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 state-of-the-art methods, exploiting multi-scale (‘scale-space’) differential operators, adaptive methods, and multi-orientation techniques..

We learn to design everything interactively with the powerful design language Mathematica version 9 (

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 – GEM-Z 2.106
NL-5600 MB Eindhoven, the Netherlands
Tel. +31-40-2475537, +31-6-24235693

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 multi-scale 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 high-level 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.

09:00-09:45 Lecture 1: We start with an intuitive introduction about the role of computer vision.

10:00-10:45 Lecture 2: We discuss why multi-scale 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.

11:00-11:45 Lecture 3: Introduction to Mathematica 9.

Powerpoint of first morning.

Notebook with examples of first morning.

12:00-13:00 Lunch

13:00-17:00 Computer lab.

Train yourself with the following notebooks. The last one has some advanced demos at the end:

The visual system is a multi-scale sampling and analysis system.

Cortical receptive field models for multi-scale differential operators.

Tutorial Mathematica notebooks:

Course part 1 of 3 (English)

Course part 2 of 3 (English)

Course part 3 of 3 (English)

When you master the basics, you can also have a look at e.g.:

       << Benchmarking`
       BenchmarkReport[ ]

(PS: don't forget the backquote `)

  •  You can inspect if your system is ready for parallel processing (on multiples cores, or on the GPU with CUDA or OpenCL) with:
    SystemInformation[ ]
Second day: Wednesday 23 April 2014, KennisPoort, Main Theatre

09:00-09:45 Lecture 1: Properties of the Gaussian kernel, and Gaussian derivatives.

10:00-10:45: 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.

11:00-11:45 Lecture 3: We derive invariant multi-scale operators for edges, corners, vesselness, colon polyp detection, and T-junction detection. We develop several notions for scale selection.

12:00-13:00 Lunch

13:00-17:00 Computer lab.

Multi-scale vesselness
(Frangi et al. 1999).

Local second order structure (eigenvectors of the Hessian).

Tasks for Wednesday:    
Third day: Thursday 24 April 2014, MetaForum 06

09:00-09:45 Lecture 1: Design of nonlinear, adaptive (geometry-driven) multi-scale diffusion algorithmsfor edge-preserving 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.

10:00-10:45 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.

11:00-11:45 Lecture 3: The multi-scale 'deep structure' of images. We discuss the notion of edge focusing for extremely noisy edge detection, the multi-scale watershed segmentation algorithm and how multi-scale feature points can be effectively used for image retrieval and image matching (registration into correspondence).

12:00-13:00 Lunch

13:00-17:00 Computer lab.


Coherence enhancing diffusion on a fingerprint (Weickert 1995).

Dense multi-scale optic flow field from MR tagging with scale selection.

Fourth day: Friday 25 April 2014, MetaForum 11/12
09:00-09:45 Practical examples of derivatives, convolutions, and features.

10:00-10:45 Keypoints in images

11:00-11:45 Questions and answers

12:00-13:00 Lunch

13:00-16:00 Computer lab.

Edge focusing for very noise edge detection.

Mluti-scale toppoints in scale-space for image retrieval and matching.

The majority of the examples discussed are from 2D, 3D and 4D (3D-time) medical imaging.
We devote some time to the efficient numerical implementation of the different techniques.

[1] B.M. ter Haar Romeny, (2004). Front-End Vision and Multi-Scale 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. 581-597) 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