## Section: New Results

### Applications to biology and medicine

#### 3D microscopy deconvolution using the Richardson-Lucy algorithm with complex wavelet regularization

Keywords : 3D confocal microscopy, deconvolution, complex wavelet regularization, Richardson-Lucy algorithm.

Participants : Mikael Carlavan, Laure Blanc-Féraud [ contact ] .

The research of Mikael Carlavan is supported by the ANR under the project `ANR Detectfine' (Laboratory I3S, CNRS/UNSA, and INRIA).

Confocal microscopy is an increasingly popular technique for the 3D imaging of biological specimens. However the images acquired with this technique are degraded by blur and Poisson noise. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy iterative algorithm regularized using a Total Variation prior. This gives good results in image restoration, but does not allow the retrieval of fine, oriented details (including textures) in the specimens. For several years, wavelet transforms have been used in image processing to restore the fine details of complex scenes. Recently, several authors have proposed improving the directional resolution of classical wavelets by using a wavelet transform with two trees. We propose to use a recent extension of these dual-tree transforms to the complex case, and to extend the iterative Richardson-Lucy algorithm to this prior. Results on real data are shown in figure 16 .

#### Blind deconvolution for confocal laser scanning microscopy

Keywords : Confocal Laser Scanning Microscopy (CLSM), blind deconvolution, Richardson-Lucy (RL) , Total-Variation (TV) , Expectation-Maximization (EM) .

Participants : Praveen Pankajakshan, Laure Blanc-Féraud, Josiane Zerubia [ contact ] .

This Ph.D. was funded by a CORDI Fellowship and is part of the P2R Franco-Israeli project (2005-2009) [http://www-sop.inria.fr/ariana/Projets/P2R/ ].

Three dimensional (3D) fluorescence microscopy through optical sectioning is a very powerful technique for visualizing biological specimens. In optical sectioning, the microscope objective is focused at different depths of the observed sample. However, the observation process is never perfect and there is blur, noise, and aberrations in the 3D images. Classical approaches that attempt to restore these images assume that the underlying degradation process is known. However, in fluorescence microscopy, often the degradation is specimen dependent and varies with the imaging conditions. Blind restoration approaches tackle this much more difficult and realistic situation where the degradation is unknown [4] . Blind deconvolution is an ill-posed underdetermined problem. For thin specimen imaging, an alternate minimization (AM) approach has been proposed within a Bayesian framework, restoring the lost frequencies beyond the diffraction limit by using regularization on the object and a constraint on the point spread function (PSF). Furthermore, new methods are proposed to learn the free-parameters, like the regularization parameter, which conventionally is set by hand-tuning.

When imaging into deeper sections of the specimen, the approximation of an
aberration-free imaging process, as was assumed previously, is no longer
good. This is because the refractive index mismatch between the specimen
and the immersion medium of the objective lens becomes significant with
depth under the cover slip. An additional difference in the path is
introduced in the emerging wave front of the light due to this difference
in the index, and the phase aberrations of this wave front are significant [38] .
The spherical aberrated (SA) PSF in this case becomes dependent on the
axially varying depth. We use geometrical optics to model the refracted
wave front phase, and so the aberrated PSF, and we show for some simulated
images that an object's location and its original intensity distribution
can be recovered from the observed intensities (*cf * figure 17 ).

#### Detecting thin structures in biological images using variational methods

Keywords : variational method, L 1 -norm, Γ-convergence, deconvolution, biology imaging.

Participants : Daniele Graziani, Laure Blanc-Féraud [ contact ] .

This work was made in collaboration with Gilles aubert from Dieudonné Institute.

Detecting filaments [35] , *i.e. * open curves in two and three dimensional images,
is a crucial task in image analysis. In biological images (see figure 18 ), a filament may
represents a cell membrane whose visibility is compromised by the presence
of other structures like isolated points or some noise. Moreover due to
microscope effects these curves can appear blurred. From these images [36] ,
biologists wish to obtain an image as close as possible to the original
one: an image with high intensity on the thin filaments and zero otherwise.
This is a segmentation problem that cannot be solved by classical detection
methods based on the gradient operator, such as active contours or total
variation models, since in general filaments in dimension 2 are not
closed curves. In particular, the initial image I_{0} , before taking the
convolution, is not a special bounded variation (SBV ) function, but rather a Radon Measure
concentrated on lines. This crucial difference make these singularities
hard to detect by means of variational methods. We propose to look at the
divergence operator of a suitable vector field as a candidate detector. We
make an initial predetection by using the gradient of the solution of a
classical Neumann problem with data I , the observed image. We obtain an
initial vector field U_{0} , whose divergence copies the singularities we
want to detect, but which is still far from being the original image. We
retrieve the original filaments by minimizing an energy involving the total
variation of the divergence, which allows singularities on thin structures.

#### Segmentation of brain tumours from tomographic data

Keywords : tomography, brain vascular network, tumour, Markov random field, Graph.

Participants : Chirag Sethi, Siddarth Dhakad, Xavier Descombes [ contact ] .

This study was partially supported by ANR project Micro-Réseaux. It was performed in collaboration with IMFT (Franck Plouraboué and Hakim El Boustani).

We consider tomographic volumes of the brain vascular network and show that the vascular network shows different properties in tumours and in healthy tissue. We compute a tumour segmentation based on these properties. We first compute the skeleton of the binarized vascular network. We then compute the watershed associated to the opposite of a distance transform of this skeleton (see figure 19 ). By rejecting the null hypothesis, we have shown that the size of the different areas from healthy tissue and tumour are statistically significantly different. In addition, we have shown that the distribution of sizes follows a Pareto distribution. Based on these results, we have defined a binary Markov random field on a graph, where each node represents a given region, and the edges are defined by the connectivity between regions. The data term is defined using region size, whereas a prior term incorporates spatial homogeneity of the solution. Optimization, based on a simulated annealing scheme, then provides a segmentation of the tumour area.

#### Multi-spectral image analysis for skin pigmentation classification

Keywords : skin hyper-pigmentation, multi-spectral images, support vector machine, independent component analysis, classification.

Participants : Sylvain Prigent, Xavier Descombes, Josiane Zerubia [ contact ] .

This work was partially funded by a contract with Galderma R&D Sophia Antipolis [http://www.galderma.fr ].

The analysis of images of the skin is important for dermatologists to evaluate precisely the evolution of a disease and the efficiency of a treatment. Usually, dermatologists use colour images or select a few bands of interest in multi-spectral images. In this work, we use the whole spectrum of bands in multi-spectral images in order to quantify skin hyper-pigmentation. We compare two types of methods: classification using a support vector machine, and source separation.

In the literature on multi- and hyper-spectral image classification, use of an SVM is often associated with a data reduction step to avoid the Hughes phenomenon. We show that using data reduction with projection pursuit before SVM classification improves the results for skin hyper-pigmentation. The projection pursuit is computed using the Kullback-Leibler divergence. Moreover, a pre-processing spectral analysis step is applied to partition the spectrum into groups.

For the source separation approach, we use independent component analysis. As shown in figure 20 , SVM in combination with projection pursuit and independent component analysis are the methods which give the best results for skin analysis. The main difference between these two semi automatic methods is the impact of the operator on the classification. The skin images contained some artefacts due to body shape and lighting in some areas. Therefore, a method was also introduced to compensate these effects, by substracting an appropriate near infra-red channel. This work resulted in two joint patent deposits (Galderma/INRIA).