Euclidian Distance Transformation, Main Axis Rotation and Noisy Dilitation Supported Cross-Section Classification With Convolutional Neural Networks

Abstract

Polygon meshes and particularly triangulated meshes can be used to describe the shape of different types of geometry such as bicycles, bridges, or runways. In engineering, such polygon meshes can be supplied as finite element meshes, resulting from topology optimization or from laser scanning. Especially from topology optimization, frame-like polygon meshes with slender parts are typical and often have to be converted into a CAD (Computer-Aided Design) format, e.g., for further geometrical detailing or performing additional shape optimization. Especially for such frame-like geometries, CAD designs are constructed as beams with cross-sections and beam-lines, whereby the cross-section is extruded along the beam-lines or beam skeleton. One major task in the recognition of beams is the classification of the cross-section type such as I, U, or T, which is addressed in this article. Therefore, a dataset consisting of different cross-sections represented as binary images is created. Noisy dilatation, the distance transformation, and main axis rotation are applied to these images to increase the robustness and reduce the necessary amount of samples. The resulting images are applied to a convolutional neuronal network.

Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections

“…In addition to the numerical calculation of spline cross-sections, alternative geometric representations such as a polygon or an image can also be used. The moments of binary images were investigated several article such as [27], [28]. By summing up the single pixels to a rectangle, the area can be calculated and considering Steiner's theorem and the center of area, the second moments of area can be calculated with…”

Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections

“…The parametric representation of various shapes and topologies has been discussed in various articles for simple polygons as common cross-section types [16,17] and also for more complex topologies consisting of multiple polygons such as hexagonal networks [18,19]. The knot positions of these for one or several polygons can be considered as control points for tensor product splines.…”

“…In addition to the numerical calculation of spline cross-sections, alternative geometric representations such as a polygon or an image can also be used. The moments of binary images were investigated in several articles such as [16,38]. By summing up the single pixels to a rectangle, the area can be calculated by considering Steiner's theorem and the center of area, and the second moments of area can be calculated with the following equations [16]:…”

“…The moments of binary images were investigated in several articles such as [16,38]. By summing up the single pixels to a rectangle, the area can be calculated by considering Steiner's theorem and the center of area, and the second moments of area can be calculated with the following equations [16]:…”