1. Algorithms and Modern Computer Science
Dr. Marina L. Gavrilova
Dept of Comp. Science, University of Calgary,
AB, Canada, T2N1N4

2. Presentation outline About my research
Data structures and algorithms to be studied
Application areas
Optimization and computer modeling
Image processing and computer graphics
Spatial data
Biometrics
Summary

3. My Research Interests Computer modeling and simulation
Computational geometry
Image processing and visualization
Voronoi diagram and Delaunay triangulation
Biometric technologies
Collision detection optimization
Terrain modeling and visualization
Computational methods in spatial analysis and GIS

4. Interests and affiliations
SPARCS Lab Co-Founder and Director
BT Lab Co-Founder and Director
Computational Geometry and Applications Founder and Chair since 2001
ICCSA Conference series Scientific Chair (since 2003)
Transactions on Computational Science Journal Springer Editor-in-Chief
Research topics: optimization, reliability, geometric algorithms, data structures representation and visualization, GIS, spatial analysis, biometric modeling

5. Data Structures to be Studied
Hashing and hash tables
Trees
Spatial subdivisions
Graphs
Flow networks
Geometric data structures

6. Algorithms to be studies
Search heuristics
Encoding and compression techniques
Linear programming
Dynamic programming
Game design techniques
Randomized algorithms

7. Long-Term Goals of Research in Computer Science
Provide a solution to a problem
Decrease possibility of an error
Improve methodology or invent a novel solution
Make solution more robust
Make solution more efficient
Make solution less memory consuming

8. Examples of data structures applications in areas of computer science
Typical applications:
Heaps for data ordering and faster access in operating systems
K-d trees for multi-dimensional database searches
B, B*, B+ trees for file accesses
Geometric data structures for geographical data representation and processing
Compression algorithms for remote access, Internet, network transmission and security
Search heuristics for game strategy implementation

9. Recent trends
The old definition of computer science—the study of phenomena surrounding computers—is now obsolete. Computing is the study of natural and artificial information processes.
ACM Communications

10. More Advanced Applications
Data structures in Optimization and Computer Simulation
Data structures in Image Processing and Computer Graphics
Data structures in GIS (Geographical Information Systems) and statistical analysis
Data structures in biometrics

11. Back then…

12. And now…
Einar Rustad, VP Business Development, Dolphin Interconnect Solutions

13. But algorithms still should work, or else …

14. State of the art in computing
Horst Simon
Director NERSC, Lawrence Berkeley National Laboratory

15. High performance computing

16. Increased Scientific Demands

17. Part 1. Optimization and Computer Modeling
Biological systems (plants, corals)
Granular-type materials (silo, shaker, billiards)
Molecular systems (fluids, lipid bilayers, protein docking)
GIS terrain modeling
Space partitioning
Trees
Geometric data structures

18. Pool of Data Structures
Dynamic Delaunay triangulation
Spatial subdivisions
Segment trees
k cells
K-d trees
Interval trees
Combination of data structures

19. Collision detection optimization
Problem: A set of n moving particles is given in the plane or 3D with equations of their motion. It is required to detect and handle collisions between objects and/or boundaries. Collisions are instantaneous and one-on-one only.
Approach: Use dynamic data structures in the context of time-step event oriented simulation model.
Data structures implemented are:
dynamic generalized DT
regular spatial subdivision
regular spatial tree
set of segment tree

20. The nearest-neighbor problem
Task: To find the nearest-neighbor in a system of circular objects {Gavrilova 01}
Approach: To use generalized Voronoi diagram in Manhattan and power metric and k-d tree as a data structure.
The Initial Distribution Generator (IDG) module:
Used to create various input configurations: the uniform distribution of sites in a square, the uniform distribution of sites in a circle, cross, ring, degenerate grid and degenerate circle. The parameters for automatic generation are: the number of sites, the distribution of their radii, the size of the area, and the type of the distribution.
The Nearest-Neighbour Monitor (NNM) module:
The program constructs the additively weighted supremum VD, the power diagram and the k-d tree in supremum metric; performs series of nearest-neighbour searches and displays statistics.
Tests: large data sets (10000 particles), silo model

21. Example: supremum VD and DT
The supremum weighted Voronoi diagram (left) and the corresponding Delaunay triangulation (right) for 1000 randomly distributed sites .

22. Study of porous materials in 3d
Collaborators: N.N. Medvedev, V.A.Luchnikov, V. P. Voloshin, Russian Academy of Sciences, Novosibirsk [Luchnikov 01].
Task: To study the properties of the system of polydisperse spheres in 3D, confined inside a cylindrical container.
Approach: A boundary of a container is considered as one of the elements of the system.
To compute the Voronoi network for a set of balls in a cylinder we use the modification of the known 3D incremental construction technique, discussed in {Gavrilova et. al.}
The center of an empty sphere, which moves inside the system so that it touches at least three objects at any moment of time, defines an edge of the 3D Voronoi network.
Tests: porous materials, molecular structures

23. Example: 3D Euclidean Voronoi diagram
3D Euclidean Voronoi diagram: hyperbolic arcs identify voids – empty spaces around items obtained by Monte Carlo method.

24. Experiments
The approach was tested on a system representing dense packing of 300 Lennard-Jones atoms. The largest channels of the Voronoi network occur near to the wall of the cylinder. A fraction of large channels along the wall is higher for the model with the fixed diameter (right) than for the model with relaxed diameter (left).

25. Part 2. Image processing and Computer Graphics
Image reconstruction
Image compression
Morphing
Detail enhancement
Image comparison
Pattern recognition
Space partitioning
Trees
Geometric data structures
Compression
Search heuristics

26. Pattern Matching
Aside from a problem of measuring the distance, pattern matching between the template and the given image is a very serious problem on its own.

27. Template Matching approach to Symbol Recognition
Compare an image with each template and see which one gives the best mach (courtesy of Prof. Jim Parker, U of C)

28. Good Match Image Template
Most of the pixels overlap means a good match (courtesy of Prof. Jim Parker, U of C)
Image
Template

29. Distance Transform
Given an n x m binary image I of white and black pixels, the distance transform of I is a map that assigns to each pixel the distance to the nearest black pixel (a feature).

30. Medial axis transform
The medial axis, or skeleton of the set D, denoted M(D), is defined as the locus of points inside D which lie at the centers of all closed discs (or spheres) which are maximal in D, together with the limit points of this locus.

31. Medial axis transform

32. Voronoi diagram in 3D

33. Part 3. Spatial Data and GIS
Terrain visualization
Terrain modeling
Urban planning
City planning
GIS systems design
Navigation and tracking problems
Statistical analysis
Space partitioning
Grids
Distance metrics
Geometric data structures

34. GIS studies - SPARCS Lab
Collaborators: S. Bertazzon, Dept. of Geography, C. Gold, Hong Kong Polytechnic, M. Goodchild, Santa Barbara
Problem: study or patterns and correlation among attributed geographical entities, including health, demographic, education etc. statistics.
Approach: pattern analysis using 3D Voronoi diagram, spatial statistics and autocorrelation using Lp metrics, pattern matching and visualization

35. Terrain models

36. Quantitative Map Analysis

37. DEM: Digital Elevation Model
Contains only relative Height
Regular interval
Pixel color determine height
Discrete resolution X
Kluanne National Park Y

38. Non-Photo-Realistic Real-time 3D Terrain RenderingB
Uses DEM as input of the application
Generates frame coherent animated view in real-time
Uses texturing, shades, particles etc. for layer visualization

39. Part 4. Biometrics Hashing Space partitioning Trees
Geometric data structures
Searching
Biometric identification
Biometric recognition
Biometric synthesis

40. Background
Biometrics refers to the automatic identification of a person based on his/her physiological or behavioral characteristics.

41. Thermogram vs. distance transform
Thermogram of an ear (Brent Griffith, Infrared Thermography Laboratory, Lawrence Berkeley National Laboratory )

42. Nearest Neighbor Approach
Voronoi diagram
Directions of feature points

43. Delaunay Triangulation of Minutiae Points

44. (a) Binary Hand (b) Hand Contour

45. Spatial Interpolation using RBF(Radial Basis Functions)
Deformation in 2D and 3D

46. Summary
Data structures and algorithms studies in the course are powerful tools not only for basic operation of computer systems and networks but also a vast array of techniques for advancing the state of the research in various computer science disciplines.