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

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

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

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

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

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

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

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

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 50-07-2007

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

Back then…

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

But algorithms still should work, or else …

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

High performance computing

Increased Scientific Demands

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

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

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

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

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

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

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

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).

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

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.

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)

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

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).

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.

Medial axis transform

Voronoi diagram in 3D

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

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

Terrain models

Quantitative Map Analysis

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

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

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

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

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

Nearest Neighbor Approach Voronoi diagram Directions of feature points

Delaunay Triangulation of Minutiae Points

(a) Binary Hand (b) Hand Contour

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

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.