Building Polygon Extraction from Aerial Images and Digital Surface Models with a Frame Field Learning Framework

Deep learning-based models for building delineation from remotely sensed images face the challenge of producing precise and regular building outlines. This study investigates the combination of normalized digital surface models (nDSMs) with aerial images to optimize the extraction of building polygons using the frame field learning method. Results are evaluated at pixel, object, and polygon levels. In addition, an analysis is performed to assess the statistical deviations in the number of vertices of building polygons compared with the reference. The comparison of the number of vertices focuses on finding the output polygons that are the easiest to edit by human analysts in operational applications. It can serve as guidance to reduce the post-processing workload for obtaining high-accuracy building footprints. Experiments conducted in Enschede, the Netherlands, demonstrate that by introducing nDSM, the method could reduce the number of false positives and prevent missing the real buildings on the ground. The positional accuracy and shape similarity was improved, resulting in better-aligned building polygons. The method achieved a mean intersection over union (IoU) of 0.80 with the fused data (RGB + nDSM) against an IoU of 0.57 with the baseline (using RGB only) in the same area. A qualitative analysis of the results shows that the investigated model predicts more precise and regular polygons for large and complex structures.

Calculation of the Shaping of a Space Umbrella Antenna During Strong Bending of Radial Rods Connected Along Parallels by Tensile Cables

Abstract— A cyclically symmetric umbrella antenna is considered, the frame of which consists of flexible inextensible radial rods connected in nodes along parallels by tensile cables. In the initial transport position, the multilink rods are packed in packages oriented in the direction of the system axis. After the packing ties are removed, the rods are deployed in radial planes under the action of elastic springs connecting the links, and are fixed in rectilinear positions at a given angle with respect to the axis, at which all cables connecting the same type of rod nodes take the form of regular polygons, while remaining loose. Further, under the action of the force of a damping hydraulic cylinder with pre-compressed springs, the root parts of all rods are slowly turned to the stops. In the final position, the radial rods, connected at the nodes by tensioned cables, take a curved shape. The tensile stiffnesses of the cables are determined so that the radial and axial coordinates of the nodes of the curved rods coincide with the coordinates of the points of the given surface of revolution. A model of strong bending of a flexible inextensible rod is constructed taking into account the unknown radial reactions of tensioned cables acting on it at the nodes. The links of the rod are considered as “cantilever” elements connected in series at the nodes in local coordinate systems, which can make large displacements and turns. The bending of each element is described by two specified functions, the shrinkage of the element due to bending is taken into account in a quadratic approximation. The obtained nonlinear deformation equations of the system, taking into account the geometric connections at the nodes, are solved by the method of successive approximations with respect to the unknown reactions of the cables. The obtained values of the reactions are then used to determine the required tensile stiffness of the cables at the given coordinates of the nodes. As an example of the calculation, a parabolic antenna is considered for various numbers of radial rods and components of links. The estimates of the accuracy of the proposed computational model of the antenna shaping are carried out.

Torsional rigidity for regular polygons

We present a simple lower bound for the torsional rigidity of a beam with regular polygonal cross-section. The methods used are applicable to other cross-sections, in particular to other tangential polygons.

Metallic Ratios in Primitive Pythagorean Triples : Metallic Means embedded in Pythagorean Triangles and other Right Triangles

The Primitive Pythagorean Triples are found to be the purest expressions of various Metallic Ratios. Each Metallic Mean is epitomized by one particular Pythagorean Triangle. Also, the Right Angled Triangles are found to be more “Metallic” than the Pentagons, Octagons or any other (n2+4)gons. The Primitive Pythagorean Triples, not the regular polygons, are the prototypical forms of all Metallic Means.