Posted September 14, 2022
Last modified September 27, 2022
Maryam Yashtini, Georgetown University
Counting Objects by Diffused Index: Geometry-Free and Training-Free Approach
Counting objects is a fundamental but challenging problem. In this talk, we 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, we 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. We 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 we refer to as an index. For computational efficiency, we stop the diffusion process before a full convergence, and propose to cluster these diffused index values. We refer to this approach as Counting Objects by Diffused Index (CODI). We explore scalar and multi-dimensional seed vectors. For scalar seeds, we use Gaussian fitting in a histogram to count, while for vector seeds, we 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. We present counting results in various applications such as biological cells, agriculture, concert crowds, and transportation. Some comparisons with existing methods are presented.
Posted November 10, 20223:30 pm Zoom
Jeffrey Rauch, University of Michigan
Earnshaw’s Theorem in Electrostatics
This result dating to 1842 asserts that a charge in a static electrostatic field can never be in a stable equilibrium. In spite of many partial results a complete proof was first given in 1987. The present talk concerns generalizations from Section 116 of Maxwell’s treatise. There Maxwell explains (but does not prove) why a rigid charged body or a perfect conducting body or a dielectric body in a static field can never be in a stable equilibrium. We prove the result for conductors and dielectrics. The charged rigid body remains open. This joint work with G. Allaire appeared in the Archive for Rational Mechanics in 2017.
Posted October 12, 2022
Last modified November 9, 2022
Yue Yu, Lehigh University
Learning Nonlocal Neural Operators for Complex Physical System Modeling
For many decades, physics-based PDEs have been commonly employed for modeling complex system responses, then traditional numerical methods were employed to solve the PDEs and provide predictions. However, when governing laws are unknown or when high degrees of heterogeneity present, these classical models may become inaccurate. In this talk we propose to use data-driven modeling which directly utilizes high-fidelity simulation and experimental measurements to learn the hidden physics and provide further predictions. In particular, we develop PDE-inspired neural operator architectures, to learn the mapping between loading conditions and the corresponding system response. By parameterizing the increment between layers as an integral operator, our neural operator can be seen as the analog of a time-dependent nonlocal equation, which captures the long-range dependencies in the feature space and is guaranteed to be resolution-independent. Moreover, when applying to (hidden) PDE solving tasks, our neural operator provides a universal approximator to a fixed point iterative procedure, and partial physical knowledge can be incorporated to further improve the model’s generalizability and transferability. As an application, we learn the material models directly from digital image correlation (DIC) displacement tracking measurements on a porcine tricuspid valve leaflet tissue, and show that the learnt model substantially outperforms conventional constitutive models.
Posted November 30, 202210:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Jacquelien Scherpen, University of Groningen
IEEE Fellow, Automatica Best Paper Prize Awardee