Multiple motions

We first studied multiple overlaid motions in the context of vision science as an extension of research on intrinsic dimension (Zetzsche & Barth, 1990) and visual motion selectivity (Barth & Watson, 2000). Initially, the research on multiple motions was supported by the DAAD grant A/99/22641 to Cicero Mota, who came to visit us from the University of Amazonas in Brazil. We worked out an analytical solution for the problem of estimating transparent motion layers (Mota et al., 2001). The solution is based on a nontrivial linearization of the nonlinear problem. We also performed experiments related to the perception of multiple motion layers (Barth et al., 2001; Mota et al., 2004) and we could predict the ability of human observers to detect the number of motion layers. We argued that detection is limited by the angular separation of the velocities of the layers.

Subsequent research was supported by the DFG - see LOCOMOTOR page - and focused on the mathematical and technical aspects of the problem. We first generalized our approach to include more robust regularization (Stuke et al., 2003) and block-matching (Stuke et al., 2003) techniques. We then extended our analysis to the case of occluded motions (Barth et al., 2003; Mota et al., 2005) and more complex patterns (Scharr et al., 2005). Then we went back to the more basic issue of estimating multiple orientations (Mota et al., 2004; Aach et al., 2006). We then succeeded in solving the more general problem of how to simulteanusly detect and estimate N subspaces (in images this would be orientations and in movies motions) for signals of any dimension (Stuke et al., 2006). This allows us, for example, to estimate an arbitrary number of overlaid orientations in any dimension. Finally, we have shown how to extent the approach to multispectral images (Mota et al., 2006).

Selected publications

• Zetzsche, C. & Barth, E. (1990). Fundamental limits of linear filters in the visual processing of two-dimensional signals. Vision Research, Vol. 30, 1111-1117.
• Barth, E. & Watson, A. B. (2000) A geometric framework for nonlinear visual coding. Optics Express Vol. 7. No. 4, 155-165.   pdf
• Barth, E., Dorr, M., Stuke, I., & Mota C. (2001). Theory and some data for up to four transparent motions. Perception, 30 (Supplement):36.
• Mota, C., Dorr, M., Stuke, I., & Barth, E. (2004). Categorization of Transparent-Motion Patterns Using the Projective Plane. International Journal of Computer & Information Science, Vol. 5, No. 2: 129-140.   pdf
• Mota, C., Stuke, I, & Barth, E. (2001). Analytic solutions for multiple motions. IEEE International Conference on Image Processing, Vol. II, 917-920.   pdf
• I. Stuke, T. Aach, C. Mota, and E. Barth (2003). Estimation of multiple motions: regularization and performance evaluation. In B. Vasudev, T. R. Hsing, A. G. Tescher, and T. Ebrahimi, editors, Image and Video Communications and Processing 2003, Proceedings of SPIE, volume 5022, pages 75-86.   pdf
• Ingo Stuke, Til Aach, Erhardt Barth, and Cicero Mota (2003). Estimation of Multiple Motions by Block Matching. In W. Dosch and R. Y. Lee, editors, Proceedings of the ACIS 4th International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD'03), Lübeck, Germany, October 16-18, 2003, pages 358-62.   pdf
• Barth, E., Stuke, I., Aach, T., & Mota, C. (2003). Spatio-Temporal Motion Estimation for Transparency and Occlusions. Proceedings of IEEE International Conference on Image Processing, Vol. III, 69-72.   pdf
• C. Mota, I. Stuke, T. Aach, and E. Barth (2005). Spatial and spectral analysis of occluded motions. Signal Processing: Image Communication. Elsevier Science, 20-6:529-536.   pdf
• H. Scharr, I. Stuke, C. Mota, and E. Barth (2005). Estimation of Transparent Motions with Physical Models for Additional Brightness Variation. In European Signal Pocessing Conference.   pdf
• C. Mota, T. Aach, I. Stuke, and E. Barth (2004). Estimation of multiple orientations in multi-dimensional signals. In IEEE International Conference on Image Processing, 2665-2668.   pdf
• Aach T., Mota C., Stuke I., Mühlich M., & Barth E. (2006) Analysis of Superimposed Oriented Patterns, IEEE Transactions on Image Processing, Vol. 15, No. 12, 3690-3700.   pdf
• Stuke, I., Barth, E. & Mota, C., (2006) Estimation of Multiple Orientations and Multiple Motions in Multi-Dimensional Signals. IEEE XIX Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI'06), 341-348.
• Mota, C., Stuke, I., & Barth, E. (2006). The Intrinsic Dimension of Multispectral Images. MICCAI Workshop on Biophotonics Imaging for Diagnostics and Treatment, Copenhagen.    pdf