Principal component analysis (PCA) is commonly used in the fields of computer graphics and geometry processing for constructing subspaces that represent the variability present in a dataset. Examples of such datasets are configurations of a non-rigid object, poses of a deformable character or snapshots from a simulation. By applying PCA to the dataset, one can generate a lower-dimensional space in which the data samples can be approximated well. Similar to PCA, one can also apply a sparse PCA technique to the geometric data. These methods aim to find components that do not only describe the deformations present in the data well, but are also sparse and localized.

One of the problems related to PCA and sparse PCA is that they do not take the correlation between the x, y and z coordinates of each vertex into account when constructing the subspace. Furthermore, the methods are not invariant to rigid motion (rotations and translations) of the data samples, which means that rigid registration has to often be applied to the samples as a preprocessing step. Ideally, we would like to construct a subspace that is invariant to these rigid motions.

This project investigates whether quaternions can be used to solve these problems. By describing each vertex as a pure quaternion, we show how quaternion PCA can be applied to geometric data and introduce a quaternion method of snapshots for improved computational efficiency. Additionally, we derive multiple quaternion sparse PCA techniques, which are inspired by the Sparse Localized Deformation Components (SPLOCS) method. Experimental results show that the quaternion PCA and sparse PCA methods are able to describe a richer space of deformations using fewer components. Furthermore, we show that quaternion PCA leads to improved rigid motion invariance.

bunq is an internationally active digital bank. At the moment, the bunq app is only available in English, Dutch, German, Italian and Spanish. Their goal is to be a worldwide player. To be able to fulfil this goal, their app should be available in multiple languages. In the past, the translation process took an unnecessary large amount of time. Due to this inefficiency in the process, the client, bunq, gave the team an assignment to create an application which helps to decrease the workload and time spent on translating. The application should solve the following issues: (1) translating the strings is time-consuming; (2) developers lose time by having to copy and paste the strings into the code; (3) inconsistency mistakes between the apps are made when inserting the strings into the code; (4) translations might be incorrect; (5) fluent speakers are needed for each language.
The final product is a web application that solves the main issues of decreasing the workload and time spent on translating.