The aim of the thesis is to propose and analyse a method for improving the segmentation process based on Statistical Shape Models (SSM) by the means of a model based on intensity proﬁles.

These proﬁles are sampled along the normals of each point of the surfaces in the training-set that were used to build the Statistical Shape Model. Once the proﬁles are sampled, they are normalised and then the proﬁles of each data-set in the training-set is clustered separately using the Neighbour- hood Expectation Maximisation (NEM) algorithm which unlike the regular EM algorithm performs a spatial regularisation by taking neighbourhood informa- tion into account which remove some noise, i.e. geometrical distance between proﬁles is added to the proﬁle comparison introducing local smoothing of the obtained clusters.

Finally a fusion step is performed on the diﬀerent clustering solutions to merge clusters that are similar. This allows to drastically diminish the number of diﬀerent clusters and provide a statistical signiﬁcance for the model. The goal is to ﬁnd zones where the proﬁles are similar on all of the surface in the training set. This would enable to enhance the segmentation process with the SSM. In fact, it could then deform the surface of the models in such a way that these zones ﬁnd their matching proﬁles in the segmented image. To determine the optimal number of clusters, the Overlap Separation Index (OSI) proposed by F. Chung was analysed. It turns out that the method isn’t suited for the use on the posterior probabilities generated by the NEM algorithm due to the sharpness of the resulting clusters. For future work I proposed to compute the OSI on a fuzzy clustering initialised with the results of the NEM algorithm.

An heuristic was developed to estimate the optimal parameter for the spa- tial regularisation performed in the NEM algorithm. It proved to be rather successful as it provided valid values for the parameter sought. Before studying the merging of the clusters itself, attention was paid to the measure that allows to compare two clusters and to ﬁnally decide if they should be merged or not. The Jaccard index was used and although it gives good results, its nature prevents to take into account big diﬀerences between the means of two clusters as it is only based on the surface delimited by the standard deviation around the mean.

The last step of the global algorithm was analysed too and it seems that another method should be found to merge clusters as the one proposed by F. Chung. In fact, merging clusters that are similar regarding their intensity values only, can dramatically expand them spatially producing clusters that cover a high percentage of the surface with small cluster memberships. As the goal is to ﬁnd zones with very high of such membership values, that particular point should also be improved.

All in all, the method works quite well and the proposed improvements should allow to move towards the realisation of a powerful intensity model which could then lead to a better segmentation using Statistical Shape Models.

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Publication

Master thesis in Computer Science, Faculté des Sciences Appliquées, Université Libre de Bruxelles