Editing Image segmentation (section)

=== Image segmentation and primal sketch ===

There have been numerous research works in this area, out of which a few have now reached a state where they can be applied either with interactive manual intervention (usually with application to medical imaging) or fully automatically. The following is a brief overview of some of the main research ideas that current approaches are based upon.

The nesting structure that Witkin described is, however, specific for one-dimensional signals and does not trivially transfer to higher-dimensional images. Nevertheless, this general idea has inspired several other authors to investigate coarse-to-fine schemes for image segmentation. Koenderink<ref>Koenderink, Jan "The structure of images", Biological Cybernetics, 50:363–370, 1984</ref> proposed to study how iso-intensity contours evolve over scales and this approach was investigated in more detail by Lifshitz and Pizer.<ref>[http://portal.acm.org/citation.cfm?id=80964&dl=GUIDE&coll=GUIDE Lifshitz, L. and Pizer, S.: A multiresolution hierarchical approach to image segmentation based on intensity extrema, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:6, 529–540, 1990.]</ref> Unfortunately, however, the intensity of image features changes over scales, which implies that it is hard to trace coarse-scale image features to finer scales using iso-intensity information.

Lindeberg<ref>[http://kth.diva-portal.org/smash/record.jsf?pid=diva2%3A472969&dswid=2693 Lindeberg, T.: Detecting salient blob-like image structures and their scales with a scale-space primal sketch: A method for focus-of-attention, International Journal of Computer Vision, 11(3), 283–318, 1993.]</ref><ref name=lin94>[http://www.csc.kth.se/~tony/book.html Lindeberg, Tony, Scale-Space Theory in Computer Vision, Kluwer Academic Publishers, 1994], {{ISBN|0-7923-9418-6}}</ref> studied the problem of linking local extrema and saddle points over scales, and proposed an image representation called the scale-space primal sketch which makes explicit the relations between structures at different scales, and also makes explicit which image features are stable over large ranges of scale including locally appropriate scales for those. Bergholm proposed to detect edges at coarse scales in scale-space and then trace them back to finer scales with manual choice of both the coarse detection scale and the fine localization scale.

Gauch and Pizer<ref>[http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=628490 Gauch, J. and Pizer, S.: Multiresolution analysis of ridges and valleys in grey-scale images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15:6  (June 1993), pages: 635–646, 1993.]</ref> studied the complementary problem of ridges and valleys at multiple scales and developed a tool for interactive image segmentation based on multi-scale watersheds. The use of multi-scale watershed with application to the gradient map has also been investigated by Olsen and Nielsen<ref>Olsen,  O. and Nielsen, M.: [https://link.springer.com/content/pdf/10.1007/3-540-63507-6_178.pdf Multi-scale gradient magnitude watershed segmentation], Proc. of ICIAP 97, Florence, Italy, Lecture Notes in Computer Science, pages 6–13. Springer Verlag, September 1997.</ref> and been carried over to clinical use by Dam.<ref>Dam, E., Johansen, P., Olsen, O. Thomsen,, A. Darvann, T., Dobrzenieck, A., Hermann, N., Kitai, N., Kreiborg, S., Larsen, P., Nielsen, M.: "Interactive multi-scale segmentation in clinical use" in European Congress of Radiology 2000.</ref> Vincken et al.<ref>{{Cite journal |doi=10.1109/34.574787 |title=Probabilistic multiscale image segmentation |year=1997 |last1=Vincken |first1=K.L. |last2=Koster |first2=A.S.E. |last3=Viergever |first3=M.A. |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |volume=19 |issue=2 |pages=109–120 }}</ref> proposed a hyperstack for defining probabilistic relations between image structures at different scales. The use of stable image structures over scales has been furthered by Ahuja<ref>[http://vision.ai.uiuc.edu/~msingh/segmen/seg/MSS.html M. Tabb and N. Ahuja, Unsupervised multiscale image segmentation by integrated edge and region detection, IEEE Transactions on Image Processing, Vol. 6, No. 5, 642–655, 1997.] {{webarchive |url=https://web.archive.org/web/20110720084911/http://vision.ai.uiuc.edu/~msingh/segmen/seg/MSS.html |date=20 July 2011 }}</ref><ref>{{cite book | chapter-url=https://doi.org/10.1007%2F978-3-642-12307-8_12 | doi=10.1007/978-3-642-12307-8_12 | chapter=From Ramp Discontinuities to Segmentation Tree | title=Computer Vision – ACCV 2009 | series=Lecture Notes in Computer Science | year=2010 | last1=Akbas | first1=Emre | last2=Ahuja | first2=Narendra | volume=5994 | pages=123–134 | isbn=978-3-642-12306-1 }}</ref> and his co-workers into a fully automated system. A fully automatic brain segmentation algorithm based on closely related ideas of multi-scale watersheds has been presented by Undeman and Lindeberg<ref>[http://kth.diva-portal.org/smash/record.jsf?pid=diva2%3A451266&dswid=-4540 C. Undeman and T. Lindeberg (2003) "Fully Automatic Segmentation of MRI Brain Images using Probabilistic Anisotropic Diffusion and Multi-Scale Watersheds", Proc. Scale-Space'03, Isle of Skye, Scotland, Springer Lecture Notes in Computer Science, volume 2695, pages 641–656.]</ref> and been extensively tested in brain databases.

These ideas for multi-scale image segmentation by linking image structures over scales have also been picked up by Florack and Kuijper.<ref>Florack, L. and Kuijper, A.: The topological structure of scale-space images, Journal of Mathematical Imaging and Vision, 12:1, 65–79, 2000.</ref> Bijaoui and Rué<ref>{{cite journal | last1 = Bijaoui | first1 = A. | last2 = Rué | first2 = F. | year = 1995 | title = A Multiscale Vision Model | journal = Signal Processing | volume = 46 | issue = 3| page = 345 | doi=10.1016/0165-1684(95)00093-4}}</ref> associate structures detected in scale-space above a minimum noise threshold into an object tree which spans multiple scales and corresponds to a kind of feature in the original signal. Extracted features are accurately reconstructed using an iterative conjugate gradient matrix method.