Novel Method to Reconstruct a Surface Grid Using Linear Regression Modelling

Abstract

The main focus of this report is to explore methods to laser scan objects by mapping the locations of the scanned pixels into real-world coordinates through an algorithm with the use of a projected laser plane. This report presents two different approaches: A simplified method to laser-assisted 3D scanning using Geometrical Relations and a proposed Linear Regression Models method that was based on the simplified one and compares the differences between the two. The general form of the regression models was chosen after observation of the main mathematical constructs used in the stack model and plane model of the line-based laser triangulation method. These geometrical concepts, utilizing mainly the equations and intersections of lines and planes were inspiration for the regression model. The process follows that a laser plane is generated using a laser diode and cylindrical lens and cast onto an object. After taking images of the object at different angles, image analysis is carried out using Python 2 and OpenCV2. Then, the Linear Regression Models are trained with pre-existing data before making predictions while the Geometric Relations method uses the measurements of the mechanism in the equipment to map the red pixel location detected in the images to the point cloud of the object.

Appendix: Similar triangle