Sandrine Mouysset

Segmentation of dynamic PET images with kinetic spectral clustering

Segmentation is often required for the analysis of dynamic positron emission tomography (PET) images. However, noise and low spatial resolution make it a difficult task and several supervised and unsupervised methods have been proposed in the literature to perform the segmentation based on semi-automatic clustering of the time activity curves of voxels. In this paper we propose a new method based on spectral clustering that does not require any prior information on the shape of clusters in the space in which they are identified. In our approach, the p-dimensional data, where p is the number of time frames, is first mapped into a high dimensional space and then clustering is performed in a low-dimensional space of the Laplacian matrix. An estimation of the bounds for the scale parameter involved in the spectral clustering is derived. The method is assessed using dynamic brain PET images simulated with GATE and results on real images are presented. We demonstrate the usefulness of the method and its superior performance over three other clustering methods from the literature. The proposed approach appears as a promising pre-processing tool before parametric map calculation or ROI-based quantification tasks.

Unsupervised Spectral Clustering for Segmentation of Dynamic PET Images

Segmentation of dynamic PET images is needed to extract the time activity curves (TAC) of regions of interest (ROI). These TAC can be used in compartmental models for in vivo quantification of the radiotracer target. While unsupervised clustering methods have been proposed to segment PET sequences, they are often sensitive to initial conditions or favour convex shaped clusters. Kinetic spectral clustering (KSC) of dynamic PET images was recently proposed to handle arbitrary shaped clusters in the space in which they are identified. While improved results were obtained with KSC compared to three state of art methods, its use for clinical applications is still hindered by the manual setting of several parameters. In this paper, we develop an extension of KSC to automatically estimate the parameters involved in the method and to make it deterministic. First, a global search procedure is used to locate the optimal cluster centroids from the projected data. Then an unsupervised clustering criterion is tailored and used in a global optimization scheme to automatically estimate the scale parameter and the weighting factors involved in the proposed Automatic and Deterministic Kinetic Spectral Clustering (AD-KSC). We validate the method using GATE Monte Carlo simulations of dynamic numerical phantoms and present results on real dynamic images. The deterministic results obtained with AD-KSC agree well with those obtained with optimal manual parameterization of KSC, and improve the ROI identification compared to three other clustering methods. The proposed approach could have significant impact for quantification of dynamic PET images in molecular imaging studies.

On a strategy for spectral clustering with parallel computation

Spectral Clustering is one of the most important method based on space dimension reduction used in Pattern Recognition. This method consists in selecting dominant eigenvectors of a matrix called affinity matrix in order to define a low-dimensional data space in which data points are easy to cluster. By exploiting properties of Spectral Clustering, we propose a method where we apply independently the algorithm on particular subdomains and gather the results to determine a global partition. Additionally, with a criterion for determining the number of clusters, the domain decomposition strategy for parallel spectral clustering is robust and efficient.

Using a Global Parameter for Gaussian Affinity Matrices in Spectral Clustering

Clustering aims to partition a data set by bringing together similar elements in subsets. Spectral clustering consists in selecting dominant eigenvectors of a matrix called affinity matrix in order to define a low-dimensional data space in which data points are easy to cluster. The key is to design a good affinity matrix. If we consider the usual Gaussian affinity matrix , it depends on a scaling parameter which is difficult to select. Our goal is to grasp the influence of this parameter and to propose an expression with a reasonable computational cost.

Spectral Clustering: Interpretation and Gaussian Parameter

Spectral clustering consists in creating, from the spectral elements of a Gaussian affinity matrix, a low-dimensional space in which data are grouped into clusters. However, questions about the separability of clusters in the projection space and the choice of the Gaussian parameter remain open. By drawing back to some continuous formulation, we propose an interpretation of spectral clustering with Partial Differential Equations tools which provides clustering properties and defines bounds for the affinity parameter.

Parallel Spectral Clustering for the Segmentation of cDNA Microarray Images

Microarray technology generates large amounts of expression level of genes to be analyzed simultaneously. This analysis implies microarray image segmentation to extract the quantitative information from spots. Spectral clustering is one of the most relevant unsupervised method able to gather data without a priori information on shapes or locality. We propose and test on microarray images a parallel strategy for the Spectral Clustering method based on domain decomposition and with a criterion to determine the number of clusters.

Optimized spectral clustering for segmentation of dynamic PET images

The quantification of dynamic PET images requires the definition of regions of interest. The manual delineation is a time consuming and unreproducible process due to the poor resolution of PET images. Approaches were proposed in the literature to classify the kinetic profiles of voxels, however, they are generally either sensitive to initial conditions or favor convex shaped clusters. Recently we have proposed a kinetic spectral clustering (KSC) method for segmentation of dynamic PET images that has the advantage of handling clusters with arbitrary shape in the space in which they are identified. However, its use for clinical applications is still hindered by the manual setting of several parameters. In this paper, we propose an extension of KSC to make it automatic (ASC). A new unsupervised clustering criterion is tailored and a global optimization by a probabilistic metaheuristic algorithm is used to select the scale parameter and the weighting factors involved in the method. We validate our approach with GATE Monte Carlo simulations. Results obtained with ASC compare closely with those obtained with optimal manual parameterization of KSC, and outperform those obtained with two other approaches from the literature.

Sparsification on Parallel Spectral Clustering

Spectral clustering is one of the most relevant unsupervised method able to gather data without a priori information on shapes or locality. A parallel strategy based on domain decomposition with overlapping interface is reminded. By investigating sparsification techniques and introducing sparse structures, this parallel method is adapted to treat very large data set in fields of Pattern Recognition and Image Segmentation.

Message scheduling to reduce AFDX jitter in a mixed NoC/AFDX architecture

Current avionics architecture are based on an avionics full duplex switched Ethernet network (AFDX) that interconnects end systems. Avionics functions exchange data through Virtual Links (VLs), which are static flows with bounded bandwidth. The jitter for each VL at AFDX entrance has to be less than 500 μs. This constraint is met, thanks to end system scheduling. The interconnection of many-cores by an AFDX backbone is envisioned for future avionics architecture. The principle is to distribute avionics functions on these many-cores. Many-cores are based on simple cores interconnected by a Network-on-Chip (NoC). The allocation of functions on the available cores as well as the transmission of flows on the NoC has to be performed in such a way that the jitter for each VL at AFDX entrance is still less than 500 μs. A first solution has been proposed, where each function manages the transmission of its VLs. The idea of this solution is to distribute functions on each many-core in order to minimize contentions for VLs which concern functions allocated on different many-cores. In this paper, we consider that VL transmissions are managed by a single task in each many-core. We propose to construct a scheduling table executed by this task using an Integer Linear Program. The access to the Ethernet interface is then only allowed to one VL leading to a significant reduction of the jitter.

Symmetry and fourier descriptor: a hybrid feature for NURBS based B-Rep models retrieval

As the number of models in 3D databases grows, an efficient 3D models indexing mechanism and a similarity measure to ease model retrieval are necessary. In this paper, we present a query-by-model framework for NURBS based B-Rep models retrieval that combines partial symmetry of the object and the Fourier shape descriptor of canonical 2D projections of the 3D models. In fact, most objects are composed by similar parts up to an isometry. By detecting the dominant partial symmetry of a given NURBS based B-Rep model, we define two canonical planes from which the Fourier descriptors are extracted to measure the similarity among 3D models.