🍩 Database of Original & Non-Theoretical Uses of Topology
(found 4 matches in 0.002002s)
Multiscale Topology Characterizes Dynamic Tumor Vascular Networks (2022)Bernadette J. Stolz, Jakob Kaeppler, Bostjan Markelc, Franziska Braun, Florian Lipsmeier, Ruth J. Muschel, Helen M. Byrne, Heather A. Harrington
Automatic Tree Ring Detection Using Jacobi Sets (2020)Kayla Makela, Tim Ophelders, Michelle Quigley, Elizabeth Munch, Daniel Chitwood, Asia Dowtin
AbstractTree 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.
Theory and Algorithms for Constructing Discrete Morse Complexes From Grayscale Digital Images (2011)V. Robins, P. J. Wood, A. P. Sheppard
AbstractWe 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.