Tucker decomposition with a temporal regularization for gap recovery in 3D motion capture data

• We propose two gap-filling algorithms based Tucker decomposition, namely Tucker and TuckerTNN for motion capture recovery. • TuckerTNN incorporates temporal nuclear norm as an efficient alternative to traditional smoothness regularization, leveraging the natural temporal continuity in motion capture data. • Both Tucker and TuckerTNN algorithms consistently outperform existing CP-based methods across all evaluation metrics (RMSE, AvE, STD) on HDM05 dataset sequences. • We demonstrate superior performance across varying gap lengths (100-200 frames), multiple gap scenarios (2-10 gaps per marker), and different motion types (locomotion, gestures, complex movements). The gap-filling problem in motion capture (MoCap) data poses a significant challenge in marker-based MoCap systems. These gaps occur due to missing markers during motion recording. MoCap sequence, a time series data characterized by high dimensionality and temporal dependencies, requires accurate recovery of missing markers to ensure smooth motion representation. Tensor decomposition is an effective solution that leverages the multi-way structure of MoCap data. This paper proposes two gap-filling algorithms based on Tucker decomposition, namely Tucker and TuckerTNN. Given the high-dimensional nature of MoCap data, traditional smoothness regularization methods, such as gradient-based techniques, are computationally expensive. Therefore, we introduce the temporal nuclear norm in TuckerTNN as an alternative regularization technique, providing a more efficient solution for large-scale datasets. Both models are minimized using the proximal block coordinate descent (Prox-BCD) method. We evaluated the proposed algorithms using motion capture sequences from the publicly available HDM05 dataset. Our results show that Tucker and TuckerTNN consistently outperform existing approaches, such as CP and SparseCP, in accuracy and efficiency, with TuckerTNN offering the best trade-off between the two.