The tutorial:
The focus is on the design of powerful computer vision algorithms for
quantitative image analysis.
Image analysis is the extraction of useful information from images. To design
useful algorithms a powerful language for geometric reasoning is needed.
In this tutorial we focus on differential geometry, a powerful concept to
understand shape, features, enhancement etc.
We treat stateoftheart methods, exploiting multiscale
(‘scalespace’) differential operators, adaptive methods, and multiorientation
techniques..
We learn to design everything interactively with the powerful design language Mathematica version 9 (www.wolfram.com).
Time: Four days, Tuesday 22 April 2014 till Friday 25 April 2014.
Location lectures: TU/e Campus, Eindhoven. MetaForum and Black Box.
Location computer lab: MetaForum, office gardens on floor 5 and 7.
Each day consists of 3 lectures of 45 minutes in the morning, and in the
afternoon we practice the concepts in a computer lab.
All lectures will be given by the tutorial speaker.
Computer lab assistants: Andrea Fuster, PhD, and Tom Dela Haije, MSc.
The tutor:
Prof. Bart M. ter Haar Romeny, PhD Eindhoven University of Technology Department of Biomedical Engineering Biomedical Image Analysis Den Dolech 2 – GEMZ 2.106 NL5600 MB Eindhoven, the Netherlands Tel. +31402475537, +31624235693 Email: B.M.terHaarRomeny@tue.nl Homepage: http://bmia.bmt.tue.nl/people/BRomeny/index.html 
Objectives of the course:
The introduction of efficient and mathematically well funded computer vision
methods, to be used in industrial applications.
The course will focus on modern and robust computer vision methods, in
particular on learning how to design advanced algorithms.
We introduce the notion of geometric reasoning', using multiscale
differential geometry.
This requires some mathematical insight, which will be discussed and
explained extensively.
The justification is that modern image
analysis needs substantial understanding of the mathematical underpinning of the
applied algorithms.
This course invites to ‘play with the math’ during the interactive
computerlab sessions.
The methods are inspired by the stunning performance of human visual
perception.
We shortly discuss modern findings in brain and visual system research, and how
they can be exploited in our algorithms.
The reason we use Mathematica 9 in the computer lab and all lectures, is that is
is is a highlevel software language
with unequalled possibilities for design, with extensive visualization of the
results, and interactive manipulation of parameters.
It integrates symbolics, fast numerics (now
faster than Matlab) and excellent graphics.
Tutorial overview:
First day: Tuesday 22 April 2014, MetaForum 11/12 Welcome and introduction of the participants. 09:0009:45 Lecture 1: We start with an intuitive introduction about the role of computer vision. 10:0010:45 Lecture 2: We discuss why multiscale image analysis is necessary for the analysis of discrete data. We develop from first principles the Gaussian derivative operators involved, trying to keep the analogy with the first stages in the human visual system as close as possible. 11:0011:45 Lecture 3: Introduction to Mathematica 9. Notebook with examples of first morning. 12:0013:00 Lunch 13:0017:00 Computer lab. Train yourself with the following
notebooks. The last one has some advanced demos at the end: 
The visual system is a multiscale sampling and analysis system. 
Cortical receptive field models for multiscale differential operators. 

When you master the basics, you can also have a look at e.g.:
<< Benchmarking` (PS: don't forget the backquote `)


Second day: Wednesday 23 April 2014, KennisPoort,
Main
Theatre 09:0009:45 Lecture 1: Properties of the Gaussian kernel, and Gaussian derivatives. 10:0010:45: Lecture 2: Introduction of first order gauge coordinates, giving a powerful framework for differential features to high order, invariant to the choice of coordinate system.
11:0011:45 Lecture 3: We derive invariant multiscale operators for edges, corners, vesselness, colon polyp detection, and Tjunction detection. We develop several notions for scale selection. 12:0013:00 Lunch 13:0017:00 Computer lab. 
Multiscale vesselness 
Local second order structure (eigenvectors of the Hessian). 

Tasks for Wednesday:


Third day: Thursday 24 April 2014, MetaForum 06 09:0009:45 Lecture 1: Design of nonlinear, adaptive (geometrydriven) multiscale diffusion algorithmsfor edgepreserving smoothing, by incorporation of proper geometric reasoning of the denoising task. We present elegant derivations of Perona and Malik anisotropic diffusion, Euclidean shortening flow, and coherence enhancing diffusion.
10:0010:45 Lecture 2: Our visual system, what can we learn from it? We go in some depth by studying modern optical recordings of the living brain, and models of visual perception.
11:0011:45 Lecture 3: The multiscale 'deep structure' of images. We discuss the notion of edge focusing for extremely noisy edge detection, the multiscale watershed segmentation algorithm and how multiscale feature points can be effectively used for image retrieval and image matching (registration into correspondence).
12:0013:00 Lunch 13:0017:00 Computer lab.

Coherence enhancing diffusion on a fingerprint (Weickert 1995). 
Dense multiscale optic flow field from MR tagging with scale selection. 

Fourth day: Friday 25 April 2014, MetaForum 11/12 10:0010:45 Keypoints in images
11:0011:45 Questions and answers 12:0013:00 Lunch 13:0016:00 Computer lab. 

Edge focusing for very noise edge detection. 
Mlutiscale toppoints in scalespace for image retrieval and matching. 
The majority of the examples discussed are from 2D, 3D and 4D (3Dtime)
medical imaging.
We devote some time to the efficient numerical implementation
of the different techniques.
Literature:
[1] B.M. ter Haar Romeny, (2004). FrontEnd Vision and MultiScale Image Analysis,
Springer Verlag.
URL.
This book is written in Mathematica, the code of every
item discussed is supplied, and can directly be used for own experiments.
[2] B.M. ter Haar Romeny, (2013). The differential structure of images.
PDF.
In V. Lakshminarayanan (Ed.), Mathematical optics. (pp. 581597) Boca Raton: CRC
Press.
Mathematica 9:
We design all our algorithms in Mathematica 9 (Wolfram
Inc., Champaign, Ill.). Mathematica 9 is a powerful software environment for symbolic and fast numerical computing. The new version 9 makes everything interactive with a single line of code, enabling easy 'playing with complex math'. 
A trial version of Mathematica 9 can be downloaded from
here (valid for 30 days).
Many universities and institutes offer it as part of their campus license
software.
If you have access to the TU/e domain, download Mathematica 9
here.
Bring your own laptop and do all experiments directly yourself!
Prof. Bart M. ter Haar Romeny, PhD
Eindhoven University of Technology, Department of Biomedical Engineering
Biomedical Image Analysis
B.M.terHaarRomeny@tue.nl