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.

Slant Helices of (k,m)-Type According to the ED-Frame in Minkowski 4-Space

In differential geometry, relations between curves are a large and important area of study for many researchers. Frame areas are an important tool when studying curves, specially the Frenet–Serret frame along a space curve and the Darboux frame along a surface curve in differential geometry. In this paper, we obtain slant helices of k-type according to the extended Darboux frame (or, for brevity, ED-frame) field by using the ED-frame field of the first kind (or, for brevity, EDFFK), which is formed with an anti-symmetric matrix for ε1=ε2=ε3=ε4∈{−1,1} and the ED-frame field of the second kind (or, for brevity, EDFSK), which is formed with an anti-symmetric matrix for ε1=ε2=ε3=ε4∈{−1,1} in four-dimensional Minkowski space E14. In addition, we present some characterizations of slant helices and determine (k,m)-type slant helices for the EDFFK and EDFSK in Minkowski 4-space.

EXPERIMENTAL ASSESSMENT OF THE EFFECT OF EXPOSURE LEVEL ON THE RESOLUTION OF A DIGITAL PHOTOGRAPHIC SYSTEM

While photographing in a wide range of brightness within the frame, the exposure devices must provide exposure control for each elementary area of ​​the frame, i.e., provide local exposure control. Cameras which equipped by well-known exposure devices with local exposure control is used a multiplicative, additive or multifunction method of image recording. Using of the multiplicative method leads to energy losses in the optical channel, which requires correction of the exposure control parameters. Using of the additive method makes it possible to reduce the effective shutter speed, but reduces the contrast of small images. The multiplicative method of image registration allows to suppress low-informative low-frequency components of the spectrum of the input signal, providing less losses from the image blur according to the multiplicative method and less losses from reducing the contrast of images of small parts according to the additive method. Comparative evaluation of cameras’ effectiveness which are equipped by exposure devices with local exposure control, which are based on different methods of image registration, is convenient to assess the criterion of "resolution averaged over the frame field". According to the developed methodology of evaluating the effectiveness of this type of cameras, the averaged field resolution can be calculated in several ways, each of which assumes a preliminary calculation or obtaining the dependence of resolution from exposure (resolvometric characteristics of the camera). The methodology of experimental determination of the resolvometric characteristic of a photographic image recorder equipped by exposure devices of local exposure control is proposed. This methodology is illustrated by the example of measuring the resolvometric characteristics of the digital camera nex-6 for different external conditions. The good convergence of results of theoretical and experimental researches is shown. The proposed methodology can be used in studies of the impact of the process of the multifunction method of image recording on the photographing efficiency. Keywords: image; resolution; measure; camera

BUILDING OUTLINE EXTRACTION FROM AERIAL IMAGERY AND DIGITAL SURFACE MODEL WITH A FRAME FIELD LEARNING FRAMEWORK

Deep learning-based semantic segmentation models for building delineation face the challenge of producing precise and regular building outlines. Recently, a building delineation method based on frame field learning was proposed by Girard et al. (2020) to extract regular building footprints as vector polygons directly from aerial RGB images. A fully convolution network (FCN) is trained to learn simultaneously the building mask, contours, and frame field followed by a polygonization method. With the direction information of the building contours stored in the frame field, the polygonization algorithm produces regular outlines accurately detecting edges and corners. This paper investigated the contribution of elevation data from the normalized digital surface model (nDSM) to extract accurate and regular building polygons. The 3D information provided by the nDSM overcomes the aerial images’ limitations and contributes to distinguishing the buildings from the background more accurately. Experiments conducted in Enschede, the Netherlands, demonstrate that the nDSM improves building outlines’ accuracy, resulting in better-aligned building polygons and prevents false positives. The investigated deep learning approach (fusing RGB + nDSM) results in a mean intersection over union (IOU) of 0.70 in the urban area. The baseline method (using RGB only) results in an IOU of 0.58 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.

Nonlinear Dynamics of Heavy Structures

At the moment, not enough attention is paid to different aspects of nonlinear dynamics for heavy structures. In this article we attempt to create a mathematical model for finding a frame (field) with predictable dynamic pattern of load-carrying capability for a heavy structure based оn the parameters of its reliable (failure-free, low-risk) operation. It is difficult to find a solution for this problem now but the following algorithm can be applied. Small dimension projection is first obtained for orthonormal vectors determining the structural load-carrying capability. Then we use available methods to find a field where any relationship (functional, logical) can be obtained between the rules (wild cards) and the load-carrying capability displayed by a heavy structure. This article carries on the cycle of activities on structural risk analysis involving heavy structures. Numerical and calculated data are based on previous studies. The analysis is performed on a metallurgical overhead crane. The obtained findings are used for adopting various engineering solutions at different stages of heavy structure operation.

Contact Kinematics between Three-Dimensional Rigid Bodies with General Surface Parameterization

This paper provides an improvement of the classic Montana's contact kinematics equations considering non-orthogonal object parameterizations. In Montana's model, the reference frame used to define the relative motion between two rigid bodies in three-dimensional space is chosen as the Gauss frame, assuming there is an orthogonal coordinate system on the object surface. To achieve global orthogonal parameterizations on arbitrarily shaped object surfaces, we define the relative motion based on the reference frame field, which is the orthogonalization of the surface natural basis at every contact point. The first- and second-order contact kinematics, including the velocity and acceleration analysis of the relative rolling, sliding, and spinning motion, are reformulated based on the reference frame field and the screw theory. We use two simulation examples to illustrate the proposed method. The examples are based on simple non-orthogonal surface parameterizations, instead of seeking for global orthogonal parameterizations on the surfaces.