ADVANCED MATHEMATICAL TOOLS IN IMAGE
PROCESSING AND COMPUTER VISION
Ebroul Izquierdo
Universidad de Londres, INGLATERRA
Abstract
When Russell Kirsch produced the first digital image, using a very sensitive lightdetecting tube (photomultiplier) to map the parts of an analogue image into black
or white square pixels, a new branch of technology was born. The generation of
that first image, of just 176 × 176 pixels, led to a wave of research and applications over the last 50 years. Most of these applications have had a profound impact
in both critical technological developments of the last century and in every day
live. Image processing and computer vision have indeed tremendously influenced
our life and society. It has also become a key element of the digital age. Substantial applications include medical imaging for non-intrusive diagnose, for instance
magnetic resonance imaging and tomography; automated surveillance in critical security applications; visual information retrieval; automated robotic navigation for
defense and remote space surveillance and assessment; entertainment including conventional broadcasting, film production and gaming; virtual, mixed and augmented
reality; space exploration and astronomical imaging; advanced customers electronics including computational photography and video production; social networking;
telecommunications and many others. Apart from the fundamental impact of image
processing and computer vision and modern technological developments; it is also
widely acknowledged that image understanding is the most important aspect of artificial intelligence. Thus, it has also substantial impact on current research trends
and will remain impacting technology and society for years to come.
However image processing and computer vision would not have developed so fast
and solidly without advanced mathematical tools and analysis. Indeed at the center of related developments one can find important mathematical tools, which have
certainly enabled this branch of science and technology to flourish. Key related
mathematical fields included advanced linear algebra for automated clustering and
classification; advanced matrix theory for visual information retrieval; partial differential equation to simulate optical flows and dynamic shape deformation; harmonic
analysis including Fourier theory and wavelets for image compression storage and
transmission; metric theories; graph theory and many others.
The objective of this short course is to present and overview of some key math1
ematical theories and they use/application in solving some of the most important
problems in image processing and computer vision. The course will outline a wide
spectrum of problems in the field and focus on some few selected topics to elaborated
and presented deeper. Current bottlenecks and still open problems in the field will
be also presented and discussed.
Course structure:
Four lectures of 30 min plus 10 min for Q&A or discussions, as follows
Two lectures the first day, one after the other with a short break in-between
Two lectures the second day, one after the other with a short break in-between
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