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Three-dimensional point cloud data generally contain complex scene information and diversified category structures. Existing point cloud semantic segmentation networks tend to learn feature information between sampled center points and their neighboring points, while ignoring the scale and structural information of the spatial context of the sampled center points. To address these issues, this paper introduces PointNAC (PointNet based on normal vector and attention copula feature enhancement), a network designed for point cloud semantic segmentation in large-scale complex scenes, which consists of the following two main modules: (1) The local stereoscopic feature-encoding module: this feature-encoding process incorporates distance, normal vectors, and angles calculated based on the cosine theorem, enabling the network to learn not only the spatial positional information of the point cloud but also the spatial scale and geometric structure; and (2) the copula-based similarity feature enhancement module. Based on the stereoscopic feature information, this module analyzes the correlation among points in the local neighborhood. It enhances the features of positively correlated points while leaving the features of negatively correlated points unchanged. By combining these enhancements, it effectively enhances the feature saliency within the same class and the feature distinctiveness between different classes. The experimental results show that PointNAC achieved an overall accuracy (OA) of 90.9% and a mean intersection over union (MIoU) of 67.4% on the S3DIS dataset. And on the Vaihingen dataset, PointNAC achieved an overall accuracy (OA) of 85.9% and an average F1 score of 70.6%. Compared to the segmentation results of other network models on public datasets, our algorithm demonstrates good generalization and segmentation capabilities. [ABSTRACT FROM AUTHOR]

In this paper, Newton's iterative method to solve the nonlinear matrix equation is studied. For the given initial matrix Q, the main results that the matrix sequence generated by the iterative method is contained in a fixed open ball, and that the matrix sequence generated by the iterative method converges to the only solution of the nonlinear matrix equation in a fixed closed ball are proved. In addition, the error estimate of the approximate solution in the closed ball and a numerical example to illustrate the convergence results are given. [ABSTRACT FROM AUTHOR]

In this paper, an iterative method to compute symmetric least-squares solution of the matrix equationAXB=Cwith the norm inequality constraint is proposed. For this method, without the error of calculation, a desired solution can be obtained with finitely iterate steps. Numerical experiments are performed to illustrate the efficiency and application of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we present an iterative method to compute the symmetric solutions of the matrix inequalityAX≥Bin least-squares sense. The presented iteration method can be also used to compute the symmetric solutions of the matrix equationAX=Band the consistent matrix inequalityAX≥B. Numerical experiments are given to illustrate the usefulness of the proposed approach. [ABSTRACT FROM PUBLISHER]

Hair is a salient feature in human face region and are one of the important cues for face analysis. Accurate detection and presentation of hair region is one of the key components for automatic synthesis of human facial caricature. In this paper, an automatic hair detection algorithm for the application of automatic synthesis of facial caricature based on a single image is proposed. Firstly, hair regions in training images are labeled manually and then the hair position prior distributions and hair color likelihood distribution function are estimated from these labels efficiently. Secondly, the energy function of the test image is constructed according to the estimated prior distributions of hair location and hair color likelihood. This energy function is further optimized according to graph cuts technique and initial hair region is obtained. Finally, K-means algorithm and image postprocessing techniques are applied to the initial hair region so that the final hair region can be segmented precisely. Experimental results show that the average processing time for each image is about 280 ms and the average hair region detection accuracy is above 90%. The proposed algorithm is applied to a facial caricature synthesis system. Experiments proved that with our proposed hair segmentation algorithm the facial caricatures are vivid and satisfying.