Three-dimensional conditional random field for the dermal-epidermal junction segmentation.

The segmentation of the dermal-epidermal junction (DEJ) in in vivo confocal images represents a challenging task due to uncertainty in visual labeling and complex dependencies between skin layers. We propose a method to segment the DEJ surface, which combines random forest classification with spatial regularization based on a three-dimensional conditional random field (CRF) to improve the classification robustness. The CRF regularization introduces spatial constraints consistent with skin anatomy and its biological behavior. We propose to specify the interaction potentials between pixels according to their depth and their relative position to each other to model skin biological properties. The proposed approach adds regularity to the classification by prohibiting inconsistent transitions between skin layers. As a result, it improves the sensitivity and specificity of the classification results.

Watershed cuts: thinnings, shortest path forests, and topological watersheds.

We recently introduced watershed cuts, a notion of watershed in edge-weighted graphs. In this paper, our main contribution is a thinning paradigm from which we derive three algorithmic watershed cut strategies: The first one is well suited to parallel implementations, the second one leads to a flexible linear-time sequential implementation, whereas the third one links the watershed cuts and the popular flooding algorithms. We state that watershed cuts preserve a notion of contrast, called connection value, on which several morphological region merging methods are (implicitly) based. We also establish the links and differences between watershed cuts, minimum spanning forests, shortest path forests, and topological watersheds. Finally, we present illustrations of the proposed framework to the segmentation of artwork surfaces and diffusion tensor images.

Topology-corrected segmentation and local intensity estimates for improved partial volume classification of brain cortex in MRI.

In magnetic resonance imaging (MRI), accuracy and precision with which brain structures may be quantified are frequently affected by the partial volume (PV) effect. PV is due to the limited spatial resolution of MRI compared to the size of anatomical structures. Accurate classification of mixed voxels and correct estimation of the proportion of each pure tissue (fractional content) may help to increase the precision of cortical thickness estimation in regions where this measure is particularly difficult, such as deep sulci. The contribution of this work is twofold: on the one hand, we propose a new method to label voxels and compute tissue fractional content, integrating a mechanism for detecting sulci with topology preserving operators. On the other hand, we improve the computation of the fractional content of mixed voxels using local estimation of pure tissue intensity means. Accuracy and precision were assessed using simulated and real MR data and comparison with other existing approaches demonstrated the benefits of our method. Significant improvements in gray matter (GM) classification and cortical thickness estimation were brought by the topology correction. The fractional content root mean squared error diminished by 6.3% (p<0.01) on simulated data. The reproducibility error decreased by 8.8% (p<0.001) and the Jaccard similarity measure increased by 3.5% on real data. Furthermore, compared with manually guided expert segmentations, the similarity measure was improved by 12.0% (p<0.001). Thickness estimation with the proposed method showed a higher reproducibility compared with the measure performed after partial volume classification using other methods.

Watershed cuts: minimum spanning forests and the drop of water principle.

We study the watersheds in edge-weighted graphs. We define the watershed cuts following the intuitive idea of drops of water flowing on a topographic surface. We first establish the consistency of these watersheds: They can be equivalently defined by their "catchment basins" (through a steepest descent property) or by the "dividing lines" separating these catchment basins (through the drop of water principle). Then, we prove, through an equivalence theorem, their optimality in terms of minimum spanning forests. Afterward, we introduce a linear-time algorithm to compute them. To the best of our knowledge, similar properties are not verified in other frameworks and the proposed algorithm is the most efficient existing algorithm, both in theory and in practice. Finally, the defined concepts are illustrated in image segmentation, leading to the conclusion that the proposed approach improves, on the tested images, the quality of watershed-based segmentations.

New characterizations of simple points in 2D, 3D, and 4D discrete spaces.

A point of a discrete object is called simple if it can be deleted from this object without altering topology. In this article, we present new characterizations of simple points which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points. In order to prove these characterizations, we establish two confluence properties of the collapse operation which hold in the neighborhood of a point in spaces of low dimension. This work is settled in the framework of cubical complexes, which provides a sound topological basis for image analysis, and allows to retrieve the main notions and results of digital topology, in particular the notion of simple point.

Building the component tree in quasi-linear time.

The level sets of a map are the sets of points with level above a given threshold. The connected components of the level sets, thanks to the inclusion relation, can be organized in a tree structure, that is called the component tree. This tree, under several variations, has been used in numerous applications. Various algorithms have been proposed in the literature for computing the component tree. The fastest ones (considering the worst-case complexity) have been proven to run in O(n ln(n)). In this paper, we propose a simple to implement quasi-linear algorithm for computing the component tree on symmetric graphs, based on Tarjan's union-find procedure. We also propose an algorithm that computes the n most significant lobes of a map.

Computer-assisted analysis helps detect inner dynein arm abnormalities.

The diagnosis of primary ciliary dyskinesia is based on demonstration of ciliary defects, mainly concerning dynein arms. Whereas the absence of outer dynein arms can be easily distinguished, the absence of inner dynein arms is difficult to confirm because of their low contrast on electron microscopy. Ciliary ultrastructure was studied in 40 patients suffering from respiratory tract infections. Conventional transmission electron microscopy showed normal cilia in 6 patients, confirmed a diagnosis of primary ciliary dyskinesia in 26 patients, and was inconclusive in 8 patients. All doubtful cases were related to inner dynein arm determination. Conventional electron microscopic analysis was able to define the ultrastructural phenotype of inner dynein arms in 40.5% of cases (6 presence of inner dynein arms, 13 absence of inner dynein arms). We developed computer-assisted analysis of electron microscopic micrographs to improve inner dynein arm visualization. Computer-assisted analysis consisted of image transformations designed to enhance the signal/noise ratio, based on the symmetry of ciliary axonemes. The sensitivity and specificity of computer-assisted analysis were 100 and 98%, respectively. The efficiency of computer-assisted analysis to visualize inner dynein arms, evaluated in the patients with undetermined phenotype after electron microscopy, was 86% (three normal cilia, seven primary ciliary dyskinesia with absence of outer dynein arms, three primary ciliary dyskinesia with absence of inner dynein arms, five partial absence of inner dynein arms). Computer-assisted analysis of ciliary micrographs improves the characterization of inherited axonemal defects.