Shape Reconstruction of Fleible Objects via the Evaluation of Tensor Fields

Sensor technologies for geometrical shape extraction currently represent an important field of research. In particular the sensor application in medical technology requires high sensing accuracy and robustness. In the scope of this project, new algorithms for of shape sensing are developed and evaluated. Shape reconstruction algorithms are commonly based on the processing of strain values, measured along the observed objects. All known algorithms are valid only under certain restrictions concerning the positions, in which the strain values are measured. This restrictions lead to shape results that are not suficient for the field of application, as complex deformation cannot be detected robustly. Therefore, a new algorithm is developed, that can be applied more generally concerning the position of the strain-measurement units. The main idea is to consider the measurement units as sensor network with arbitrary but consistent position. The measured data is represented as a discrete tensor field. A continuous field is generated via interpolation, while the interpolation is determined by the material and deformation characteristics. This new approach for shape reconstruction allows the reconstruction not only for one dimensional shapes as object axis but also two dimensional or even three dimensional shapes as surfaces or three-dimensional bodies.