Abstract
Applying computer technology, such as computer vision in driver assistance, implies that processes and data are modeled as being discretized rather than being continuous. The area of stereo vision provides various examples how concepts known in discrete mathematics (e.g., pixel adjacency graphs, belief propagation, dynamic programming, max-flow/min-cut, or digital straight lines) are applied when aiming for efficient and accurate pixel correspondence solutions. The paper reviews such developments for a reader in discrete mathematics who is interested in applied research (in particular, in vision-based driver assistance). As a second subject, the paper also discusses lane detection and tracking, which is a particular task in driver assistance; recently the Euclidean distance transform proved to be a very appropriate tool for obtaining a fairly robust solution.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Analysis Machine Intelligence 23, 1222–1239 (2001)
Felzenszwalb, P.F., Huttenlocher, D.P.: Distance transform of sampled functions. Cornell Computing and Information Science, TR 2004-1963 (September 2004)
Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient belief propagation for early vision. Int. J. Computer Vision 70, 41–54 (2006)
Ford, L.R., Fulkerson, D.R.: Flows in networks. Technical report R-375-PR, US Air Force Project RAND (1962)
Guan, S., Klette, R., Woo, Y.W.: Belief propagation for stereo analysis of night-vision sequences. In: Wada, T., et al. (eds.) PSIVT 2009. LNCS, vol. 5414, pp. 932–943. Springer, Heidelberg (2009)
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2000)
Herman, S., Klette, R.: The naked truth about cost functions for stereo matching. MI-tech TR 33, University of Auckland (2009)
Hermann, S., Klette, R., Destefanis, E.: Inclusion of a second-order prior into semi-global matching. In: Wada, T., et al. (eds.) PSIVT 2009. LNCS, vol. 5414, pp. 633–644. Springer, Heidelberg (2009)
Hirschmüller, H.: Accurate and efficient stereo processing by semi-global matching and mutual information. In: Proc. CVPR, vol. 2, pp. 807–814 (2005)
Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–203 (1981)
Ishikawa, H.: Exact optimization for Markov random fields with convex priors. IEEE Trans. Pattern Analysis Machine Intelligence 25, 1333–1336 (2003)
Jiang, R., Klette, R., Wang, S., Vaudrey, T.: New lane model and distance transform for lane detection and tracking. In: Proceedings of CAIP (to appear, 2009)
Kimmel, R.: Numerical Geometry of Images. Springer, New York (2004)
Klette, R., Rosenfeld, A.: Digital Geometry. Morgan Kaufmann, San Francisco (2004)
Kolmogorov, V., Zabih, R.: Multi-camera scene reconstruction via graph cuts. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352, pp. 82–96. Springer, Heidelberg (2002)
Liu, Z., Klette, R.: Dynamic programming stereo on real-world sequences. In: Köppen, M., et al. (eds.) ICONIP 2009, Part I. LNCS, vol. 5506, pp. 527–534. Springer, Heidelberg (2009)
Morales, S., Klette, R.: Prediction error evaluation of various stereo matching algorithms on long stereo sequences. MI-tech TR 38, University of Auckland (2009)
Ohta, Y., Kanade, T.: Stereo by two-level dynamic programming. In: Proc. IJCAI, pp. 1120–1126 (1985)
Vaudrey, T., Klette, R.: Residual images remove illumination artifacts for correspondence algorithms! In: Proc. DAGM (to appear, 2009)
Wu, T., Ding, X.Q., Wang, S.J., Wang, K.Q.: Video object tracking using improved chamfer matching and condensation particle filter. In: Proc. SPIE-IS & T Electronic Imaging, vol. 6813, pp. 04.1–04.10 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Klette, R., Jiang, R., Morales, S., Vaudrey, T. (2009). Discrete Driver Assistance. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds) Mathematical Morphology and Its Application to Signal and Image Processing. ISMM 2009. Lecture Notes in Computer Science, vol 5720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03613-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-03613-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03612-5
Online ISBN: 978-3-642-03613-2
eBook Packages: Computer ScienceComputer Science (R0)