Cell zone determination – Watershed separation

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Mathematical Morphology

By its denition, mathematical morphology is a set of nonlinear lters used together to lter binary and gray-scale images, which we then extend to apply to our 3D context. Morphological operators consist of two basic operations `dilation’ and `erosion’. Dilation expands the features of the shape whereas erosion suppresses them. The basic eect of dilation on a binary image is to gradually enlarge the boundaries of regions of foreground pixels, typically white pixels. Thus areas of foreground pixels grow in size while holes within those regions become smaller. On the other hand, the basic eect of erosion is to erode away the boundaries of regions of foreground pixels. Thus areas of foreground pixels shrink in size while holes within those areas become larger. Morphology operators are based on set theory. Assuming that a binary 3D image X and B is its set of coordinates for the structuring elements. A structuring element, also known as kernel, determines the eect of the operator upon the image. Several popular structuring elements in 3D images are a 3 3 3 structure with the central pixel and its direct 26 neighbors or a disk of a given radius. Given BS is the symmetric of B, we have the following denition:
dilation : X BS = fx 2 Z3 : Bx \ X 6= 0g.
erosion : X BS = fv 2 Z3 : Bv Xg.
closing : (X BS) B.
opening : (X BS) B.

Cell Phenotype Detection

The development of automated uorescent confocal microscopes allows researchers to collect high throughput biological images. Moreover, it increases the possibility of high- lighting and capturing the complex sub-cellular phenotypes using specic uorescent labeled proteins, a.k.a. staining. As a result, the door is now open to the identication of the cell biological phenotypes. However, it is also a big challenge for automated image analysis and computation.
Grys et al.(2016) [2] discuss the commonly used computer vision and machine learning methods to identify phenotypic proles. They come up with a general two-stage work ow for the generation and classication of phenotypic proles as shown in Fig. 2.4.
1. Generating phenotypic proles. This step performs image analysis approaches including high throughput image acquisition, segmentation, object recognition, feature extraction, and feature selection.
2. Clustering and classifying phenotypic proles. Depending on the characteristics of image modalities and the research goals, dierent strategies can be applied such as clustering, machine learning classiers, and outlier detection. The diculty of generating phenotypic proles The rst and foremost diculty for cell phenotype detection is feature extraction. Cell- Proler platform [24] can extract hundreds to thousands of dierent features for each object and use these information to generate the phenotypic prole. Some common features are the object volume, shape, texture, and the histogram of intensity inside segmented cells. Due to such large number of extracted features, feature selection and dimensionality reduction are a must so that only relevant features are kept [47, 48].
In addition, the high level of noise is also a major obstacle. This is especially important when the tissue consists of many cell phenotypes, each is highlighted by one marker. In such case, each pixel coordinate can be a label on one image and noise on another one.

Spatial Tissue Organization Analysis

Past researches about the extraction of features focused mostly on a set of individual objects and did not take into account the relationship between these objects. Spatial organization is a new approach that focuses on such relations to describe, detect, and recognize these objects. It is particularly useful when objects are located in a complex and dynamic biomedical environment. In addition, spatial information can be more reliable than the characteristic of the objects themselves. In this section, we describe some approaches to exploit the spatial organization of objects and perform a certain level of mechanical reasoning about the image contents. We observe the spatial organization at dierent scales, at local scale, between two objects, to global scale, between each object and a set of objects or a population.

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Analysis at Local Scale

Analysis at local scale focuses on the relationship between two objects or between an object and its local surrounded area. In biological application, the relationship between two or a small number of objects can be modelled as the spatial relationship of one component to another. For example, the spatial relationship of cell to cell, cell to nucleus, cell to vesicle, nucleoli to nucleus, or between cells within a tissue. A spatial relation can be classied as a metric relation, or a topological relation, or a more complex one [50].
Metric relations consist of directional relation and distance relation. Examples of direc- tional relations are `right to’, `left to’, `in front of’, `above’, `below’, `behind’. Examples of distance relations are `close to’, `far from’. Metric relations are quite simple to un- derstand but play an important role in describing the object positions. More complex relations can base on this such as `between’, `surround’, `among’. Hudelot et al(2008)[50]. represented metric relations and the links between them as ontologies. This work com- bined ontology of spatial relations with fuzzy representation of distance relations in order to guide image interpretation and the recognition of its structures. Topological relation is commonly used for qualitative spatial reasoning. Randell et al. [3] implemented a set of spatial relations such as contact, overlap, and the relation of part to whole in order to describe the topology and structural organization of biomedical images. In this work, the authors proposed the usage of Discrete Mereotopology (DM), a spatial logic which combines mereology, the theory of part-hood relations, and topol- ogy to model discrete spaces. Particularly, DM can be represented as Mathematical Morphology operations that enables the representation of spatial models in computer program.

Table of contents :

Abstract
Acknowledgements
Abbreviations
1 Resume en Francais
2 Introduction & Literature Review 
2.1 Biological Background
2.1.1 Tissue Organization
2.1.2 Islets of Langerhans
2.1.3 Methods to Study the Islet of Langerhans
2.2 Image Analysis
2.2.1 Confocal Microscopy
2.2.2 Methods for Studying Tissue Organization
2.2.3 Image Enhancement
2.2.4 Nuclei Segmentation
2.2.5 Mathematical Morphology
2.2.6 Cell Segmentation
2.2.7 Cell Phenotype Detection
2.3 Spatial Tissue Organization Analysis
2.3.1 Analysis at Local Scale
2.3.2 Analysis at Global Scale
2.3.3 Modeling of Spatial Organization
2.4 Objectives of the Thesis
3 Materials and Methods 
3.1 Materials
3.2 Methodology Overview
3.3 Segmentation and Cell Phenotype Detection
3.3.1 Nuclei segmentation
3.3.2 Cell zone computation
3.3.2.1 Cell membrane segmentation
3.3.2.2 Cell zone determination – Watershed separation
3.3.3 3D cell phenotype computation
3.4 Analysis of Spatial Organization
3.4.1 Cells composition and cellular interaction
3.4.2 Analysis of spatial organization at global scale
3.4.3 Cluster analysis
3.5 Delta Cell Analysis and Modeling
3.5.1 Analysis of spatial organization of delta-cells
3.5.2 Modeling and simulation of dynamic morphology of delta cell
3.6 Modeling of Spatial Organization
3.6.1 Modeling of the spatial organization at the local scale
3.6.2 Modeling of the spatial organization at global scale
3.7 Developing Environment
4 Results 
4.1 Program Description
4.1.1 Experimental datasets
4.1.2 Developed toolbox to investigate tissue spatial organization
4.2 Tissue Quantication and Analysis
4.2.1 Nuclei Segmentation Result
4.2.1.1 Parameters selection
4.2.1.2 Nuclei segmentation result
4.2.1.3 Comparison of nuclei segmentation methods
4.2.2 Cell Zone Computation Results
4.2.2.1 Cell segmentation using plasma membrane labeling
4.2.2.2 Cell zone computation using watershed separation
4.2.3 3D Cell Phenotype Computation
4.2.3.1 Parameter selection
4.2.3.2 Results of cell type identication
4.2.4 Analysis of Cellular Interaction
4.2.5 Analysis of Spatial Organization
4.3 Delta Cell Analysis and Modeling
4.3.1 Quantication and analysis of delta cells
4.3.2 Results of modeling and simulation of dynamic morphology of delta cell
4.4 Modeling Spatial Organization
5 Conclusion & Discussion 
5.1 Discussion
5.2 Conclusion
A Toolbox to Investigate Tissue Spatial Organization (TITSO) 
B Tissue Quantication and Analysis Results 
Bibliography 

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