# Applications

Finance

Genetics

Image Analysis: Mathematical morphology

## Finance

TODO

## Genetics

The structure of this section could be:
- Microarrays, gene clustering (SOM)
- Phylogenetics
- QTL
I could mention the following packages:
qtl (quantitative traits loci)
bqtl
GeneSOM Clustering genes using Self-Organizing Maps (SOMs).
ape Analyses of Phylogenetics and Evolution
sma micro-array analysis
permax (DNA array)
genetics
PHYLOGR (devel)
See also the Bioconductor, that mainly focuses on DNA microarrays.
http://www.bioconductor.org/packages/devel/html/

## Image Analysis: Mathematical morphology

### Introduction

"Mathematical morphology" refers to local image transformation
algorithms -- "local" means that the new colour of a pixel depends on
that of the neighbouring pixels.

For instance, the game of life is local transformation.

TODO: Explain, insert a few plots.

(The more rigorous definition, should you want it, refers to
non-decreasing, involutive and local transformations.)

### TODO

Introduction: explain what mathematical morphology is.
Give a few examples of images one could want to process.
http://www.mmorph.com/pymorph/
http://www.ensta.fr/~manzaner/Publis/These.ps.gz
morphology.R
http://zoonek.free.fr/Ecrits/2004_BioRet.pdf.bz2
Images (plot.image, plot3d.image)
Packages: mainly EBImage, but also rimage, pixmap
Basic operations:
translations
rotations
Structuring elements (plot.structuring.element)
Hit-and-Miss transform ("pattern matching")
Intersection (inf), union (sup), complementary, difference
Dilatation, Erosion
Opening, closing
Gradient, internal gradient, external gradient, laplacian
Top hat
Reconstruction: Hysteresis threshold, Hole filling
Local maxima, max.loc.hys,
regional maxima, geodesic dilatation, r.h.maxima
skeleton, hairy or not
Homotopic kernel (median axis)

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Vincent Zoonekynd

<zoonek@math.jussieu.fr>

latest modification on Sat Jan 6 10:28:26 GMT 2007