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ACMD Seminar: Counting Objects by Diffused Index: geometry-free and training-free approach

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.)


Created October 19, 2022, Updated January 17, 2023