Optimization of road networks is a common concern worldwide, primarily for safety purposes. Because the extent of these networks is substantial, automation of their inventory is highly desirable. This paper concentrates on the road inventory process that is necessary for regular maintenance. The key part of our road marking detection and reconstruction is based on spanning tree usage. The spanning trees are obtained from alpha shapes of the detected road markings. The spanning trees application enables the reliable identification of the road markings and precise reconstruction of their contours even with noisy data. Our method processes the point cloud data obtained from LiDAR measurements, and provides a common vector layer with road lane polygons. Such a vector layer is stored in a common file format supported by the majority of geographical information systems, thus producing an output that can be conveniently used for decision-making based on the road inventory process.

Three-dimensional (3-D) reconstruction is an indispensable tool in areas such as biology, chemistry, medicine, material sciences, etc. The sample can be reconstructed using confocal or nonconfocal mode of a microscope. The limitation of the confocal approach is the sample size. Currently used devices work mostly with sample surface area up to 1 cm2. We suggest a three-step method that creates 3-D reconstruction from multifocal images in nonconfocal mode that is qualitatively comparable to the confocal results. Our method, thus, takes advantage of both microscope modes—high-quality results without sample size limitation. The preprocessing step eliminates the additive noise with Linderberg-Lévi theorem. The main focus criterion is based on adjusted Fourier transform. In the final step, we eliminate the defective clusters using the adaptive pixel neighborhood algorithm. We proved the effectiveness of our noise reduction and 3-D reconstruction method by the statistical comparisons; the correlation coefficients average 0.987 for all types of Fourier transforms.

Industry 4.0 comprises a wide spectrum of developmental processes within the management of manufacturing and chain production. Presently, there is a huge effort to automate manufacturing and have automatic control of the production. This intention leads to the increased need for high-quality methods for digitization and object reconstruction, especially in the area of reverse engineering. Commonly used scanning software based on well-known algorithms can correctly process smooth objects. Nevertheless, they are usually not applicable for complex-shaped models with sharp features. The number of the points on the edges is extremely limited due to the principle of laser scanning and sometimes also low scanning resolution. Therefore, a correct edge reconstruction problem occurs. The same problem appears in many other laser scanning applications, i.e., in the representation of the buildings from airborne laser scans for 3D city models. We focus on a method for preservation and reconstruction of sharp features. We provide a detailed description of all three key steps: point cloud segmentation, edge detection, and correct B-spline edge representation. The feature detection algorithm is based on the conventional region-growing method and we derive the optimal input value of curvature threshold using logarithmic least square regression. Subsequent edge representation stands on the iterative algorithm of B-spline approximation where we compute the weighted asymmetric error using the golden ratio. The series of examples indicates that our method gives better or comparable results to other methods.

The 3D reconstruction of simple structured materials using a confocal microscope is widely used in many different areas including civil engineering. Nonetheless, scans of porous materials such as concrete or cement paste are highly problematic. The well-known problem of these scans is low depth resolution in comparison to the horizontal and vertical resolution. The degradation of the image depth resolution is caused by systematic errors and especially by different random events. Our method is focused on the elimination of such random events, mainly the additive noise. We use an averaging method based on the Lindeberg-Lévy theorem that improves the final depth resolution to a level comparable with horizontal and vertical resolution. Moreover, using the least square method, we also precisely determine the limit value of a depth resolution. Therefore, we can continuously evaluate the difference between current resolution and the optimal one. This substantially simplifies the scanning process because the operator can easily determine the required number of scans.

This paper discusses new methods for 3-D processing of confocal microscope outputs - single optical cuts through an explored object. The method can model cell illumination by an external light source and is a next important step in the realist...

NURBS (Non-Uniform Rational B-Splines) belong to special approximation curves and surfaces which are described by control points with weights and B-spline basis functions. They are often used in modern areas of computer graphics as free-form modelling, modelling of processes. In literature, NURBS surfaces are often called tensor product surfaces. In this article we try to explain the relationship between the classic algebraic point of view and the practical geometrical application on NURBS.