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EPFL   Student Projects: Alex Omar Prudencio Arispe
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Extended Depth of Field Using Hidden Markov Models in Wavelet Domain

Alex Omar Prudencio Arispe
Section Systèmes de Communication, EPFL

Diploma Project
September 2005



Light microscopy imaging usually suffers of a limited depth of field. That is the region in front and behind the object focal plane that will be in acceptable focus. Most of the times, the specimen depth is much larger that the depth of field. Thus, in order to study the entire specimen we have to move it along the optical axis, obtaining several images with different regions appearing in focus on each of them. Extended depth of field (EDF) is a fusion algorithm that from the obtained stack of images produces one assembled image containing all the in focus regions. In this way we obtain one in focus image as if the depth of field of the optical system was “extended”. There are different EDF algorithms among which we can mention those based on the discrete wavelet transform; these giving the most promising results. However, these algorithms tend to produce some artifacts on the resulting images and require some heuristic processing to give acceptable results.

In this project we propose a new EDF algorithm that avoids this empirical approach by using hidden Markov models (HMM) in wavelet domain [1]. We use HMM to model depencies between wavelet coefficients. We obtain a very rich model of the wavelet coefficients, that can be used to estimate the topology of the specimen.


Depth of Field.
Stack of Images.
Composite Image
Specimen's Topology


[1] M. Crouse, R. Nowak, and R. Baraniuk. Wavelet -Based Statistical Signal Processing Using Hidden Markov Models. IEEE Transactions on Signal Processing, 46(4), April 1998.