Academic Appointments

Contact

  • Academic
    genebkim@stanford.edu
    University - Academic staff Department: Statistics Position: Marie Anne Burkhard H&S Lecturer in Undergraduate Teaching
    • 390 JANE STANFORD WAY
    • SEQUOIA HALL
    • STANFORD,  California  94305 

Additional Info

  • Mail Code: 4065

2024-25 Courses

All Publications

  • Ultrasound Lesion Detectability as a Distance Between Probability Measures IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL Hyun, D., Kim, G. B., Bottenus, N., Dahl, J. J. 2022; 69 (2): 732-743

    Abstract

    Lesion detectability (LD) quantifies how easily a lesion or target can be distinguished from the background. LD is commonly used to assess the performance of new ultrasound imaging methods. The contrast-to-noise ratio (CNR) is the most popular measure of LD; however, recent work has exposed its vulnerability to manipulations of dynamic range. The generalized CNR (gCNR) has been proposed as a robust histogram-based alternative that is invariant to such manipulations. Here, we identify key shortcomings of CNR and strengths of gCNR as LD metrics for modern beamformers. Using the measure theory, we pose LD as a distance between empirical probability measures (i.e., histograms) and prove that: 1) gCNR is equal to the total variation distance between probability measures and 2) gCNR is one minus the error rate of the ideal observer. We then explore several consequences of measure-theoretic LD in simulation studies. We find that histogram distances depend on bin selection that LD must be considered in the context of spatial resolution and that many histogram distances are invariant under measure-preserving isomorphisms of the sample space (e.g., dynamic range transformations). Finally, we provide a mathematical interpretation for why quantitative values such as contrast ratio (CR), CNR, and signal-to-noise ratio should not be compared between images with different dynamic ranges or underlying units and demonstrate how histogram matching can be used to reenable such quantitative comparisons.

    View details for DOI 10.1109/TUFFC.2021.3138058

    View details for Web of Science ID 000748372800030

    View details for PubMedID 34941507

  • Central Limit Theorem for Peaks of a Random Permutation in a Fixed Conjugacy Class of S-n ANNALS OF COMBINATORICS Fulman, J., Kim, G. B., Lee, S. 2021

    View details for DOI 10.1007/s00026-021-00561-4

    View details for Web of Science ID 000728240900001

  • On the joint distribution of descents and signs of permutations ELECTRONIC JOURNAL OF COMBINATORICS Fulman, J., Kim, G. B., Lee, S., Petersen, T. 2021; 28 (3)

    View details for DOI 10.37236/10222

    View details for Web of Science ID 000685639400001

  • THE SYMMETRIC GROUP, ORDERED BY REFINEMENT OF CYCLES, IS STRONGLY SPERNER PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Harper, L. H., Kim, G. B. 2021; 149 (7): 2753-2761

    View details for DOI 10.1090/proc/15183

    View details for Web of Science ID 000651701800004

  • A central limit theorem for descents and major indices in fixed conjugacy classes of S-n ADVANCES IN APPLIED MATHEMATICS Kim, G. B., Lee, S. 2021; 124

    View details for DOI 10.1016/j.aam.2020.102132

    View details for Web of Science ID 000604732200007

  • COVID-19 highlights the issues facing blind and visually impaired people in accessing data on the web W4A: Web Accessibility Siu, A. F., Fan, D., Kim, G. S., Rao, H. V., O'Modhrain, S., Follmer, S. 2021: 1-15

    View details for DOI 10.1145/3430263.3452432

  • The absolute orders on the Coxeter groups A(n) and B-n are Sperner ELECTRONIC JOURNAL OF COMBINATORICS Harper, L. H., Kim, G. B., Livesay, N. 2020; 27 (3)

    View details for DOI 10.37236/8874

    View details for Web of Science ID 000551390100001