Wavelet analysis for morphological characterization of Saccharomyces Cerivisiae A. Doncescu*, L. Manyri, & S. Regis Laboratory of Biotechnology and Bioprocesses-INSA, Toulouse 1 Introduction Saccharomyces cerevisiae is used extensively in a large field of applications in biotechnology, e.g. biofuel, alcoholic beverages, baker yeast and recombinant protein. The intensification of bioreaction processes based on cell culture engineering can lead to changes of metabolic activ- ities and biological functions (budding) because of high concentration of inhibitors, limitation of substrate. Exposed to increasing ethanol concentrations for instance, yeast cell morphology and activity are notably affected. The quantification of the budding and the cellular size of the yeast cells allow us to characterize the cell cycle and phenomena of stress encounter by the yeast. The analysis of microbial cells at the single-cell level may also lead to the quantification of subpopulations at different physiological states. Thereby, we have characterized the mor- phology of different population of yeasts during two discontinuous fed-batch fermentation by using image analysis. However the weakness of the traditional microscopy (with coloration or fluorescent probes) is the absence of the direct image analysis of cells and the time consuming of the image analysis. One of the image processing is the detection of the budding cells. The idea is to find with a lot of precision the H¨ older Coefficient corresponding to the curvature changing. The H¨ older Coefficient is carry out by Wavelet Transform coupled to Genetic Algorithms. 2 H¨ older’s Coefficient, Wavelet Transform and Genetic Al- gorithms A singularity in a point is characterized by the H¨ older exponent. This exponent is defined like the most important exponent allowing to verify the next inequality: (1) We must remark that is the Taylor Development and basically . The H¨ older exponent could be extended to the distribution. For example the H¨ older exponent of a Dirac is . A fast computing leads to a very interesting result of the Wavelet Transform : (2) This relation is remarkable because it allows to measure the H¨ older exponent using the behavior of the Wavelet Transform. Therefore, at a given scale the will be maximum in the neighborhood of the signal singularities. The detection of the H¨ older is linked to the vanishing moment of the wavelet: if is the vanishing moment of the wavelet, then it can detect H¨ older coefficient (Mallat and Whang, 1992). The H¨ older coefficient enables us to characterize the variation of the signals and to find the meaningful maxima. 123