🍩 Database of Original & Non-Theoretical Uses of Topology

(found 4 matches in 0.002917s)
  1. Classification of COVID-19 via Homology of CT-SCAN (2021)

    Sohail Iqbal, H. Fareed Ahmed, Talha Qaiser, Muhammad Imran Qureshi, Nasir Rajpoot
    Abstract In this worldwide spread of SARS-CoV-2 (COVID-19) infection, it is of utmost importance to detect the disease at an early stage especially in the hot spots of this epidemic. There are more than 110 Million infected cases on the globe, sofar. Due to its promptness and effective results computed tomography (CT)-scan image is preferred to the reverse-transcription polymerase chain reaction (RT-PCR). Early detection and isolation of the patient is the only possible way of controlling the spread of the disease. Automated analysis of CT-Scans can provide enormous support in this process. In this article, We propose a novel approach to detect SARS-CoV-2 using CT-scan images. Our method is based on a very intuitive and natural idea of analyzing shapes, an attempt to mimic a professional medic. We mainly trace SARS-CoV-2 features by quantifying their topological properties. We primarily use a tool called persistent homology, from Topological Data Analysis (TDA), to compute these topological properties. We train and test our model on the "SARS-CoV-2 CT-scan dataset" i̧tep\soares2020sars\, an open-source dataset, containing 2,481 CT-scans of normal and COVID-19 patients. Our model yielded an overall benchmark F1 score of \$99.42\% \$, accuracy \$99.416\%\$, precision \$99.41\%\$, and recall \$99.42\%\$. The TDA techniques have great potential that can be utilized for efficient and prompt detection of COVID-19. The immense potential of TDA may be exploited in clinics for rapid and safe detection of COVID-19 globally, in particular in the low and middle-income countries where RT-PCR labs and/or kits are in a serious crisis.
  2. 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.
  3. Lung Topology Characteristics in Patients With Chronic Obstructive Pulmonary Disease (2018)

    Francisco Belchi, Mariam Pirashvili, Joy Conway, Michael Bennett, Ratko Djukanovic, Jacek Brodzki
    Abstract Quantitative features that can currently be obtained from medical imaging do not provide a complete picture of Chronic Obstructive Pulmonary Disease (COPD). In this paper, we introduce a novel analytical tool based on persistent homology that extracts quantitative features from chest CT scans to describe the geometric structure of the airways inside the lungs. We show that these new radiomic features stratify COPD patients in agreement with the GOLD guidelines for COPD and can distinguish between inspiratory and expiratory scans. These CT measurements are very different to those currently in use and we demonstrate that they convey significant medical information. The results of this study are a proof of concept that topological methods can enhance the standard methodology to create a finer classification of COPD and increase the possibilities of more personalized treatment.
  4. Pore Geometry Characterization by Persistent Homology Theory (2018)

    Fei Jiang, Takeshi Tsuji, Tomoyuki Shirai
    Abstract Rock pore geometry has heterogeneous characteristics and is scale dependent. This feature in a geological formation differs significantly from artificial materials and makes it difficult to predict hydrologic and elastic properties. To characterize pore heterogeneity, we propose an evaluation method that exploits the recently developed persistent homology theory. In the proposed method, complex pore geometry is first represented as sphere cloud data using a pore-network extraction method. Then, a persistence diagram (PD) is calculated from the point cloud, which represents the spatial distribution of pore bodies. A new parameter (distance index H) derived from the PD is proposed to characterize the degree of rock heterogeneity. Low H value indicates high heterogeneity. A new empirical equation using this index H is proposed to predict the effective elastic modulus of porous media. The results indicate that the proposed PD analysis is very efficient for extracting topological feature of pore geometry.