret the planar supporting surfaces of the scene, recognize and segment the object classes into their primitive parts in 6 degrees of freedom (6DOF) so that the robot knows what it is attempting to use and where it may be handled. The scene interpretation algorithm uses a two-layer classification scheme: i) we estimate Fast Point Feature Histograms (FPFH) as local 3D point features to segment the objects of interest into geometric primitives; and ii) we learn and categorize object classes using a novel Global Fast Point Feature Histogram (GFPFH) scheme which uses the previously estimated primitives at each point. To show the validity of our approach, we analyze the proposed system for the problem of recognizing the object class of 20 objects in 500 table settings scenarios. Our algorithm identifies the planar surfaces, decomposes the scene and objects into geometric primitives with 98.27 accuracy and uses the geometric primitives to identify the object's class with an accuracy of 96.69 . Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep autoencoder (AE) network with excellent reconstruction quality and generalization ability. The learned representations outperform the state of the art in 3D recognition tasks and enable basic shape editing applications via simple algebraic manipulations, such as semantic part editing, shape analogies and shape interpolation. We also perform a thorough study of different generative models including GANs operating on the raw point clouds, significantly improved GANs trained in the fixed latent space our AEs and, Gaussian mixture models (GMM). Interestingly, GMMs trained in the latent space of our AEs produce samples of the best fidelity and diversity. To perform our quantitative evaluation of generative models, we propose simple measures of fidelity and diversity based on optimally matching between sets point clouds. Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep autoencoder (AE) network with excellent reconstruction quality and generalization ability. The learned representations outperform the state of the art in 3D recognition tasks and enable basic shape editing applications via simple algebraic manipulations, such as semantic part editing, shape analogies and shape interpolation. We also perform a thorough study of different generative models including GANs operating on the raw point clouds, significantly improved GANs trained in the fixed latent space our AEs and, Gaussian mixture models (GMM). Interestingly, GMMs trained in the latent space of our AEs produce samples of the best fidelity and diversity. To perform our quantitative evaluation of generative models, we propose simple measures of fidelity and diversity based on optimally matching between sets point clouds. A hierarchical Bayes Gaussian Mixture Model (HBGMM) with adaptive sparsity is proposed.We impose our hierarchical Bayes prior on the entries of precision matrices in GMM to encourage sparsity.Our adaptive sparsity can reduce the dimensionality of the parameters in GMM to be estimated.Our HBGMM method does not involve any hyperparameters to be estimated, i.e., it is hyperparameter-free. Gaussian Mixture Model (GMM) has been widely used in statistics for its great flexibility. However, parameter estimation for GMM with high dimensionality is a challenge because of the large number of parameters and the lack of observation data. In this paper, we propose an effective method named hierarchical Bayes based Adaptive Sparsity in Gaussian Mixture Model (ASGMM) to estimate the parameters in a GMM by incorporating a two-layer hierarchical Bayes based adaptive sparsity prior. The prior we impose on the precision matrices can encourage sparsity and hence reduce the dimensionality of the parameters to be estimated. In contrast to the l 1 -norm penalty or Laplace prior, our approach does not involve any hyperparameters that must be tuned, and the sparsity adapts to the observation data. The proposed method is achieved by three steps: first, we formulate an adaptive hierarchical Bayes model of the precision matrices in the GMM with a Jeffrey's noninformative hyperprior, which expresses scale-invariance and, more importantly, is hyperparameter-free and unbiased. Second, we perform a Cholesky decomposition on the precision matrices to impose the positive definite property. Finally, we exploit the expectation maximization (EM) algorithm to obtain the final estimated parameters in the GMM. Experimental results on synthetic and real-world datasets demonstrate that ASGMM cannot only adapt the sparsity of high-dimensional data with small estimated error, but also achieve better clustering performance comparing with several classical methods.