Given this realization, the foundation of near sets is developed for further applications.Įvery biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. The resulting dual meshes constitute a light discrete representation of the cell surfaces that enables fast visualization, and quantitative analysis, and allows in silico physical and mechanical simulations on real-world data.Ī measure of the quality of Vorono\" diagrams expose neighbourhood relations between pattern units. We present a method for optimizing such complexes using an energy minimization process, designed to make them fit to the actual adjacencies in the tissue. In the presented method, the problem is tackled under the angle of topology, and the shape of the cells is seen as the dual geometry of a 3-d simplicial complex accounting for their adjacency relationships. Based on time sequences of meristem images of the model plant Arabidopsis thaliana, displaying fluorescence markers on either cell membranes or cell nuclei under confocal laser scanning microscopy, we aim at obtaining faithful reconstructions of all the cell walls in the tissue.
The goal of this paper is the reconstruction of topo-logically accurate 3-dimensional triangular meshes representing a complex, multi-layered plant tissue structure. Within the meristem and explore the applicability of simple, standard In this chapter we explore some of the properties of these patterns That is suggestive of Voronoi diagrams derived from the centroids of cellular As the plant grows, organs (primordia) form on its surface flanks inĪ phyllotactic pattern that develop into new shoots, leaves, and flowers.Ĭross-sections through the meristem reveal a pattern of polygonal tessellation Maintain their topological and functional relationships throughout the life of These cells are organized into several distinct zones that In Arabidopsis thaliana (thale cress), a small flowering weed of theīrassicaceae family (related to mustard and cabbage), the SAM typicallyĬontains some three to five hundred cells that range from five to ten microns The shoot apical meristem (SAM) is a dome-shaped collection of cells at theĪpex of growing plants from which all above-ground tissue ultimately derives.
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