ICPR 2010 Tutorial:
The focus is on the design of basic multi-scale 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 with multi-scale (‘scale-space’) differential operators. We show everything interactively with Mathematica version 7.
Time, place, duration:
Sunday 22 August 2010. The tutorial consists of a half day, with 4 lectures of 45 minutes. All lectures will be given by the tutorial speaker.
|Prof. Bart M. ter Haar Romeny, PhD
Eindhoven University of Technology
Den Dolech 2 – WH2.106
NL-5600 MB Eindhoven, the Netherlands
Webpage course at Eindhoven University of Technology: http://bmia.bmt.tue.nl/Education/Courses/FEV/course/index.html
The teaching of efficient and mathematically well funded multi-scale differential geometry for the design of advanced algorithms to the ICPR 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 7, is that is has unequalled possibilities for manipulating parameters in a design. It integrates symbolics, fast numerics (now faster than Matlab) and excellent graphics.
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.
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.
Local second order structure (eigenvectors of the Hessian)
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.
Full attention to toppoints in scale-space.
The majority of the examples discussed are from 2D, 3D and 4D (3D-time)
We devote some time to the efficient numerical implementation of the different techniques.
 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 ICPR the CD-ROM can be purchased for US$ 35,-.
 J. Weickert: Anisotropic Diffusion in Image Processing. ECMI Series, Teubner-Verlag, Stuttgart, Germany, 1998.
 D. Hubel: Eye, Brain and Vision. Scientific American Press, 1988. Now
available on the web.
Excellent start for exploring mechanisms of human vision.
 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
 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
We design all our algorithms in Mathematica 7 (Wolfram
Inc., Champaign, Ill.).
Mathematica 7 is a powerful software environment for symbolic and fast numerical computing.
The new version 7 makes everything interactive with a single line of code, enabling easy 'playing with complex math'.
A trial version of Mathematica 7 can be downloaded from
here (valid for 15 days).
Many universities and institutes offer it as part of their campus license software.
Bring your own laptop and do all experiments directly yourself.
See you all at ICPR 2010.
Prof. Bart M. ter Haar Romeny, PhD
Eindhoven University of Technology, Department of Biomedical Engineering
Biomedical Image Analysis