In this paper, we propose a simple and effective geometric model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking problem on hypergraphs. Specifically, a hypergraph is first constructed, where the vertices represent model hypotheses and the hyperedges denote data points. The hypergraph involves higher-order similarities (instead of pairwise similarities used on a simple graph), and it can characterize complex relationships between model hypotheses and data points. In addition, we develop a hypergraph reduction technique to remove “insignificant” vertices while retaining as many “significant” vertices as possible in the hypergraph. Based on the simplified hypergraph, we then propose a novel mode-seeking algorithm to search for representative modes within reasonable time. Finally, the proposed mode-seeking algorithm detects modes according to two key elements, i.e., the weighting scores of vertices and the similarity analysis between vertices. Overall, the proposed fitting method is able to efficiently and effectively estimate the number and the parameters of model instances in the data simultaneously. Experimental results demonstrate that the proposed method achieves significant superiority over several state-of-the-art model fitting methods on both synthetic data and real images.
In addition to the above-mentioned robust fitting methods, there are several other related fitting methods, such as KF @cite_11 , J-linkage @cite_19 , T-linkage @cite_24 , SCAMS @cite_4 , PM @cite_27 , PEARL @cite_1 , AKSWH @cite_14 , HS @cite_18 , RELRT @cite_31 and GMD @cite_33 . KF, J-linkage, T-linkage and SCAMS directly deal with data points for model fitting but they are sensitive to unbalanced data distributions that are quite common in practical applications . In addition, these methods have difficulties in dealing with the data points near the intersection of model instances. The computational costs of J-linkage and T-linkage are high due to the use of the agglomerative clustering procedure. The other robust fitting methods also have some problems. For example, PM requires the input of the number of model instances in data; PEARL is sensitive to the initial generated hypotheses; AKSWH may remove some good model hypotheses corresponding to the correct model instances involving a small number of data points, during the procedure of selecting significant hypotheses; HS encounters the computational complexity problem due to the expansion and dropping strategy used; both RELRT and GMD only work for single-structure data.
@cite_18 @cite_14 @cite_4 @cite_33 @cite_1 @cite_24 @cite_19 @cite_27 @cite_31 @cite_11
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This paper tackles the problem of fitting multiple instances of a model to data corrupted by noise and outliers. The proposed solution is based on random sampling and conceptual data representation. Each point is represented with the characteristic function of the set of random models that fit the point. A tailored agglomerative clustering, called J-linkage, is used to group points belonging to the same model. The method does not require prior specification of the number of models, nor it necessitate parameters tuning. Experimental results demonstrate the superior performances of the algorithm. We propose a robust fitting framework, called Adaptive Kernel-Scale Weighted Hypotheses (AKSWH), to segment multiple-structure data even in the presence of a large number of outliers. Our framework contains a novel scale estimator called Iterative Kth Ordered Scale Estimator (IKOSE). IKOSE can accurately estimate the scale of inliers for heavily corrupted multiple-structure data and is of interest by itself since it can be used in other robust estimators. In addition to IKOSE, our framework includes several original elements based on the weighting, clustering, and fusing of hypotheses. AKSWH can provide accurate estimates of the number of model instances and the parameters and the scale of each model instance simultaneously. We demonstrate good performance in practical applications such as line fitting, circle fitting, range image segmentation, homography estimation, and two--view-based motion segmentation, using both synthetic data and real images. Recently, methods with learning procedure have been widely used to solve person re-identification (re-id) problem. However, most existing databases for re-id are smallscale, therefore, over-fitting is likely to occur. To further improve the performance, we propose a novel method by fusing multiple local features and exploring their structural information on different levels. The proposed method is called Structural Constraints Enhanced Feature Accumulation (SCEFA). Three local features (i.e., Hierarchical Weighted Histograms (HWH), Gabor Ternary Pattern HSV (GTP-HSV), Maximally Stable Color Regions (MSCR)) are used. Structural information of these features are deeply explored in three levels: pixel, blob, and part. The matching algorithms corresponding to the features are also discussed. Extensive experiments conducted on three datasets: VIPeR, ETHZ and our own challenging dataset MCSSH, show that our approach outperforms stat-of-the-art methods significantly. 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.