Applications of CGAL in the Gel Analysis Software CAROL

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Applications of CGAL in the Gel Analysis
Software CAROL

• Klaus Kriegel
• Freie Universität Berlin
• Deutsches Herzzentrum Berlin
• DFG Projekt FL 165/4-2

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CAROL (DFG 1997-2000)
FU Berlin H. Alt F. Hoffmann K. Kriegel C.
Schultz C. Wenk
German Heart Center E. Fleck K.-P. Pleißner I.
Seefeldt
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Outline of the talk

• Application Background (Electrophoresis)
• Gel Matching with CAROL
  . The Algorithmic Approach
• Using CGAL in CAROL
• Experience, Problems, and Further Perspectives

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2D Gel Electrophoresis

• Two-dimensional Gel Electrophoresis (2DE) is an
  important method in proteome research
• It is a high resolution technique which is
  capable to separate thousands of protein spots
  from a tissue sample

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2D Gel Electrophoresis

• Proteins are concentrated in so called SPOTS of
  elliptic shape
• Protein analysis by mass spectrometry
  (expensive)
• Gel Matching Protein identification by gel
  image comparison is faster and not expensive

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Gel Matching The Assumptions

• Images which have to be compared are similar,
  but, possibly there are
• Local and global geometric distortions
• Corresponding spot pairs with (very) different
  intensities
• Missing spots

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The Algorithmic Problem
Partial Approximate Point Pattern Matching
The CAROL Approach Design first an efficient
algorithm finding all occurrencies of a small
local pattern in a target image (Local
Matching) Global Matching via Local Matching
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The Local Matching Approach
Find a k-pattern in a set of n points Naive
Alignment Approach O(k³n²log
n) Alignment with Delaunay Edges O(k²n
log n) Scoring Scheme (Geometric Hashing)
O(kn) (O(G) where G size of the scheme)
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Incremental Delaunay Triangulation
Alt et al. If the intensity orderings are
consistent with the matching then it is
sufficient to use the history edges of the
incremental Delaunay Triangulation where points
are inserted by decreasing intensity. Seidel The
expected number of edges in the history of the
incremental Delaunay Triangulation is O(n). To
cope with differences in the intensity orderings
we add all flip edges to the history!
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Scoring Schemes
It is also possible to take into account image
scalings simple scaling --gt 3-dimensional
scheme independend scalings of x-axis and
y-axis --gt 4-dimensional scheme
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Global Matching
........via local matching 1) Cover the source
image by small patterns (5x5) 2) Compute all
local matchings of the patterns 3) For many of
the patterns the correct local matching will
be included (within a lot of proposals) 4) Find
out the correct local matchings by a
consistency test
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CGAL Components in CAROL
Geometric primitives from the CGAL
kernel CGAL_Point_2 CGAL_Bbox_2 CGAL_squared
_distance
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CGAL Components in CAROL

• The Delaunay Triangulation
• from the CGAL basic library
• Delaunay Traits
• Vertex Circulators

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Delaunay Traits
class CAROL_Point CGAL_Point_2
private double intensity
.................. Defining special
Traits classes triangulation vertices can be
represented by CAROL_Points
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Vertex Circulators

• Vertex circulators are used to get a list of the
  neighbors of an inserted vetex
• Vertex circulators are used to construct flip
  edges

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The Use of CGAL

• CGAL supplies various useful data structures
  and basic algorithms.
• The concept is very flexible according to the
  users needs.
• The user can be sure to get efficient
  implementations.
• Several compilers are supported ( gnu, sun,
  virtual c )

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CGAL with Visual C
PDQUEST
Interface
CAROL library with CGAL components
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CGAL with Visual C
PDQUEST virtual c stl
Interface_1 Points Interface_2
CAROL library with CGAL components stl_port
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The End
http//gelmatching.inf.fu-berlin.de