Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.Comment: 41 pages, single column, 10 figure

Markerless motion capture for 3D human model animation using depth camera

3D animation is created using keyframe based system in 3D animation software such as Blender and Maya. Due to the long time interval and the need of high expertise in 3D animation, motion capture devices were used as an alternative and Microsoft Kinect v2 sensor is one of them. This research analyses the capabilities of the Kinect sensor in producing 3D human model animations using motion capture and keyframe based animation system in reference to a live motion performance. The quality, time interval and cost of both animation results were compared. The experimental result shows that motion capture system with Kinect sensor consumed less time (only 2.6%) and cost (30%) in the long run (10 minutes of animation) compare to keyframe-based system, but it produced lower quality animation. This was due to the lack of body detection accuracy when there is obstruction. Moreover, the sensor’s constant assumption that the performer’s body faces forward made it unreliable to be used for a wide variety of movements. Furthermore, standard test defined in this research covers most body parts’ movements to evaluate other motion capture system

Cost-effective quaternion minimum mean square error estimation:From widely linear to four-channel processing

Widely linear estimation plays an important role in quaternion signal processing, as it caters for both proper and improper quaternion signals. However, widely linear algorithms are computationally expensive owing to the use of augmented variables and statistics. To reduce the computation cost while maintaining the performance level, we propose a four-channel estimation framework as an efficient alternative to quaternion widely linear estimation. This is achieved by using four linear models to estimate the four components of quaternion signals. We also show that any of the four channels is able to replace a strictly linear quaternion estimator when estimating strictly linear systems. The proposed method is shown to reduce computational complexity and provide more flexible algorithms, while preserving the physical meaning inherent in the quaternion domain. The proposed framework is next applied to quaternion minimum mean square error estimation to yield the reduced-complexity versions of the quaternion least mean square (QLMS), quaternion recursive least squares (QRLS), and quaternion nonlinear gradient decent (QNGD) algorithms. For the proposed QLMS algorithm, an adaptive step-size strategy is also explored. The effectiveness of the so introduced estimation techniques is validated by simulations on synthetic and real-world signals