PROPOSAL OF A
MAJOR IN GEOMETRIC AND VISUAL COMPUTING
BACKGROUND
The last decade has witnessed a remarkable emergence and maturing of technologies
dealing with visual and geometric data. Many methods that were in the domain of research
labs have become classical and standard industrial practice.
Recent cool examples include Google Goggles (a web service allowing the user to take a
street image with a mobile phone and get information about the depicted objects), Google
Street View and Microsoft Photosynth (photo tourism service, based on computer vision
algorithms for building 3D models of cities from very large sets of images), Microsoft Kinect
(an add-on to Xbox console allowing gesture-based control, based on computer vision
technology to scan the 3D scene in real time and pattern recognition algorithms to analyze
the gestures), and the movie Avatar (setting a new standard both in computer graphics
realism, but also remarkable for the use of very sophisticated 3D vision technologies during
production).
These examples belong to the field of Geometric and Visual Computing, dealing with
processing and analyzing visual and geometric information. The world we live in is
geometric, both on the physical (objects that surround us) and abstract levels
(representation of data). Hence, diverse application areas must deal with geometric
information.
Geometric and Visual Computing is a combination of computer science (discrete algorithms,
data structures, software engineering), mathematical modeling (theoretical foundations and
computational methods), which are used in the domains of computer graphics, computer
vision, 2D and 3D signal processing, and pattern recognition.
Applications include CAD/CAM systems, geology, geographic information systems, search
engines, and navigation systems, computer games, robotics, molecular biology, medical
imaging, drug design, computer aided medicine, computer games, home entertainment, and
movie industry, some of which have already brought a revolution into our life.
DEMAND
Various aspects of geometric computing are required for jobs dealing with CAD/CAM
systems, VLSI, geographic information systems, engineering, numerical simulations, special
effects and graphics (e.g. movie industry), image processing and analysis, computer vision,
and multidimensional data analysis. These jobs demand specialists combining strong
theoretical background in math, expertise in geometry, knowledge of computational
methods, and software development skills.
In Switzerland, prominent companies include Google (computer vision), Disney (computer
graphics and advanced numerical methods), IBM (nanotechnology and electronic design
automation), as well as Liberovision (realistic 3D displays), Procedural Inc (3D city modeling),
Meteomedia (weather visualization).
SIMILAR PROGRAMS
Mathématiques/Vision/Apprentissage (MVA) – joint Master program between ENS, Ecole
Polytechnique, ENPC, and Ecole Centrale in France
Geometric Modeling and Scientific Visualization – KAUST.
Computer Visualistik – University of Magdeburg
UNIQUENESS
Using geometry as a common denominator allows to present topics in graphics, vision, and
pattern recognition in a unified and consistent way. Compared to other programs that offer
separate and unrelated courses, the proposed program has tightly-coupled and related
courses that, if taken together, allow the students to see a broader perspective of the field,
and use the same tools and background.
The proposed program is based on a synergy between curricula in (i) informatics, (ii) applied
mathematics and numerical methods, and (iii) domain-specific curricula in computer
graphics, computational geometry, image and geometry processing, computer vision and
pattern recognition.
In particular, the program is a nice way to use tools and methods taught also in
computational science in different and less traditional domains (e.g., using numerical
solutions of diffusion equations for image enhancement). Moreover, some of the methods
taught (e.g. geometric data structures and algorithms) are useful in many other areas of
informatics as well.
PROGRAM TECHNICAL DETAILS
The study program consists of three blocks with five courses each:
1. The mandatory basic courses of the Master (30 ECTS),
2. the tagged courses that form the “core” of this major (30 ECTS),
3. additional elective courses (30 ECTS).
The core courses on Geometrical Algorithms (Papadopoulou), Computer graphics and
Geometry processing (Hormann) already exist, while the courses on Geometric image
processing and computer vision and Geometric shape analysis (Bronstein) will be new.
RELATIONS BETWEEN TOPICS IN GEOMETRIC AND VISUAL COMPUTING
Color code:
Blue – mathematical background
Orange – algorithmic background (geometrical algorithms and data structures)
Green – technical background (visualization techniques, GPU programming)
Cyan – image processing and computer vision
Red – geometry processing
Purple – pattern recognition
STUDY PROGRAM (new courses in italics, core courses in bold)
Semester 1:
Basic courses
Algorithms and Complexity
Software Engineering
Programming Languages
6
6
6
Tagged courses
Computer Graphics
PDEs – Math Modeling and Numerical Simulations
6
6
Semester 2:
Tagged courses
Geometrical Algorithms
Geometric image processing and computer vision
Geometry processing
Elective courses
e.g. Modelling, Simulation, and Optimization /
Linear and Nonlinear Multiscale Solution Strategies /
Computational Fluid Dynamics /
Software Architecture + Lab / etc.
6
6
6
12
Semester 3:
Basic courses
Intelligent systems
Distributed systems
6
6
Tagged courses
Geometric shape analysis
6
Elective courses
e.g. Heuristics + Lab / Computer Aided Verification /
Introduction to Advanced Computational Methods / etc.
Semester 4:
Master thesis
12
30
COURSE SUMMARIES
Computer graphics
In this course we cover the following topics: ray tracing, local illumination, geometric
transformations, 3D object modelling, mesh processing, graphics pipeline, rasterization,
texture mapping. While the theoretical foundations are taught in the lectures, the
homework assignments and exercise sessions cover the practical aspects, including the
implementation of all techniques. The latter is done using C (programming language), Qt
(GUI library), and OpenGL (graphics API). For all programming tasks we provide a rough
framework, so that the students can concentrate on implementing the core methods and
algorithms.
Geometrical algorithms
Computational geometry is a subfield of design and analysis of algorithms dealing with
geometric problems. The course will cover various techniques needed in designing and
analyzing efficient algorithms and data structures for computational problems in discrete
geometry such as convex hulls, triangulations, geometric intersections, Voronoi diagrams,
arrangements of lines, geometric retrieval, range searching, arrangements of lines and
hyperplanes. Computational geometry is well related to a variety of application domains in
which geometric algorithms play a fundamental role, such as computer-aided design (CAD),
pattern recognition, image processing, computer graphics, information retrieval, geographic
information systems (GIS), robotics, and many others.
Geometry processing
3D geometry is fundamental to many applications, including virtual characters for animated
motion pictures, interactive design of cars and airplanes, and complex simulations of
materials and matter. This course covers the whole 3D geometry processing pipeline from
measuring real objects with laser scanners or tomography to finally rendering the 3D
geometry on screen.
Geometric image processing and computer vision
The course focuses on geometric computational methods and algorithms in image
processing and understanding. Many problems in these fields can be formalized using the
notions of calculus of variations and brought down to the solution of a partial differential
equation, such as the non-linear diffusion equation. Examples of applications shown will
include: shape from stereo reconstruction, color image enhancement and segmentation,
edge-preserving image denoising, edge detection and integration, mathematical
morphology.
Geometrics shape analysis
Geometric shapes are used to model the world around us at all levels, from macro to nano,
and the need to study and analyze such shapes and model their behavior arises in a wide
spectrum of applications, ranging from medicine to security. This course covers basic notions
in mathematical modeling of shape similarity, geometric invariants, and problems of shape
comparison and correspondence. One of the main emphases of the course will be on
practical methods, and examples of applications from pattern recognition and computer
graphics will be shown.
ACTIONS TAKEN SO FAR
1. Integration of all five basic courses into the curriculum as requested by the general rules
of the master (some of them were missing before).
2. Simplified the study program so that only the five core courses are mandatory and the
remaining courses are elective (before we had two versions, one with electives from the
majors except Comp. Sc., one with electives mainly from the major in Comp. Sc.).
3. An additional page for the Master Booklet was created.
4. All information about this major (or rather “specialization”) is available online at
www.master.inf.usi.ch.
5. Kick-off even on May 13, 2011 with Markus Gross (Director of Disney Research in Zurich,
and Professor at ETH); attendance from the student side was very good (about 75–100
students attended), but very few faculty members and people from outside USI came.