University of Birmingham
Pattern Recognition in Super Resolution Images
Cross, Daniel; Wand, Nathaniel O.; Styles, Iain B.; Thomas, Steven G.; Poulter, Natalie S.
DOI:
10.1364/BODA.2015.JT3A.7
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Peer reviewed version
Citation for published version (Harvard):
Cross, D, Wand, NO, Styles, IB, Thomas, SG & Poulter, NS 2015, Pattern Recognition in Super Resolution
Images. in Optics in the Life Sciences. Optical Society of America, pp. JT3A.7, Bio-Optics: Design and
Application 2015, Vancouver, Canada, 12/04/15. https://doi.org/10.1364/BODA.2015.JT3A.7
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Download date: 10. Aug. 2022
Pattern Recognition in Super Resolution Images
Daniel J. Cross
1
, Nathaniel O. Wand
1
, Iain B. Styles
1,2
, Steven G. Thomas
3
and Natalie S. Poulter
3
1
PSIBS Doctoral Training Centre, University of Birmingham, Edgbaston, Birmingham, UK;
2
School of Computer Science, University of Birmingham, Edgbaston, Birmingham, UK;
3
Institute of Biomedical Research, University of Birmingham, Edgbaston, Birmingham, UK;
D.J.C.: E-mail: DJC919@bham.ac.uk,
N.O.W.: Email: NOW348@bham.ac.uk,
I.B.S.: E-mail: I.B.Styles@cs.bham.ac.uk,
S.G.T.: Email: S.Thomas@bham.ac.uk,
N.S.P.: Email: N.Poulter@bham.ac.uk
Abstract: Super resolution microscopy techniques allow for high precision localisation of
individually labeled GPVI receptors. In this work we apply a quadtree-based pattern recognition
scheme to identify patterns and structure from STORM images.
OCIS codes: (100.6640) Superresolution; (100.5010) Pattern Recognition;
1. Introduction
The GPVI collagen receptor has long been known to play a key role in the activation and aggregation of platelets
following trauma. However, what is less well understood is whether the spatial localisation of the receptor is
indicative of the underlying biochemistry of thrombus formation and evolution [1].
The activation of the GPVI receptor is typically the result of damage to a vessel wall, exposing the highly
collagenous sub-endothelial matrix to the contents of the circulatory system. Initially, platelets are drawn out of
circulation by interaction of the GPIb-IX-V receptor complex with von Willebrand Factor; following this, GPVI
receptors present on the platelet surface bind to the exposed collagen matrix, resulting in spreading and adhesion of
further platelets to form a thrombus.
Issues with elucidating the process of thrombus formation are mainly encountered when attempting to quantify
the interactions of the multimeric complexes responsible, which often occur on spatial scales below that of the
diffraction limit of light. With the development of super resolution imaging systems capable of resolving structure
on the order of 20 nanometers, this limit has effectively been overcome, allowing for investigations into the spatial
distributions of surface proteins and receptors to be undertaken, as can be seen in the STORM image and point
localisations shown in figure 1 and 2.
Previous studies have studied the effectiveness of using a combination of Ripley's K-function and heat mapping
to produce a density based threshold used to identify structure in super resolution images [1]. This has lead to
investigations into the interactions between clusters of the Lat adaptor protein and T-cell antigen receptor (TCR),
ultimately revealing that adaptor clusters assembled prior to signaling events do not undergo phosphorylation or
transport to activation sites during TCR signaling [2].
In addition to identifying structures within images, clustering algorithms are capable of quantifying various
different parameters associated with these structures. These include the spacing and density of points within
clusters, in addition to their size and shape, allowing for automated extraction of parameters that would have
previously required analysis by hand.
2. Background
Methods of clustering can be loosely grouped into two major families, those that rely on the distance metric between
points to determine their cluster assignment, and those that utilise local point density.
Quadtree decomposition belongs to the family of clustering techniques which rely on evaluating the density of
points to be clustered. This is particularly useful when dealing with long filamentary structures, such as the
distribution of GPVI along collagenous fibres in adherent platelets, as there is no inherent bias towards forming
specific cluster shapes.
The algorithm uses the following process to perform the decomposition:
• Divide the dataset into four subsets of equal dimensions.
• Count the population of each subset; if the count is greater than the minimum cluster size defined by the
operator, label the subset for further division, else assign a label to each point in the subset corresponding to
the division rank at which the subdivision check fails.
• Once all subsets of a given rank have been assessed, repeat step 2 until no further divisions can be made.
Once completely decomposed, elements of the dataset labelled similarly can be said to reside in areas of equal
density (as shown in figure 3). However, in doing this all information regarding the horizontal relationships
between data points is lost i.e. the membership of two separate points to the same density rank or even subset doesn't
necessarily imply their membership of the same cluster.
In order to extract the relationships between elements, a percolation algorithm was applied to the decomposed
dataset using the following method:
• Label all elements of a given density rank with identical labels, calculate euclidean distance between all
points.
• Iterate through all points, determining the points that lie within a distance of half the associated
subdivision. Check these points for an existing cluster label.
• If already clustered, apply the existing cluster label to the new point; if not, apply a unique label to both
points. Repeat across all points.
3. Results
Figures 3 and 4 qualitatively demonstrate the ability of the quadtree decomposition algorithm to identify clusters in
point localisation datasets. The filamentary structure visible in the highest density regions of figure 3, those
coloured dark blue/purple, are characteristic of adherent platelets indicating this method's suitability for analysing
thise particular type of data. Whilst figure 4 does not contain structures of filamentary nature, it does contain
multiple small circular objects, which the algorithm readily identifies. This is important, as it shows that whilst the
algorithm was selected for its non-bias towards circular structures, it is still capable of identifying them.
Fig 2: GPVI point localisations extracted from a STORM image of
platelets adhered to a collagenous surface. Image courtesy of N .S.
Poulter
Fig 1: STORM image of fluorescently labelled GPVI molecules in
platelets on a collagenous surface. Image courtesy of N.S. Poulter.
The promising nature of these observations indicates that the quadtree algorithm will likely be suitable for
performing further pattern analysis on other structures. However, as mention in section 2, this will require the
application of an algorithm capable of assembling clusters from the decomposed datasets. Future work on this
technique will primarily focus on the development and application of such algorithms, as well as the fabrication of
known structures in order to provide quantitative analysis of the technique.
References
[1] D.M. Owen, C. Rentero, J. Rossy, A. Magenau, D. Williamson, M. Rodriguez and K. Gaus, “PALM imaging and cluster analysis of protein
heterogeneity at the cell surface.” in Journal of Biophotonics, Vol. 3 (2010), pp. 446-454
[2] D.J. Williamson, D.M. Owen, J. Rossy, A. Magenau, M. Wehrmann, J.J. Gooding and K. Gaus, “Pre-existing clusters of the adaptor
Lat do not participate in early T cell signaling events.” in Nature Immunology, Vol. 12 (2011), pp. 655-662
Fig 3: Results of the quadtree decomposition algorithm applied to the
dataset shown in figure 2. Minimum cluster size is was defined as 100
points, and varying density ranks are denoted by a rainbow colour map,
with red representing lowest density rank and purple representing
highest.
Fig 4: Results of quadtree decomposition on a wide field dataset,
minimum cluster size defined as 100 points with a rainbow density
colour map applied.