Statistical solution of 3D transformation problem

Abstract

Obtaining the 3D model of an object is currently one of the most important issues that image processing is dealing with. Measurement of the points on 3D objects requires different scans from different positions in different coordinate systems. At our disposal are measured coordinates of an identical point, which can be obtained from a laser 3D scanner, depth sensor, or any motion input device as Microsoft Kinect. A point whose coordinates are known in both coordinate systems is called an identical point. Data transformation of identical points from one coordinate system to another coordinate system is therefore required. The aim of this contribution is to present a possible approach on how to estimate the unknown transformation parameters by regression models in a special transformation problem. This transformation in its standard version has been derived under the assumption that non-negligible random errors occur at points of that coordinate system into which the transformation is performed. Points of the inverse image coordinate system are assumed to be errorless.