Alexandre Dupas

First results for 3D image segmentation with topological map

This paper presents the first segmentation operation defined within the 3D topological map framework. Firstly we show how a traditional segmentation algorithm, found in the literature, can be transposed on a 3D image represented by a topological map. We show the consistency of the results despite of the modifications made to the segmentation algorithm and we study the complexity of the operation. Lastly, we present some experimental results made on 3D medical images. These results show the process duration of this method and validate the interest to use 3D topological map in the context of image processing.

Partial volume effect estimation and correction in the aortic vascular wall in PET imaging.

We evaluated the impact of partial volume effect (PVE) in the assessment of arterial diseases with (18)FDG PET. An anthropomorphic digital phantom enabling the modeling of aorta related diseases like atherosclerosis and arteritis was used. Based on this phantom, we performed GATE Monte Carlo simulations to produce realistic PET images with a known organ segmentation and ground truth activity values. Images corresponding to 15 different activity-concentration ratios between the aortic wall and the blood and to 7 different wall thicknesses were generated. Using the PET images, we compared the theoretical wall-to-blood activity-concentration ratios (WBRs) with the measured WBRs obtained with five measurement methods: (1) measurement made by a physician (Expert), (2) automated measurement supposed to mimic the physician measurements (Max), (3) simple correction based on a recovery coefficient (Max-RC), (4) measurement based on an ideal VOI segmentation (Mean-VOI) and (5) measurement corrected for PVE using an ideal geometric transfer matrix (GTM) method. We found that Mean-VOI WBRs values were strongly affected by PVE. WBRs obtained by the physician measurement, by the Max method and by the Max-RC method were more accurate than WBRs obtained with the Mean-VOI approach. However Expert, Max and Max-RC WBRs strongly depended on the wall thickness. Only the GTM corrected WBRs did not depend on the wall thickness. Using the GTM method, we obtained more reproducible ratio values that could be compared across wall thickness. Yet, the feasibility of the implementation of a GTM-like method on real data remains to be studied.

Fully deformable 3D digital partition model with topological control

We propose a purely discrete deformable partition model for segmenting 3D images. Its main ability is to maintain the topology of the partition during the minimization process. To do so, our main contribution is a new definition of multi-label simple points (ML simple point) that is easily computable. An ML simple point can be relabeled without modifying the overall topology of the partition. The definition is based on intervoxel properties, and uses the notion of collapse on cubical complexes. This work is an extension of a former restricted definition (Dupas et al., 2009) that prohibits the move of intersections of boundary surfaces. A deformation process is carried out with a greedy energy minimization algorithm. A discrete area estimator is used to approach at best standard regularizers classically used in continuous energy minimizing methods. We illustrate the potential of our approach with the segmentation of 3D medical images with known expected topology.

Multi-label simple points definition for 3D images digital deformable model

The main contribution of this paper is the definition of multilabel simple points that ensures that the partition topology remains invariant during a deformable partition process. The definition is based on simple intervoxel properties and is easy to implement. A deformation process is carried out with a greedy energy minimization algorithm. A discrete area estimator is used to approach at best standard regularizers classically used in continuous energy minimizing methods. The effectiveness of our approach is shown on several 3D image segmentations.

Grouping/Degrouping Point Process, a Point Process Driven by Geometrical and Topological Properties of a Partition in Regions

Abstract In the context of image segmentation, we introduce a new kind of point process, called grouping/degrouping point process (GDPP) that aims to aggregate regions from an initial partition of the image according to geometrical and topological criteria. The initial partition, produced by a low-level region-based segmentation process, is represented using a topological map that represents all the geometrical information and topological features of the image partition. Points in the process are localized in regions and newly defined energies of the partition allow to take into account geometrical and topological features like the number of holes or the area of contact between regions. The simulation of the point population is driven by birth and death moves used in a Reversible Jump Markov Chain Monte Carlo method. We propose special birth and death moves using the adjacency relation between regions. Experiments are provided on a sample partition that show the effects of the different potentials. In a 3D medical image, a GDPP based application is provided to segment brain tumor. The results are compared to a region merging approach and to a reference segmentation proposed by an expert. This approach emphasizes the ability of the GDPP to solve real world segmentation problem.

Region merging with topological control

This paper presents a region merging process controlled by topological features on regions in three-dimensional (3D) images. Betti numbers, a well-known topological invariant, are used as criteria. Classical and incremental algorithms to compute the Betti numbers using information represented by the topological map of an image are provided. The region merging algorithm, which merges any number of connected components of regions together, is explained. A topological control of the merging process is implemented using Betti numbers to control the topology of an evolving 3D image partition. The interest in incremental approaches of the computation of Betti numbers is established by providing a processing time comparison. A visual example showing the result of the algorithm and the impact of topological control is also given.

Comparison of local and global region merging in the topological map

The topological map is a model that represents 2D and 3D images subdivision. It aims to allow the use of topological and geometrical features of the subdivision in image processing operations. When handling regions in an image, one of the main operation is the region merging, for example in segmentation process. This paper presents two algorithms of region merging in 3D topological maps: one local which modifies locally the map around merged regions, and another one global which runs through all the elements of the map. We study their complexities and present experimental results to compare both approaches.

Combining topological maps, multi-label simple points, and minimum-length polygons for efficient digital partition model

Deformable models have shown great potential for image segmentation. They include discrete models whose combinatorial formulation leads to efficient and sometimes optimal minimization algorithms. In this paper, we propose a new discrete framework to deform any partition while preserving its topology. We show how to combine the use of multilabel simple points, topological maps and minimum-length polygons in order to implement an efficient digital deformable partition model. Our experimental results illustrate the potential of our framework for segmenting images, since it allows the mixing of region-based, contour-based and regularization energies, while keeping the overall image structure.

Combinatorial Maps for 2D and 3D Image Segmentation

This chapter shows how combinatorial maps can be used for 2D or 3D image segmentation. We start by introducing combinatorial maps and we show how they can be used to describe image partitions. Then, we present a generic segmentation algorithm that uses and modifies the image partition represented by a combinatorial map. One advantage of this algorithm is that one can mix different criteria and use different image features which can be associated with the cells of the partition. In particular, it is interesting that the topological properties of the image partition can be controlled through this approach. This property is illustrated by the computation of classical topological invariants, known as Betti numbers, which are then used to control the number of cavities or the number of tunnels of regions in the image partition. Finally, we present some experimental results of 2D and 3D image segmentation using different criteria detailed in this chapter.