Estimating Multiple Pathways of Object Growth Using Nonlongitudinal Image Data

Abstract

This article presents an infinite Bayesian mixture of monotonic regression models for analyzing multiple growth pathways of star-shaped objects growing over time by using nonlongitudinal data. A motivating example is the analysis of nanocrystal growth processes. A radius function representation used for the outlines of star-shaped objects allows us to represent an object growth (i.e., expansion of outlines) by an increasing sequence of random radius functions. We propose a monotonic regression model to fit the increasing sequence to nonlongitudinal data ensuring that the fitted radius functions always monotonically increase in the sequence. To model the multiple pathways of object growth, we propose the Dirichlet infinite location mixture of multiple monotonic regression models and use a block Gibbs sampler as a numerical solver. We apply the proposed model to nonlongitudinal sets of microscopic image data for inferring multiple growth pathways of nanocrystals. Comparing the inference result with real nanocrystal growth trajectories, we conclude that the growth pathways inferred from the nonlongitudinal data are consistent with the real nanocrystal growth trajectories. Our implementation of the proposed method in Matlab and example datasets are available online as supplementary materials.

Gaining Control over Radiolytic Synthesis of Uniform Sub-3-nanometer Palladium Nanoparticles: Use of Aromatic Liquids in the Electron Microscope

“…For quantitative evaluation of particle nucleation kinetics, we have applied multitarget particle tracking statistical analysis 55 to our raw STEM data sets to determine the number of particles in each movie frame (see Experimental Section for details of the analysis). The number of particles detected in each separate frame per unit time is plotted as solid red circles in Figure 1b (same data set as for Figure 1a).…”

“…The multitarget particle tracking approach has been previously applied to analysis of video frames of silver nanoparticles grown via in situ liquid STEM , and has provided insights into the attack mechanisms that occur during degradation of electrolyte solutions in Li ion batteries . First, an image segmentation algorithm was applied to successive images in order to extract a set of image pixel locations for nanoparticles, and an object tracking algorithm was applied to associate the pixel locations over multiple time frames . Further details can be found in refs ,, and .…”

“…First, an image segmentation algorithm was applied to successive images in order to extract a set of image pixel locations for nanoparticles, and an object tracking algorithm was applied to associate the pixel locations over multiple time frames . Further details can be found in refs ,, and .…”

Registration‐free monitoring of multimode near‐circular shape profiles

“…They followed the Procrustes approach to register a mixture of shape profiles in advance before using basis functions to represent profiles and then used the Dirichlet process mixture model as a Bayesian prior distribution to handle basis function coefficients from multimode shape profiles. Unfortunately, as discussed in Park, this registration may not provide a good result, which would distort the charting performance. Additionally, the Gibbs sampling procedure to construct charting statistics based on the Bayesian hypothesis testing may seem to be too intensive in computation and storage resources to be applied in online process monitoring.…”

“…As a result, the products in a sample would exhibit different types of shape outlines, termed as multimode shape profiles. These situations are common in practice, such as the nanoparticle engineering in Park, and Park and Shrivastava, where a group of nanoparticles grow through multiple different modes and finally converge to different shapes, such as rods, triangles, circles, and rectangles. In our motivating example of a powder material production process described in Section 2, the powders in a batch have 3 distinct near‐circular shapes.…”