Research
My research interests 
I am currently perform a role of co-leader of two newly established research labs:
- Spatial Analysis Research in Computational Science Lab - SPARCS (sponsored by GEOIDE),
- Biometric Technologies Laboratory (sponsored by CFI)
More information is available from the corresponding web sites.
My recent (short) CV is available for more information on recent publications, teaching and service.
Selected research topics
Solving proximity problems in parallel:
The goal is to develop efficient parallel
algorithms for such computational geometry problems as finding a
nearest-neighbor, convex hull and generalized Voronoi Diagram construction. 
Nearest-neighbor problem under various distance functions: The goal is to investigate the general property of closeness of geometric objects in the plane. The metrics considered are Euclidean, power and Minkowski metrics.
Space of triangulations: If we consider the space of all triangulations for a given point set, we can calculate the shortest topological path from one particular triangulation to another. This provides some interesting research implications, such as, for example, an efficient solution of nearest-neighbor problem.
Feature transform and distance transform computation: This project deals with development of optimal distance transform and feature transform algorithms in Euclidean metric in the plane. Both sequential and parallel algorithms are given consideration. The possibility of application of the developed methods to efficient construction of the Voronoi diagram on the plane is also considered.
Object-oriented simulation of granular-type materials: The project was a joined effort between Department of Computer Science and Department of Mechanical and Manufacturing Engineering. Although the project is almost completed, analysis of performance of various collision optimization methods in the rigid-body simulation depending on such parameters as density of packing, mass distribution of particles, is being conducted.
Computer Modeling of Sphere Packings in 3D:
The flow of a fluid within boundaries can be simulated by a set
of spheres, contained within given boundaries. Granular and porous materials can
also be simulated using the packings of polysized spheres. One approach for
system modeling is to use the Voronoi diagram as a "navigation map". The
optimization of data structure construction and maintenance, and some algorithms for efficient analysis of large models has been developed
together with Prof. N. Medvedev at Institute
of Chemical Kinetics and Combustion, Novosibirsk, Russia.
Constrained Delaunay triangulation in 3D: The problem of efficient construction of generalized Delaunay tessellation in 3D space, confined by the cylinder, is solved.
Medial axis transform for biological 3D models: The problem of constructing the medial axis transform, for the purpose of efficient analysis and rendering of 3D biological model is studies. Model represents triangulated surface of a 3D polyhedra with holes. Applications of the developed algorithms will be considered on an example of modeling growing corals and sponges, in collaboration with Prof. Jaap Kaandorp, Section Computational Science research group, University of Amsterdam, the Netherlands.
Problem of exact computation of Mobius mapping: The project concerned with application of ESSA exact computation method to the problem of computing exactly Mobius mapping.
Exact computation of segment intersection and generalized VD: Algorithm to determine exactly the intersection between two segments is being developed. The application of the method to generalized VD construction is currently considered.
DBLP List of Co-Authors of Marina L. Gavrilova
Sample of graduate projects currently available:
3D Terrain Rendering System for GIS (Geographic Information System)
Biometrics Synthesis and Reconstruction
Finding a skeleton in 3D geometric objects
Computing the distance between two images
Morphing: application of the fast feature transform algorithm
Advanced collision detection optimization methods in application to multi-particle granular system modelling
Theoretical research on Generalized Voronoi diagram and Delaunay triangulations
Proximity Problems
Image recognition in biometrics
Computer Vision
Postdoctoral Research
In 1999 Prof. Gavrilova has received PIMs Postdoctoral Fellow Award. Her primary interests at that time lied in the area of exact computation methods in applications to computer graphics and Geographical Information Systems (GIS). Prof. Gavrilova developed algorithms for determining the line intersection point exactly in variable precision floating-point arithmetic. She also applied exact computation method and interval analysis to exact Voronoi and power triangulation construction.
Ph. D. Research
Prof. Gavrilova have obtained her Doctoral degree from Department of Computer Science and Department of Mechanical and Manufacturing Engineering at the University of Calgary. Design and analysis of computational geometry algorithms with the application to object-oriented simulation of dynamics of multi-body systems was the primary area of her research. The project concentrated on the simulation of granular-type materials and involved research in computer science, mathematics and mechanical engineering fields. Particular area of interest was investigation of generalized Voronoi Diagrams and Delaunay Tesselations in dynamic environment and under various distance functions.
Diploma (Honours) Research
The topic of Prof. Gavrilova research at Moscow Lomonosov State University was design and implementation of the knowledge-based computer system for mathematical research. The project used recent developments in the field of artificial intelligence and applied them to the problem of computer supported theorem proving. The result of this research was described in my thesis project, which was successfully defended in June 1993. Prof. Gavrilova has graduated from the MSU with Diploma with Honours (M.Sc. Equivalent).
