Computational geometry is concerned with algorithms and data structures for geometric
objects. The primary goal of research in computational geometry has been to develop efficient
algorithms and data structures for solving problems stated in terms of basic geometrical objects,
such as points, line segments, polygons, polyhedra , arrangements (of lines, planes, geometric
shapes), etc. During the years computational geometry has evolved and took diverse paths to
many applications, such as robotics (collision free motion planning), computer graphics and
computer vision (ray tracing, shape obscuring), facility location (locating antennae on terrains),
and more. In parallel to theoretical algorithms new algorithmic paradigms are being used, such
as geometric optimization, random sampling, and randomized geometric algorithms.
Our strong group in computational geometry is involved in research in, e.g., combinatorial
issues of computational geometry, Euclidean Steiner trees, approximation algorithms, devising
efficient geometric data structures and algorithms for real world problems, and more.
The goal of computer vision is visual inference; i.e., extracting information, or
drawing conclusions, from visual data such as pictures or videos. More loosely
speaking, it is about teaching computers to see. The field combines elements
from computer science, mathematics, statistics, engineering, physics, cognitive
sciences and more. Real-world applications are omnipresent as is evident by the
high demand for computer-vision researchers in both Academia and the industry.
Examples include automatic face recognition and an autonomous car using
visual sensors to avoid collisions.
Computer graphics studies the manipulation of visual and geometric information using
computational techniques. It focuses on the mathematical and computational foundations of
image generation and processing while also considering aesthetic issues. Research in
computer graphics focuses on geometry acquisition and processing, on interactive techniques,
and on related areas such as computer vision, machine learning and AR/VR.
Imaging sciences is a broad field that involves the processing, analyzing, reconstructing,
compressing and visualizing of digital images and videos. A digital image is a numeric
representation of a two-dimensional image, using a grid of values called pixels that represent the color of the image at any specific point. Many imaging applications involve with given
(corrupted) data that is related to an unknown image, and the goal is to reconstruct the unknown image using mathematical algorithms and software.