Constrained Dynamic Mode Decomposition.

Frequency-based decomposition of time series data is used in many visualization applications. Most of these decomposition methods (such as Fourier transform or singular spectrum analysis) only provide interaction via pre- and post-processing, but no means to influence the core algorithm. A method that also belongs to this class is Dynamic Mode Decomposition (DMD), a spectral decomposition method that extracts spatio-temporal patterns from data. In this paper, we incorporate frequency-based constraints into DMD for an adaptive decomposition that leads to user-controllable visualizations, allowing analysts to include their knowledge into the process. To accomplish this, we derive an equivalent reformulation of DMD that implicitly provides access to the eigenvalues (and therefore to the frequencies) identified by DMD. By utilizing a constrained minimization problem customized to DMD, we can guarantee the existence of desired frequencies by minimal changes to DMD. We complement this core approach by additional techniques for constrained DMD to facilitate explorative visualization and investigation of time series data. With several examples, we demonstrate the usefulness of constrained DMD and compare it to conventional frequency-based decomposition methods.

Unsupervised and Generic Short-Term Anticipation of Human Body Motions.

Various neural network based methods are capable of anticipating human body motions from data for a short period of time. What these methods lack are the interpretability and explainability of the network and its results. We propose to use Dynamic Mode Decomposition with delays to represent and anticipate human body motions. Exploring the influence of the number of delays on the reconstruction and prediction of various motion classes, we show that the anticipation errors in our results are comparable to or even better for very short anticipation times ( < 0 . 4 sec) than a recurrent neural network based method. We perceive our method as a first step towards the interpretability of the results by representing human body motions as linear combinations of previous states and delays. In addition, compared to the neural network based methods large training times are not needed. Actually, our methods do not even regress to any other motions than the one to be anticipated and hence it is of a generic nature.

Cloth Animation Retrieval Using a Motion-Shape Signature.

In cloth simulation, the behavior of textiles largely depends on initial conditions, parameters, and simulation techniques. Usually, several combinations of those aspects are altered until a simulation setting is found to create a satisfying animation. However, if an initial condition, such as a collision object, is changed afterward or the cloth behavior is transferred to a different scene, the existing set of simulation parameters could no longer be suitable for the desired look. In this case, it is difficult to find a new configuration by changing parameters manually and to determine if it conforms the desired properties. This article introduces a feature vector that is used as a motion-shape signature to capture the spatiotemporal shape characteristics of cloth and can be applied as a similarity measure for physics-based cloth animations.