Quaternion fourier transform for character motions

The Fourier transform plays a crucial role in a broad range of signal processing applications, including enhancement, restoration, analysis, and compression. Since animated motions comprise of signals, it is no surprise that the Fourier transform has been used to filter animations by transforming joint signals from the spatial domain to the frequency domain and then applying filtering masks. However, in this paper, we filter motion signals by means of a new approach implemented using hyper-complex numbers, often referred to as Quaternions, to represent angular joint displacements. We use the novel quaternion Fourier transform (QFT) to perform filtering by allowing joint motions to be transformed as a 'whole', rather than as individual components. We propose a holistic Fourier transform of the joints to yield a single frequency-domain representation based on the quaternion Fourier coefficients. This opens the door to new types of motion filtering techniques. We apply the concept to the frequency domain for noise reduction of 3-dimensional motions. The approach is based on obtaining the QFT of the joint signals and applying Gaussian filters in the frequency domain. The filtered signals are then reconstructed using the inverse quaternion Fourier transform (IQFT).