🍩 Database of Original & Non-Theoretical Uses of Topology

(found 5 matches in 0.001413s)

  2. Diverse 3D Cellular Patterns Underlie the Development of Cardamine Hirsuta and Arabidopsis Thaliana Ovules (2023)

    Tejasvinee Atul Mody, Alexander Rolle, Nico Stucki, Fabian Roll, Ulrich Bauer, Kay Schneitz
    Abstract A fundamental question in biology is how organ morphogenesis comes about. The ovules of Arabidopsis thaliana have been established as a successful model to study numerous aspects of tissue morphogenesis; however, little is known regarding the relative contributions and dynamics of differential tissue and cellular growth and architecture in establishing ovule morphogenesis in different species. To address this issue, we generated a 3D digital atlas of Cardamine hirsuta ovule development with full cellular resolution. We combined quantitative comparative morphometrics and topological analysis to explore similarities and differences in the 3D cellular architectures underlying ovule development of the two species. We discovered that they show diversity in the way the three radial cell layers of the primordium contribute to its growth, in the formation of a new cell layer in the inner integument and, in certain cases, in the topological properties of the 3D cell architectures of homologous tissues despite their similar shape. Our work demonstrates the power of comparative 3D cellular morphometry and the importance of internal tissues and their cellular architecture in organ morphogenesis. Summary Statement Quantitative morphometric comparison of 3D digital ovules at full cellular resolution reveals diversity in internal 3D cellular architectures between similarly shaped ovules of Cardamine hirsuta and Arabidopsis thaliana.

  4. Theory and Algorithms for Constructing Discrete Morse Complexes From Grayscale Digital Images (2011)

    V. Robins, P. J. Wood, A. P. Sheppard
    Abstract We present an algorithm for determining the Morse complex of a two or three-dimensional grayscale digital image. Each cell in the Morse complex corresponds to a topological change in the level sets (i.e., a critical point) of the grayscale image. Since more than one critical point may be associated with a single image voxel, we model digital images by cubical complexes. A new homotopic algorithm is used to construct a discrete Morse function on the cubical complex that agrees with the digital image and has exactly the number and type of critical cells necessary to characterize the topological changes in the level sets. We make use of discrete Morse theory and simple homotopy theory to prove correctness of this algorithm. The resulting Morse complex is considerably simpler than the cubical complex originally used to represent the image and may be used to compute persistent homology.

  5. Automatic Tree Ring Detection Using Jacobi Sets (2020)

    Kayla Makela, Tim Ophelders, Michelle Quigley, Elizabeth Munch, Daniel Chitwood, Asia Dowtin
    Abstract Tree ring widths are an important source of climatic and historical data, but measuring these widths typically requires extensive manual work. Computer vision techniques provide promising directions towards the automation of tree ring detection, but most automated methods still require a substantial amount of user interaction to obtain high accuracy. We perform analysis on 3D X-ray CT images of a cross-section of a tree trunk, known as a tree disk. We present novel automated methods for locating the pith (center) of a tree disk, and ring boundaries. Our methods use a combination of standard image processing techniques and tools from topological data analysis. We evaluate the efficacy of our method for two different CT scans by comparing its results to manually located rings and centers and show that it is better than current automatic methods in terms of correctly counting each ring and its location. Our methods have several parameters, which we optimize experimentally by minimizing edit distances to the manually obtained locations.