Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using quaternions for coding 3D transformations
Graphics gems
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
General Construction of Time-Domain Filters for Orientation Data
IEEE Transactions on Visualization and Computer Graphics
CA '96 Proceedings of the Computer Animation
PDE-based filtering of motion sequences
Journal of Computational and Applied Mathematics
IEEE Transactions on Image Processing
Nonlinear multiscale analysis of motion trajectories
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part I
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Information about the rotation of an object can be described by different representations, e.g. Euler angles, rotation matrices or quaternions. The latter representation is being intensively exploited in many applications, because of the compact description and interesting properties. In the paper the filtering method for rotational trajectories is proposed. We generalize anisotropic diffusion process defined for two dimensional images, taking into consideration specific properties of rotational motion. Filtering of trajectories in Euclidean space has already been researched in detail using different approaches. However, the straightforward application of well known filtering methods for the rotational space fails to produce appropriate results. We propose a new algorithm for processing trajectories directly in four dimensional space of unit quaternions. In the paper practical examples of the process, theoretical properties and numerical evaluation of the algorithm are presented.