U.S. flag
        An official website of the United States government
          Here’s how you know
        Here’s how you know**Official websites use .gov**
              
              A **.gov** website belongs to an official government organization in the United States.
        **Secure .gov websites use HTTPS**
              
              A **lock** (  A locked padlock
) or **https://** means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites. https://www.nist.gov/itl/math/acmd-seminar-counting-objects-diffused-index-geometry-free-and-training-free-approach
  Search NIST
    Search
              Menu

      


Close
    Topics
        All Topics
                                                        Advanced communications
                                                        Artificial intelligence
                                                        Bioscience
                                                        Buildings and construction
                                                        Chemistry
                                                        Climate
                                                        Cybersecurity
                                                        Electronics
                                                        EnergyEnvironment
                                                        Fire
                                                        Forensic science
                                                        Health
                                                        Information technology
                                                        Infrastructure
                                                        Manufacturing
                                                        Materials
                                                        Mathematics and statisticsMetrology
                                                        Nanotechnology
                                                        Neutron research
                                                        Performance excellence
                                                        Physics
                                                        Public safety
                                                        Resilience
                                                        Standards
                                                        Transportation
            Publications
            Labs & Major Programs
        Laboratories
                                Communications Technology Laboratory
                                  Engineering Laboratory
                                  Information Technology Laboratory
                                  Material Measurement Laboratory
                                  Physical Measurement LaboratoryUser Facilities
                                NIST Center for Neutron Research
                                  CNST NanoFab
                                                        Research Test Beds
                                                        Research Projects
                                                        Tools & InstrumentsMajor Programs
                                Baldrige Performance Excellence Program
                                  CHIPS for America Initiative
                                  Manufacturing Extension Partnership (MEP)
                                  Office of Advanced Manufacturing
                                  Special Programs Office
                                  Technology Partnerships Office
            Services & Resources
        Standards and Measurements
                                Calibration Services
                                  Laboratory Accreditation (NVLAP)
                                  Quality System
                                  Standard Reference Materials (SRMs)
                                  Standards.gov
                                  Time Services
                                  Office of Weights and MeasuresSoftware
                                                        Data
                                Chemistry WebBook
                                  National Vulnerability Database
                                  Physical Reference Data
                                  Standard Reference Data (SRD)
                                                        Storefront
                                                        License & PatentsComputer Security Resource Center (CSRC)
                                                        NIST Research Library
            News & Events
        News
                                                        Events
                                                        Blogs
                                                        Feature Stories
                                                        AwardsVideo Gallery
                                                        Image Gallery
                                                        Media Contacts
            About NIST
        About Us
                                Leadership
                                  Organization Structure
                                  Budget & Planning
                                                        Contact Us
                                                        Visit
                                                        Careers
                                Student programsWork with NIST
                                                        History
                                NIST Digital Archives
                                  NIST Museum
                                  NIST and the Nobel
                                                        Educational Resources
 
 Information Technology Laboratory
      Applied and Computational Mathematics Division
    
      
  Projects/Programs
          How to Work With Us
          NIST Publications Searchable Database
          Staff Directory
          News & Updates
          Resources/ServicesACMD Seminar: Counting Objects by Diffused Index: geometry-free and training-free approach

Share
  Facebook
                      Linkedin
                      Twitter
                      Email

Maryam Yashtini*Assistant Professor of Mathematics, Mathematics & Statistics Dept., Georgetown University*

Tuesday, December 13, 2022, 3:00-4:00 ET (1:00-2:00 MT)

**A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page. It will be taken down from NISTube after 12 months at which point it can be requested by emailing the ACMD Seminar Chair.**

**Abstract**: Counting objects is a fundamental but challenging problem. In this talk, I propose diffusion-based, geometry-free, and learning-free methodologies to count the number of objects in images. The main idea is to represent each object by a unique index value regardless of its intensity or size, and to simply count the number of index values. First, I place different vectors, referred to as seed vectors, uniformly throughout the mask image. The mask image has boundary information of the objects to be counted. Secondly, the seeds are diffused using an edge-weighted harmonic variational optimization model within each object. I propose an efficient algorithm based on an operator splitting approach and alternating direction minimization method, and theoretical analysis of this algorithm is given. An optimal solution of the model is obtained when the distributed seeds are completely diffused such that there is a unique intensity within each object, which I refer to as an index. For computational efficiency, I stop the diffusion process before a full convergence, and propose to cluster these diffused index values. I refer to this approach as Counting Objects by Diffused Index (CODI). I explore scalar and multi-dimensional seed vectors. For scalar seeds, I use Gaussian fitting in histogram to count, while for vector seeds, I exploit a high-dimensional clustering method for the final step of counting via clustering. The proposed method is flexible even if the boundary of the object is not clear nor fully enclosed. I present counting results in various applications such as biological cells, agriculture, concert crowd, and transportation. Some comparisons with existing methods are presented.

**Bio**: Maryam Yashtini is an Assistant Professor in the Department of Mathematics and Statistics at Georgetown University. Prior to joining the faculty at Georgetown, she was a Postdoctoral Fellow at Georgia Institute of Technology. She received a PhD Degree in Computational Mathematics, and two Master's Degrees one in Applied Mathematics and one in Industrial Systems and Engineering from University of Florida. Maryam’s main area of expertise is numerical optimization with special emphasis on non-differentiable and nonconvex problems. These problems often arise in applications such as machine learning, imaging, sparse and low-rank approximations, and compressive sensing to name a few.

**Host**: Gunay Dogan

**Note**: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)
  Mathematics and statistics

    
    Contacts
      
        

Gunay Dogan
    
      
  gunay.dogan@nist.gov
  (301) 975-8883

  Zachary Grey
    
      
  zachary.grey@nist.gov
  (303) 497-5920

  Lochi Orr
    
      
  lochi.orr@nist.gov
  (410) 598-6986

Created October 19, 2022, Updated January 17, 2023
 HEADQUARTERS
            100 Bureau Drive
              Gaithersburg, MD 20899301-975-2000
            Webmaster | Contact Us | Our Other Offices
        Twitter
            
Facebook
            
LinkedIn
            
Instagram
            
YouTube
            
Giphy
            
RSS Feed
            
Mailing List
                              How are we doing? Feedback

  
  Site Privacy
                      Accessibility
                      Privacy Program
                      Copyrights
                      Vulnerability Disclosure
                      No Fear Act Policy
                      FOIA
                      Environmental Policy
                      Scientific Integrity
                      Information Quality Standards
                      Commerce.gov
                      Science.gov
                      USA.gov
                      Vote.gov