Dynamic Distribution-Sensitive Point Location

We propose a dynamic data structure for the distribution-sensitive point location problem in the plane. Suppose that there is a fixed query distribution within a convex subdivision S , and we are given an oracle that can return in O (1) time the probability of a query point falling into a polygonal region of constant complexity. We can maintain S such that each query is answered in O opt (S) ) expected time, where opt ( S ) is the expected time of the best linear decision tree for answering point location queries in S . The space and construction time are O(n log 2 n ), where n is the number of vertices of S . An update of S as a mixed sequence of k edge insertions and deletions takes O(k log 4 n) amortized time. As a corollary, the randomized incremental construction of the Voronoi diagram of n sites can be performed in O(n log 4 n ) expected time so that, during the incremental construction, a nearest neighbor query at any time can be answered optimally with respect to the intermediate Voronoi diagram at that time.

Convex Polygonal Hull for a Pair of Irregular Objects

Introduction. Optimization placement problems are NP-hard. In most cases related to cutting and packing problems, heuristic approaches are used. The development of analytical methods for mathematical modeling of the problems is of paramount important for expanding the class of placement problems that can be solved optimally using state of the art NLP-solvers. The problem of placing two irregular two-dimensional objects in a convex polygonal region of the minimum size, which is a convex polygonal hull of the minimum area or perimeter, is considered. Continuous rotations and translations of non-overlapping objects are allowed. To solve the problem of optimal compaction of a pair of objects, two algorithms are proposed. The first is a sequentially search for local extrema on all feasible subdomains using a solution tree. The second algorithm searches for a locally optimal extremum on a single subdomain using a "good" feasible starting point. Purpose of the paper. Show how to construct a minimal convex polygonal hull for two continuously moving irregular objects bounded by circular arcs and line segments. Results. A mathematical model is constructed in the form of a nonlinear programming problem using the phi-function technique. Two algorithms are proposed for solving the problem of placing a pair of objects in order to minimize the area and perimeter of the enclosing polygonal area. The results of computational experiments are presented. Conclusions. The construction of a minimal convex polygonal hull for a pair of two-dimensional objects having an arbitrary spatial shape and allowing continuous rotations and translations makes it possible to speed up the process of finding feasible solutions for the problem of placing a large number of objects with complex geometry. Keywords: convex polygonal hull, irregular objects, phi-function technique, nonlinear optimization.

Joint spectral radius and ternary hermite subdivision

In this paper we construct a family of ternary interpolatory Hermite subdivision schemes of order 1 with small support and ${\mathscr{H}}\mathcal {C}^{2}$ H C 2 -smoothness. Indeed, leaving the binary domain, it is possible to derive interpolatory Hermite subdivision schemes with higher regularity than the existing binary examples. The family of schemes we construct is a two-parameter family whose ${\mathscr{H}}\mathcal {C}^{2}$ H C 2 -smoothness is guaranteed whenever the parameters are chosen from a certain polygonal region. The construction of this new family is inspired by the geometric insight into the ternary interpolatory scalar three-point subdivision scheme by Hassan and Dodgson. The smoothness of our new family of Hermite schemes is proven by means of joint spectral radius techniques.

On the convergence the barycentric method in solving diffraction problems on conductive thin screens

Annotation In this article, the use of the barycentric method is proposed for the numerical solution of problems of diffraction of electromagnetic waves on infinitely thin perfectly conducting screens of arbitrary shape. The numerical solution is formed in the projection formulation of the Galerkin method. The essence of the barycentric method is to form a global system of basic functions for opening the screen when determining the approximation of the desired function of the current plane on its surface. Basis functions are defined by Bernstein-type polynomials in terms of barycentric coordinates that are entered for opening the screen when it is represented as a closed simply connected polygonal region. The features of the algorithmic implementation of the barycentric method in solving diffraction problems on conducting thin screens are considered. The rate of convergence is estimated. Comparative results of calculations performed under equivalent conditions using the barycentric method and the RWG method are presented.

Voxel-Based Scene Representation for Camera Pose Estimation of a Single RGB Image

Deep learning has been utilized in end-to-end camera pose estimation. To improve the performance, we introduce a camera pose estimation method based on a 2D-3D matching scheme with two convolutional neural networks (CNNs). The scene is divided into voxels, whose size and number are computed according to the scene volume and the number of 3D points. We extract inlier points from the 3D point set in a voxel using random sample consensus (RANSAC)-based plane fitting to obtain a set of interest points consisting of a major plane. These points are subsequently reprojected onto the image using the ground truth camera pose, following which a polygonal region is identified in each voxel using the convex hull. We designed a training dataset for 2D–3D matching, consisting of inlier 3D points, correspondence across image pairs, and the voxel regions in the image. We trained the hierarchical learning structure with two CNNs on the dataset architecture to detect the voxel regions and obtain the location/description of the interest points. Following successful 2D–3D matching, the camera pose was estimated using n-point pose solver in RANSAC. The experiment results show that our method can estimate the camera pose more precisely than previous end-to-end estimators.

Quantitative analysis of ipsilateral and contralateral supracerebellar infratentorial and occipital transtentorial approaches to the cisternal pulvinar: laboratory anatomical investigation

OBJECTIVEThe cisternal pulvinar is a challenging location for neurosurgery. Four approaches for reaching the pulvinar without cortical transgression are the ipsilateral supracerebellar infratentorial (iSCIT), contralateral supracerebellar infratentorial (cSCIT), ipsilateral occipital transtentorial (iOCTT), and contralateral occipital transtentorial/falcine (cOCTF) approaches. This study quantitatively compared these approaches in terms of surgical exposure and maneuverability.METHODSEach of the 4 approaches was performed in 4 cadaveric heads (8 specimens in total). A 6-sided anatomical polygonal region was configured over the cisternal pulvinar, defined by 6 reachable anatomical points in different vectors. Multiple polygons were subsequently formed to calculate the areas of exposure. The surgical freedom of each approach was calculated as the maximum allowable working area at the proximal end of a probe, with the distal end fixed at the posterior pole of the pulvinar. Areas of exposure, surgical freedom, and the working distance (surgical depth) of all approaches were compared.RESULTSNo significant difference was found among the 4 different approaches with regard to the surgical depth, surgical freedom, or medial exposure area of the pulvinar. In the pairwise comparison, the cSCIT approach provided a significantly larger lateral exposure (39 ± 9.8 mm2) than iSCIT (19 ± 10.3 mm2, p < 0.01), iOCTT (19 ± 8.2 mm2, p < 0.01), and cOCTF (28 ± 7.3 mm2, p = 0.02) approaches. The total exposure area with a cSCIT approach (75 ± 23.1 mm2) was significantly larger than with iOCTT (43 ± 16.4 mm2, p < 0.01) and iSCIT (40 ± 20.2 mm2, p = 0.01) approaches (pairwise, p ≤ 0.01).CONCLUSIONSThe cSCIT approach is preferable among the 4 compared approaches, demonstrating better exposure to the cisternal pulvinar than ipsilateral approaches and a larger lateral exposure than the cOCTF approach. Both contralateral approaches described (cSCIT and cOCTF) provided enhanced lateral exposure to the pulvinar, while the cOCTF provided a larger exposure to the lateral portion of the pulvinar than the iOCTT. Medial exposure and maneuverability did not differ among the approaches. A short tentorium may negatively impact an ipsilateral approach because the cingulate isthmus and parahippocampal gyrus tend to protrude, in which case they can obstruct access to the cisternal pulvinar ipsilaterally.

MR texture analysis in differentiating renal cell carcinoma from lipid-poor angiomyolipoma and oncocytoma

Objectives: To assess the utility of magnetic resonance texture analysis (MRTA) in differentiating renal cell carcinoma (RCC) from lipid-poor angiomyolipoma (lpAML) and oncocytoma. Methods: After ethical approval, 42 patients with 54 masses (34 RCC, 14 lpAML and six oncocytomas) who underwent MRI on a 1.5 T scanner (Avanto, Siemens, Erlangen, Germany) between January 2011 and December 2012 were retrospectively included in the study. MRTA was performed on the TexRAD research software (Feedback Plc., Cambridge, UK) using free-hand polygonal region of interest (ROI) drawn on the maximum cross-sectional area of the tumor to generate six first-order statistical parameters. The Mann-Whitney U test was used to look for any statically significant difference. The receiver operating characteristic (ROC) curve analysis was done to select the parameter with the highest class separation capacity [area under the curve (AUC)] for each MRI sequence. Results: Several texture parameters on MRI showed high-class separation capacity (AUC > 0.8) in differentiating RCC from lpAML and oncocytoma. The best performing parameter in differentiating RCC from lpAML was mean of positive pixels (MPP) at SSF 2 (AUC: 0.891) on DWI b500. In differentiating RCC from oncocytoma, the best parameter was mean at SSF 0 (AUC: 0.935) on DWI b1000. Conclusions: MRTA could potentially serve as a useful non-invasive tool for differentiating RCC from lpAML and oncocytoma. Advances in knowledge: There is limited literature addressing the role of MRTA in differentiating RCC from lpAML and oncocytoma. Our study demonstrated several texture parameters which were useful in this regard.

Geometric Model for Generation of Contour- Parallel Lines’ Family for Cutting Tool’s Path Automated Computation

In this paper has been proposed a geometric model for forming problem of contour-parallel lines (equidistant lines) for a flat contour with an island, and has been obtained the problem’s analytical solution, which is relevant for computer-aided design of cutting tools processing pocket surfaces on CNC machines. The proposed geometric model is based on cyclograph mapping of space on a plane. Beyond the analytical solution the geometric model differs from the known algebraic models and their solutions for considered forming problem also by the fact that it allows obtain a more complete and evident representation on the relationship and interaction for all its geometric components at the stages of 3D computer visualization. A 3D geometric model based on a cyclograph mapping of space has been proposed for obtaining the families of equidistant lines for connected and multiply connected regions with closed contours taken as a basis for pocket surfaces modeling. An algorithm for the analytical solution of the problem related to equidistant families generation is getting from the geometric model. All stages of the analytical solution are accompanied by a figurative representation of geometric objects and their relations in the geometric model’s virtual electronic space. The proposed in this paper algorithm for the case of a doubly connected polygonal region can be used as a basis for generation of equidistant families for multiply connected polygonal regions. The presence of the analytical solution for the problem related to equidistant families generation simplifies greatly the automated calculation of the tool path and preparation of control programs for pocket surfaces manufacturing on CNC machines. Have been presented an example and algorithm providing support for working capacity of the proposed geometric model for considered forming problem.