MICCAI 2008 Tutorial:
Designing
multi-scale algorithms
medical image analysis
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MICCAI 2008 Tutorial: Designing |
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The tutorial:
The focus is on the design of basic multi-scale algorithms for
medical 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 with multi-scale (‘scale-space’)
differential operators. We show everything interactively in the new Mathematica
version 6.
Time, place, duration:
Wednesday morning 10 September 2008, 08:00 am - 12:00 noon.
The tutorial consists of a half day, with 4 lectures of 45 minutes. All lectures will be given by the tutorial speaker.
Registration.
The tutor:
| Prof. Bart M. ter Haar Romeny, PhD Eindhoven University of Technology Den Dolech 2 – WH2.106 NL-5600 MB Eindhoven, the Netherlands Tel. +31-40-2475537 Email: B.M.terHaarRomeny@tue.nl Homepage: http://bmia.bmt.tue.nl/people/BRomeny/index.html Webpage course at Eindhoven University of Technology: http://bmia.bmt.tue.nl/Education/Courses/FEV/course/index2008-BME.html |
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Objectives:
The teaching of efficient and mathematically well funded
multi-scale differential geometry for the design of advanced algorithms to the
MICCAI community, especially the PhD students. Justification: Modern image
analysis needs substantial understanding of the mathematical underpinning of the
applied algorithms. This course invites to ‘play with the math’ by introducing
the multi-scale framework.
We show that we can learn a lot from models of human visual perception. Some
examples we will touch:
- the retina can actually be seen as a multi-resolution camera, sending a
scale-space stack to the brain;
- the retina consists of two types of ganglion cells, so is effectively two
multi-resolution cameras, one for shape and one for motion;
- cortical 'simple cells' can be modelled as Gaussian derivatives, taking high
order multi-scale derivatives at each pixel;
- feedback from cortex to the thalamus can be modelled as adaptive diffusion,
for many forms of geometry-driven, edge preserving smoothing;
- brain plasticity (self-organization) can be mimicked by eigen-analysis of
small image patches, leading to optimal kernels for each image type;
- modern optical techniques by voltage sensitive dyes have revealed an intricate
structure for multi-orientation analysis (http://www.weizmann.ac.il/brain/grinvald/);
this invites to generalize the notion of convolution (normal convolution:
translation of the kernel; wavelet convolution: dilation of the kernel;
multi-scale convolution: blurring of the kernel; oriented convolution: rotation
of the kernel), all leading to very rich high dimensional 'deep' data
structures, which the visual system seems to exploit simultaneously. So does
e.g. the 'multi-orientation score' contain tensor voting, and opens nice and
natural possibilities for HARDI analysis.
The reason we use Mathematica 6, is that is has now unequalled possibilities for
manipulating parameters in a design. It integrates symbolics, fast numerics (now
faster than Matlab) and excellent graphics.
Tutorial overview:
| First lecture: We start with an intuitive introduction (45 min) 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. |
  The visual system is a multi-scale sampling and analysis system. |
 Cortical receptive field models for multi-scale differential operators. |
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| Second lecture: We then proceed (45 min) with the introduction of first order gauge coordinates, giving a powerful framework for differential features to high order, invariant to the choice of coordinate system. We derive invariant multi-scale operators for corners, vesselness, colon polyp detection, and T-junction detection. We develop several notions for scale selection. |
Multi-scale vesselness |
 Local second order structure (eigenvectors of the Hessian) |
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| Third lecture: This lecture (45 min) is focused on the design of nonlinear geometry-driven diffusion algorithms, 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. All with short-code live demonstrations. We also focus on the multi-scale analysis of optic flow. We introduce the multi-scale Horn & Schunck equation, and show how high order dense flow fields can be extracted, for the calculation of e.g. strain and strainrate in the ventricular wall. |
Coherence enhancing diffusion on a fingerprint (Weickert 1995). |
 Dense multi-scale optic flow field from MR tagging with scale selection. |
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Fourth lecture: |
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Edge focusing. |
Full attention to toppoints in scale-space. |
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.
Literature:
[1] B.M. ter Haar Romeny, Front-End Vision and Multi-Scale Image Analysis,
Springer Verlag, 2004. This book is written in Mathematica, the code of every
item discussed is supplied, and can be used for own experiments. The
accompanying CD-ROM covers all 22 notebooks of the text of the book. It contains
almost 800 references.
During the tutorial at MICCAI the CD-ROM can be purchased for US$ 35,-.
[2] J. Weickert: Anisotropic Diffusion in Image Processing. ECMI Series,
Teubner-Verlag, Stuttgart, Germany, 1998.
[3] D. Hubel: Eye, Brain and Vision. Scientific American Press, 1988. Now
available on the web.
Excellent start for exploring mechanisms of human vision.
[4] B. Platel, E. Balmachnova, L.M.J. Florack, B.M. ter Haar Romeny, Top-Points as Interest Points for Image Matching, Lecture notes in computer science, 3951, 418-429, (2006) PDF
[5] R. Duits, M.Felsberg, G.Granlund, Bart ter Haar Romeny, Image Analysis and Reconstruction using a Wavelet Transform Constructed from a Reducible Representation of the Euclidean Motion Group, IJCV, 72, 79-102, (2007) PDF
Mathematica 6:
We design all our algorithms in Mathematica 6 (Wolfram
Inc., Champaign, Ill.).
Mathematica 6 is a powerful software environment for
symbolic and fast numerical computing.
The new version 6 makes everything
interactive with a single line of code, enabling easy 'playing with complex
math'.
Mathematica tutorials:
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During MICCAI 2008 an unrestricted professional trial version of Mathematica 6 can be downloaded from here (valid for 15 days).
Bring your own laptop and do all experiments directly yourself.
Page with presented materials.
See you all at MICCAI 2008.
Prof. Bart M. ter Haar Romeny, PhD
Eindhoven University of Technology, Dept. of Biomedical Engineering
Biomedical Image Analysis
B.M.terHaarRomeny@tue.nl
Mathematica
tutorial
part 1 of 3