1. Applications of CGAL in the Gel Analysis Software CAROL Klaus Kriegel Freie Universität Berlin Deutsches Herzzentrum Berlin DFG Projekt FL 165/4-2

2. 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

3. Outline of the talk  Application Background (Electrophoresis)  Gel Matching with CAROL:. The Algorithmic Approach  Using CGAL in CAROL  Experience, Problems, and Further Perspectives

4. 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

7. 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

8. 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

14. The Algorithmic Problem 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

20. The Local Matching Approach 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)

24. 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!

32. Scoring Schemes It is also possible to take into account image scalings: simple scaling --> 3-dimensional scheme independend scalings of x-axis and y-axis --> 4-dimensional scheme

33. 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

35. CGAL Components in CAROL CGAL Components in CAROL Geometric primitives from the CGAL kernel: CGAL_Point_2 CGAL_Bbox_2 CGAL_squared _distance

36. CGAL Components in CAROL CGAL Components in CAROL The Delaunay Triangulation from the CGAL basic library  Delaunay Traits  Vertex Circulators

37. Delaunay Traits Delaunay Traits class CAROL_Point : CGAL_Point_2 { private: double intensity;.................. } Defining special Traits classes triangulation vertices can be represented by CAROL_Points

38. 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

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

43. CGAL with Visual C++ PDQUEST CAROL library with CGAL components Interface

44. CGAL with Visual C++ PDQUEST virtual c++ stl CAROL library with CGAL components stl_port Interface_1 Points Interface_2

45. The End http://gelmatching.inf.fu-berlin.de