Pulse Reformation Algorithm for Leakage of Connected Operators

Gene Stoltz, Inger Fabris-Rotelli


The Discrete Pulse Transform (DPT) is a hierarchical decomposition of a signal in n-dimensions, built from iteratively applying the LULU operators. The DPT is a fairly new mathematical framework with minimal application and is prone to leakage within the domain, as are most other connected operators. Leakage is the unwanted union of two connected sets and thus provides false connectedness information regarding the data. The Pulse Reformation Framework (PRF) is developed to address the leakage problem within the DPT. It was specifically tested with circular probes and showed successful object extraction of blood cells.


  1. Anguelov, R. and Fabris-Rotelli, I. (2010). LULU operators and Discrete Pulse Transform for multidimensional arrays. Image Processing, IEEE Transactions on, 19(11):3012-3023.
  2. Fabris-Rotelli, I. and Stoltz, G. (2012). On the leakage problem with the Discrete Pulse Transform decomposition. In de Waal, A., editor, Proceedings of the 23rd Annual Symposium of the Pattern Recognition Association of South Africa, pages 179-186.
  3. Fabris-Rotelli, I. N. (2012). Discrete Pulse Transform of images and applications. PhD thesis, University of Pretoria.
  4. Goutsias, J., Vincent, L., and Bloomberg, D. S. (2000). Mathematical morphology and its applications to image and signal processing, volume 18, chapter Practical extensions of connected operators, pages 97-110. Springer.
  5. Graham, M. W., Gibbs, J. D., and Higgins, W. E. (2008). Robust system for human airway-tree segmentation. In Medical Imaging, pages 69141J-69141J. International Society for Optics and Photonics.
  6. Law, W. and Chung, A. C. (2006). Minimal weighted local variance as edge detector for active contour models. In Computer Vision-ACCV 2006, pages 622-632. Springer.
  7. Li, C.-T. and Wilson, R. (1998). Image segmentation based on a multiresolution bayesian framework. In Image Processing, 1998. ICIP 98. Proceedings. 1998 International Conference on, pages 761-765. IEEE.
  8. LVincent and Dougherty, E. (1994). Digital Image Processing Methods, chapter Morphological segmentaion fro textures and particles, page Chapter 2. Marcel Dekker, Inc.
  9. Morales, A., Acharya, R., and Ko, A.-J. (1995). Morphological pyramids with alternating sequential filters. IEEE Transactions on Image Processing, 4(7):965- 977.
  10. O'Callaghan, R. J. and Bull, D. R. (2005). Combined morphological-spectral unsupervised image segmentation. Image Processing, IEEE Transactions on, 14(1):49-62.
  11. Ouzounis, G. K. and Wilkinson, M. H. (2005). Countering oversegmentation in partitioning-based connectivities. In Image Processing, 2005. ICIP 2005. IEEE International Conference on, volume 3, pages III-844. IEEE.
  12. Powers, D. M. (2011). Evaluation: from precision, recall and f-measure to roc, informedness, markedness & correlation. Journal of Machine Learning Technologies, 2(1):37-63.
  13. Raj, A., van den Bogaard, P., Rifkin, S. A., van Oudenaarden, A., and Tyagi, S. (2008). Imaging individual mrna molecules using multiple singly labeled probes. Nature methods, 5(10):877-879.
  14. Rohwer, C. (2005). Nonlinear Smoothers and Multiresolution Analysis. Birkhauser.
  15. Rohwer, C. and Laurie, D. (2006). The Discrete Pulse Transform. SIAM journal on mathematical analysis, 38(3):1012-1034.
  16. Rohwer, C. and Toerien, L. (1991). Locally monotone robust approximation of sequences. Journal of computational and applied mathematics, 36(3):399-408.
  17. Salembier, P. and Serra, J. (1995). Flat zones filtering, connected operators, and filters by reconstruction. IEEE Transactions on Im, 4(8):1153 - 1160.
  18. Serra, J. (1982). Image Analysis and Mathematical Morphology. Vol I, and Image Analysis and Mathematical Morphology. Vol II: Theoretical Advances. Academic Press, London.
  19. Serra, J. (2005). Viscous lattices. Journal of Mathematical Imagin, 22:269-282.
  20. Soille, P. (2011). Preventing chaining through transitions while favouring it within homogeneous regions. In Soille, P., Pesaresi, M., and Ouzounis, G., editors, Mathematical Morphology and Its Applications to Image and Signal Processing, volume 6671 of Lecture Notes in Computer Science, pages 96-107. Springer Berlin Heidelberg.
  21. Terol-Villalobos, I. R., Mendiola-Santibán˜ez, J. D., and Canchola-Magdaleno, S. L. (2006). Image segmentation and filtering based on transformations with reconstruction criteria. Journal of Visual Communication and Image Representation, 17(1):107-130.
  22. Tzafestas, C. S. and Maragos, P. (2002). Shape connectivity: multiscale analysis and application to generalized granulometries. Journal of Mathematical Imaging and Vision, 17(2):109-129.
  23. Vincent, L. (1193). Grayscale area opening and closings, their efficient implementation and applications. In Proceedings of the EURASIP Workshop on Mathematical Morphology and its Applications to Signal Processing, Barcelona, Spain.
  24. Wilkinson, M. (2005). Attribute-space connected filters. In Ronse, C., Najman, L., and Decencire, E., editors, Mathematical Morphology: 40 Years On, volume 30 of Computational Imaging and Vision, pages 85-94. Springer Netherlands.
  25. Wilkinson, M. H. (2008). Connected filtering by reconstruction: Basis and new advances. In Image Processing, 2008. ICIP 2008. 15th IEEE International Conference on, pages 2180-2183. IEEE.

Paper Citation

in Harvard Style

Stoltz G. and Fabris-Rotelli I. (2015). Pulse Reformation Algorithm for Leakage of Connected Operators . In Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015) ISBN 978-989-758-089-5, pages 583-590. DOI: 10.5220/0005313205830590

in Bibtex Style

author={Gene Stoltz and Inger Fabris-Rotelli},
title={Pulse Reformation Algorithm for Leakage of Connected Operators},
booktitle={Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015)},

in EndNote Style

JO - Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015)
TI - Pulse Reformation Algorithm for Leakage of Connected Operators
SN - 978-989-758-089-5
AU - Stoltz G.
AU - Fabris-Rotelli I.
PY - 2015
SP - 583
EP - 590
DO - 10.5220/0005313205830590