The commutant and similarity invariant of analytic Toeplitz operators on Bergman space

The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator M B(z) is similar to n + 1 copies of the Bergman shift if and only if B(z) is an n + 1-Blaschke product. From the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K 0-group term.

Quantifying the quantumness of ensembles via unitary similarity invariant norms

The quantification of the quantumness of a quantum ensemble has theoretical and practical signif- icance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles using the unitary similarity invariant norms of the commutators of the con- stituent density operators of an ensemble. Rigorous proof shows that they share desirable properties for a measure of quantumness, such as positivity, unitary invariance, concavity under probabilistic union, convexity under state decomposition, decreasing under coarse graining, and increasing under fine graining. Several specific examples illustrate the applications of these measures of quantumness in studying quantum information.

Keypoint Description Using Statistical Descriptor with Similarity-Invariant Regions

This article presents a method for the description of key points using simple statistics for regions controlled by neighboring key points to remedy the gap in existing descriptors.Usually,the existent descriptors such as speeded up robust features(SURF),Kaze,binary robust invariant scalable keypoints(BRISK),features from accelerated segment test(FAST),and oriented FAST and rotated BRIEF(ORB)can competently detect,describe,and match images in the presence of some artifacts such as blur,compression,and illumination.However,the performance and reliability of these descriptors decrease for some imaging variations such as point of view,zoom(scale),and rotation.The intro-duced description method improves image matching in the event of such distor-tions.It utilizes a contourlet-based detector to detect the strongest key points within a specified window size.The selected key points and their neighbors con-trol the size and orientation of the surrounding regions,which are mapped on rec-tangular shapes using polar transformation.The resulting rectangular matrices are subjected to two-directional statistical operations that involve calculating the mean and standard deviation.Consequently,the descriptor obtained is invariant(translation,rotation,and scale)because of the two methods;the extraction of the region and the polar transformation techniques used in this paper.The descrip-tion method introduced in this article is tested against well-established and well-known descriptors,such as SURF,Kaze,BRISK,FAST,and ORB,techniques using the standard OXFORD dataset.The presented methodology demonstrated its ability to improve the match between distorted images compared to other descriptors in the literature.

Automatic registration of MLS point clouds and SfM meshes of urban area

Recent advances in 3D scanning technologies allow us to acquire accurate and dense 3D scan data of large-scale environments efficiently.Currently,there are various methods for acquiring largescale 3D scan data,such as Mobile Laser Scanning(MLS),Airborne Laser Scanning,Terrestrial Laser Scanning,photogrammetry and Structure from Motion(SfM).Especially,MLS is useful to acquire dense point clouds of road and road-side objects,and SfM is a powerful technique to reconstruct meshes with textures from a set of digital images.In this research,a registration method of point clouds from vehicle-based MLS(MLS point cloud),and textured meshes from the SfM of aerial photographs(SfM mesh),is proposed for creating high-quality surface models of urban areas by combining them.In general,SfM mesh has non-scale information;therefore,scale,position,and orientation of the SfM mesh are adjusted in the registration process.In our method,first,2D feature points are extracted from both SfM mesh and MLS point cloud.This process consists of ground-and building-plane extraction by region growing,random sample consensus and least square method,vertical edge extraction by detecting intersections between the planes,and feature point extraction by intersection tests between the ground plane and the edges.Then,the corresponding feature points between the MLS point cloud and the SfM mesh are searched efficiently,using similarity invariant features and hashing.Next,the coordinate transformation is applied to the SfM mesh so that the ground planes and corresponding feature points are adjusted.Finally,scaling Iterative Closest Point algorithm is applied for accurate registration.Experimental results for three data-sets show that our method is effective for the registration of SfM mesh and MLS point cloud of urban areas including buildings.

A novel method for multi-angle SAR image matching

Multi-angle synthetic aperture radar（SAR） image matching is very challenging, because the same object may cause different backscattering patterns, heavily depending on the radar incident angle. A technique based on the relations between the invariant positions of ground targets among the reference and sensed images is proposed to accommodate the nonmatching patterns. It involves a target extraction using wavelet coefficient fusion, as well as a geometric voting matching routine for searching the matched control points（CPs） in the reference and sensed images, respectively. To accelerate the speed of the search, a robust, rapidly corresponding CPs determination strategy is exploited by utilizing the global spatial transformation model, as well as a procedure of outlier removal to ensure the desired accuracy. Meanwhile, the positions of the matched point pairs are relocated using mutual information. The final warping of the images according to the CPs is performed by using a polynomial function. The results show the possibility of matching multi-angle SAR images in general cases.