Imagebased finite element analysis
Numerical analysis of objects without the necessity of geometric recovery and mesh generation
Setting
The reconstruction of threedimensional objects from images is a widely applied approach in many engineering fields. The main goal of these techniques is to transform the pixel data that are available in the images into a–potentially application dependent–threedimensional representation. Apart from standard applications, there has been an increasing interest towards methods that provide threedimensional geometric representations which are suitable for numerical analysis by means of the Finite Element Method (FEM). The research conducted at the chair for Computation in Engineering addresses the possibilities of coupling photobased shape measurement techniques to FEM and its derivatives, e.g. the Finite Cell Method.
Imagebased finite elements: the standard approach
Traditional approaches employ a multistage procedure which progressively transforms the pixel data in the images of a given object towards an analysissuitable highorder finite element mesh (see Figure below). The goal of generating a mesh of high order elements is motivated by the superior approximation properties of pFEM compared to standard, linear finite elements, especially for smooth problems. Such problems arise for example in the field of biomechanics, especially in the study of the biomechanical behaviour of soft human tissues [1].
Point cloudbased Finite Cell Method
Since mesh generation represents a severe bottleneck in the complete analysis pipeline, alternative approaches, like the Finite Cell Method (FCM) may be applied. In its simplest implementation, the only information that the FCM needs from the analysis geometry is point membership information: given a point in space, does this point belong to the geometry of interest or not?
In the context of shape measurement techniques, the point clouds stemming from photogrammetric algorithms are equipped with normal vectors: they carry information about the orientation of the local tangent plane associated to the given point. This information is precisely enough to carry out the necessary point membership tests required by the FCM.
To determine whether a given query point q is located within the geometric model or not, the following steps are performed:

Find the point p_{i} and its associated normal vector n_{i} that lies closest to q.

Evaluate

If d < 0, then q lies outside the domain. Otherwise, it lies inside.
The possibility to perform insideoutside queries directly on the pointcloud representation of the geometric model allows for significant simplifications in the imagetoanalysis pipeline: the steps for recovering a geometric model and the generation of an analysissuitable mesh become unnecessary, making the whole procedure easier. This way, a seamless connection between imagebased shape measurements and numerical analyses can be established.
Example: static analysis of the statue “Athlete” from the Glyptothek, Munich
The statue was recorded by a commercial cellphone camera and processed by VisualSFM, an open source StructureFromMotion software. The results depict the deformation and stresses of the statue under its self weight.
Publications
[1] Kudela, L., Frischmann, F., Yossef, O.E., Kollmannsberger, S., Yosibash, Z. and Rank, E., 2018. Imagebased mesh generation of tubular geometries under circular motion in refractive environments. Machine Vision and Applications, 29(5), pp.719733.

[2] Kudela, L., Kollmannsberger, S. and Rank, E., An immersed boundary approach for the numerical analysis of objects represented by oriented point clouds. In: COMPIMAGE '18, International Symposium on Computational Modeling of Objects Presented in Images, Cracow, Poland 
[3]  In: EUROMED 2018: International Conference on Digital Heritage, Cyprus, 2018