MSER and Sieve Details

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What is the connection between MSER's and sieves'?

The papers by George Matas((Matas, et. al. 2002<ref>Matas, J., M. Urban, O. Chum and T. Pajdla (2002). Robust Wide baseline Stereo from Maximally Stable Extremal Regions. BMVC, Cardiff</ref>))((Matas et al., 2004)<ref>Matas, Jiri, et al. Robust wide-baseline stereo from maximally stable extremal regions. Image and vision computing 22.10 (2004): 761-767.</ref>)) (Mishkin et al., 2013)<ref>Dmytro Mishkin, Michal Perdoch,Jiri Matas (2013) Two-view Matching with View Synthesis Revisited arXiv preprint arXiv:1306.3855 </ref> put together an effective way of finding distinguished regions (DR’s) namely maximally stable extremal regions (MSER’s ) with a powerful way of describing the regions at multiple scales and robustly matching such measurements with others in a second image. Since then many authors have confirmed the algorithms as a powerful tool for finding objects in images (review Mikolajczyk et al 2006: <ref>Krystian Mikolajczyk, Tinne Tuytelaars, Cordelia Schmid, Andrew Zisserman, Jiri Matas, Frederik Schaffalitzky, Timor Kadir, L Van Gool, (2006) A Comparison of Affine Region Detectors.International Journal of Computer Vision. DOI: 10.1007/s11263-005-3848-x</ref>, Kimmel 2011 <ref>Kimmel, R., Zhang, C., Bronstein, A.M., Bronstein, M. (2011) Are MSER features really interesting? IEEE Trans. Pattern Analysis and Machine Intelligence 33:2316–2320</ref>

The algorithm underlying that for finding Maximally stable extremal regions (MSER's) is an 'o' sieve. Such algorithms relate closely to mathematical morphology (dilations-erosion (Jackway et al 1996<ref>P. T. Jackway and M. Deriche. Scale-space properties of multiscale morphological dilation-erosion. IEEE Trans. Pattern Analysis and Machine Intelligence , 18(1):38–51</ref>) openings, closings and in particular watersheds (Vincent et al 1991 <ref>Vincent, Luc, and Pierre Soille. "Watersheds in digital spaces: an efficient algorithm based on immersion simulations." IEEE transactions on pattern analysis and machine intelligence 13.6 (1991): 583-598.</ref>) and reconstruction filters (Salembier, P. et. al. 1995<ref>Salembier P, Serra J (1995). Flat zones filtering, connected operators, and filters by reconstruction. IEEE Trans Image Process 4:1153</ref>). In mathematical morphology the 'filtering' element of the MSER algorithm might be called a 'connected-set opening' ('o' sieve) . It is one of a family of closely related algorithms which for which I coined the term sieves. Why?

Why call them sieves and not filters? It never caught on but at the time I thought it may be helpful to distinguish between two very different signal simplifying algorithms both of which preserve scale-space. Linear 'filters' and non-linear 'sieves'. In a linear-filter-bank (e.g. the Gaussian/Gabor filters) separate the input signal into frequency related scale bands (large and small blobs). However, like all linear filters they spread outliers such as impulses and sharp edges over many scales. Sieves are the opposite (c.f. mechanical sieves in which particles (granules) either go through holes or they do not Particle filters and sieves.) They do however, spread smooth waveforms over many scales. Gaussian filter banks and filter banks based on sieves are complementary to each other.

Superficially it is clear that, by 'knocking off' outliers at increasingly large scales, sieves cannot introduce new extrema but to clarify the issue we formally proved that they do not introduce new extrema, i.e. preserve scale-space (Bangham et al 1996<ref>Bangham, JA, Harvey, RW, Ling, PD and Aldridge, RV (1996) Morphological scale-space preserving transforms in many dimensions. The Journal of Electronic Imaging (JEI), 5 (3). pp. 283-299.</ref>Bangham et al 1996b<ref>Bangham, JA, Chardaire, P, Pye, CJ and Ling, PD (1996) Multiscale nonlinear decomposition: The sieve decomposition theorem. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18 (5). pp. 529-539. ISSN 0162-8828</ref>, c.f. the properties of multiscale dilation and erosion, Jackway et al 1996<ref>Jackway, P.T. and Deriche, M. (1996) Scale-space properties of the multiscale morphological dilation-erosion IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, no.1, pp.38,51</ref>)

One dimensional sieves are easily implemented by run-length coding the signal, each extremum has a list of just two neighbours. Indeed, in collaboration with CCL we implemented the algorithm on a PC board to characterise the output, in real time, from line-scan cameras (often used industrially when, in the early 1990's, 2D digital camera's were not easily available). Implementations for images in higher dimensions are similar but keeping track of lists of neighbours is a little more complex.

Applications in addition to their role finding in objects in 2D images we have used sieves to analyse 1, 2 and 3D signals. We started in 1D (digital images were not available at the time). For example analysing protein hydrophobicity plots(Bangham, 1988<ref>Bangham, J.A. (1988). Data-sieving hydrophobicity plots. Anal. Biochem. 174, 142–145</ref>), de-noising single channel current data(Bangham et al, 1984<ref>Bangham, J.A., and T.J.C. Jacob (1984). Channel Recognition Using an Online Hardware Filter in The Journal of Physiology, (London: Physiological Society), pp. 3–5</ref>). Much later we used them for texture analysis(Southam et al, 2009<ref>Southam, P., and Harvey, R. (2009). Texture classification via morphological scale-space: Tex-Mex features. J. Electron. Imaging 18, 043007–043007</ref>), lipreading(Matthews et al., 2002<ref>Matthews, I., Cootes, T.F., Bangham, J.A., Cox, S., and Harvey, R. (2002). Extraction of visual features for lipreading. Pattern Anal. Mach. Intell. Ieee Trans. 24, 198–213</ref>). In 2D for segmenting 2D through extremal trees(Bangham et al., 1998<ref>Bangham, J.A., Hidalgo, J.R., Harvey, R., and Cawley, G. (1998). The segmentation of images via scale-space trees. In Proceedings of British Machine Vision Conference, pp. 33–43</ref>), maximally stable contours(Lan et al., 2010<ref>Lan, Y., Harvey, R., and Perez Torres, J.R. (2010). Finding stable salient contours. Image Vis. Comput. 28, 1244–1254</ref>), creating painterly pictures from photos(Bangham et al., 2003<ref>Bangham, J.A., Gibson, S.E., and Harvey, R. (2003). The art of scale-space. In Proc. British Machine Vision Conference, pp. 569–578</ref>); and in 3D for segmenting volumes in CAT scans.

Could sieves have evolved in biological systems?

It is commonplace to interpret biological data on animal vision systems as having similarities with linear filter banks, e.g. Gaussian/Gabor. However, now that the value of non-linear filter banks has been appreciated perhaps we should go back to the original experiments of the 1960-80's when biologists started interpreting them thus and ...

• Appreciate that although the biological data is consistent with Gaussian/Gabor linear filter banks,
• Do the biological data actually reject the non-linear alternatives?
• Why might it matter? Because if they do not then ...
  • it might be sensible to reconsider what we look for in the brain and how we interpret its behaviour.
  • Our hardware implementation of the 1D sieve was very different to a linear filter.
  • Likewise the linear time implementation of the 2D MSER algorithm (Nister and Stewenius, <ref>D. Nister and H. Stewenius Linear time maximally stable extremal regions ECCV 2008 part II LNCS 5303 pp 183-196. </ref>)

Summary of basic properties of sieves, linear and non-linear filters?

	Sieve 1D	Sieve 2D	Sieve 3D	Gaussian 1D	Gaussian 2D	Median 1D	Median 2D
Preserve Scale space	Yes	Yes	Yes	Yes	Yes	No	No
Separate signals by	Length	Area	Volume	Pulse Frequency	Blob Frequency 2D	Roughly Pulse length	Roughly Blob Area

As low-pass one dimensional filters, sieves robustly reject short lived outliers, e.g. impulses (Bangham, J.A. 1993<ref>Bangham, JA (1993) Properties of a Series of Nested Median Filters, Namely the Data Sieve. IEEE Transactions on Signal Processing, 41 (1). pp. 31-42. ISSN 1053-587X</ref>). They are more effective than Gaussian filters.

References

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