Quantitative Delineation of the Morphological Heterogeneity of Anisotropic Nanostructures via Machine-Learning-Augmented Electron Microscopy

Abstract

Precise synthesis and engineering of homogeneous anisotropic nanostructures are essential to realize their shape-dependent physicochemical properties for different applications. However, due to the difficulty in controlling factors influencing nucleation and growth, many reported anisotropic nanostructures exhibit substantial heterogeneity, particularly in their size and shape distributions. Current methods for assessing nanostructure heterogeneity, whether ensemble- or single-particle-based techniques, are limited in the types of readout information, resolution, and throughput. Although machine-learning-assisted microscopy approaches have facilitated nanomaterial heterogeneity characterization to a certain extent, strategies that transform microscopy images into quantitative morphology feature spaces for population-level heterogeneity analysis remain underexplored. Herein, a quantitative approach combining transmission electron microscopy (TEM) imaging with machine learning is demonstrated for delineating the projected morphological heterogeneity of anisotropic nanostructures. Following supervised pixel classification and thresholding, TEM images are converted to probability maps and image masks, from which a series of interpretable projected size- and shape-related morphological descriptors are extracted. Dimensionality reduction and unsupervised clustering are subsequently employed to analyze the acquired morphological feature space and identify putative nanostructure subpopulations based on morphological similarities or differences. Feature scoring is further performed to identify descriptors associated with variations among nanostructure subpopulations while considering correlations among related geometric parameters. This study establishes a machine-learning-augmented framework for quantitative and objective analysis of anisotropic nanostructure heterogeneity and provides a foundation for future integration with synthesis metadata and predictive modeling approaches.

1. Introduction

Owing to their unique shape-dependent physicochemical properties, anisotropic nanostructures are widely exploited for a plethora of biomedical and nanomedicine applications. − For instance, the exceptional light absorption and thermal generation of gold (Au) nanorods have facilitated their application for photothermal therapy. − In parallel, the strong surface plasmon localization at the tips of the branched Au nanostructures have enabled their utilization for surface-enhanced Raman scattering imaging. − To achieve these shape-dependent properties and applications, precise synthesis and engineering of highly homogeneous anisotropic nanostructures with uniform size, shape, and aspect ratio are essential.

The preparation of homogeneous anisotropic nanostructures is known to be extremely challenging. Specifically, the synthesis and engineering of anisotropic nanostructures require precise control over multiple factors influencing nucleation and growth, notably competing growth pathways, surface energy differences, and sensitivity to reaction conditions (e.g., reactant concentrations, surfactant concentrations, temperature, and pH). − Coupled with nonstandardized experimental protocols and high batch-to-batch variations, many reported anisotropic nanostructures exhibit substantial heterogeneity, especially in their size and shape distributions. Therefore, analytical approaches capable of quantitatively resolving particle-to-particle variation within nanostructure populations are needed to complement conventional ensemble measurements.

To date, the size and shape heterogeneity of anisotropic nanostructures has been characterized predominantly using spectroscopy and microscopy techniques. − For example, dynamic light scattering (DLS) spectroscopy is commonly used to estimate the hydrodynamic size distributions and polydispersity of nanomaterials in solution. , Although the polydispersity index can provide information regarding sample heterogeneity, this metric primarily reflects statistical properties of bulk populations rather than individual nanomaterials. Similarly, visible-near-infrared (Vis-NIR) absorption spectroscopy provides information regarding nanomaterial heterogeneity through spectral shifts and peak broadening. , However, such ensemble measurements cannot directly resolve particle-to-particle morphological variations. In contrast, microscopy imaging techniques, particularly transmission electron microscopy (TEM) and its variants such as high-resolution TEM and cryo-TEM, provide direct visualization of individual nanomaterials. − However, careful sampling is required to capture overall nanomaterial heterogeneity.

Unfortunately, although TEM enables single-particle observation, conventional TEM-based heterogeneity analysis is frequently limited by qualitative interpretation of morphology, which is prone to subjective interpretation of morphological features and inter- and intraobserver variations. For studies attempting quantitative characterization, many microscopy images require manual processing, rendering the analytical process labor intensive and time inefficient. Encouragingly, recent years have seen the emergence and active implementation of artificial intelligence and machine learning approaches to automate and streamline microscopy image processing and analysis. − These strategies have demonstrated significant utility in various tasks, including image segmentation, particle detection, localization, and automated classification. However, many existing machine-learning-assisted microscopy workflows have primarily focused on improving image processing efficiency, segmentation, particle detection, or classification, whereas methods that integrate quantitative morphology extraction with population-level heterogeneity analysis remain less explored.

This study proposed a machine-learning-augmented TEM workflow that integrates supervised image segmentation, quantitative morphology feature extraction, dimensionality reduction, unsupervised clustering, and feature ranking to quantitatively delineate the projected morphological heterogeneity of anisotropic nanostructures at the single-particle level. The present work established an interpretable analytical framework to transform TEM images into quantitative morphological feature spaces and enabled identification of putative nanostructure subpopulations based on their projected morphological characteristics (Supporting Table S1). Beyond descriptive characterization, the quantitative morphological feature space developed in this work may provide a foundation for future integration with synthesis metadata to investigate the relationships between processing conditions and resulting nanostructure morphology. Such integration can ultimately support predictive modeling and more rational nanomaterial design.

2. Results and Discussion

2.1. Machine-Learning-Assisted Workflow for Quantitative Delineation of Anisotropic Nanostructure Morphological Heterogeneity

An overview of the workflow adopted in this study, which combines TEM imaging and machine learning, for interrogating the projected morphological heterogeneity of anisotropic nanostructures is illustrated in Figure .

1.

An overview of the workflow adopted in this study for delineating the morphological heterogeneity of anisotropic nanostructures quantitatively.

In this proof-of-concept work, two types of Au nanostructures were selected as model anisotropic nanomaterials. Au nanorods and Au nanobranches were first prepared based on the protocols described in previous studies. − Leveraging a series of spectroscopic techniques, these Au nanostructures were subsequently characterized to elucidate their physicochemical properties, including hydrodynamic size, polydispersity index (PDI), zeta-potential, and optical absorbance (Figure ). Au nanorods had a hydrodynamic size of about 47.5 ± 8.9 nm, while that of Au nanobranches was approximately 83.8 ± 3.8 nm (Figure a). Both types of nanostructures exhibited similar average PDI values, although Au nanorods showed a broader PDI distribution (Figure b). In terms of zeta-potential, Au nanorods were positively charged, with a zeta-potential of about 38.9 ± 3.8 mV (Figure c). In contrast, Au nanobranches were negatively charged, with a zeta-potential of approximately −35.9 ± 0.8 mV. Evaluation of the Vis-NIR absorbance profiles revealed that Au nanorods exhibited a peak absorbance at about 787 nm, whereas Au nanobranches displayed a peak absorbance at approximately 587 nm (Figure d). These spectroscopic characterization collectively verified the preparation of two anisotropic Au nanostructure systems with distinct physicochemical properties.

2.

Physicochemical properties of anisotropic Au nanostructures. (a) Hydrodynamic size, (b) polydispersity index, (c) zeta-potential, and (d) UV–vis absorbance. Data are represented as mean ± standard deviation. n ≥ 3. The quantitative values obtained from spectroscopic measurements are reported with appropriate significant figures based on the resolution and reproducibility of the respective characterization methods.

2.2. Quantitative Assessment of Au Nanostructure Morphological Heterogeneity

The projected morphological heterogeneity of the anisotropic Au nanostructures was next characterized qualitatively and quantitatively through TEM imaging and machine-learning-assisted image processing and analysis (Figure ). Visualization of the acquired TEM images revealed that most Au nanorods exhibited a characteristic elongated morphology and relatively higher morphological uniformity compared with Au nanobranches (Figure a). Au nanobranches, in contrast, adopted unique architectures comprising a central core surrounded by several radiating tips. Some nanobranches exhibited relatively circular cores, whereas others showed more irregular ellipsoidal cores. In terms of the number of tips surrounding the central core, most Au nanobranches contained approximately three to five radiating tips.

3.

Quantitative delineation of the morphological features of anisotropic Au nanostructures. (a) Representative TEM images of Au nanorods and nanobranches and the corresponding probability maps and image masks. All scale bars represent 100 nm. (b, c) The delineated quantitative (b) size and (c) shape features of Au nanorods. n = 178. (d, e) The delineated quantitative (d) size and (e) shape features of Au nanobranches. n = 151.

Following a computational pipeline established in previous studies, , all TEM images were first processed to generate probability maps. A supervised random forest classifier was trained to recognize Au nanostructures in TEM images based on differences in pixel intensity between nanostructures and background regions. Through limited iterations of manual labeling, probability maps describing the regions corresponding to nanostructures and background were generated. The probability maps were subsequently processed to generate the corresponding image masks. Accurate segmentation is essential because errors introduced during particle delineation can directly influence downstream quantitative morphological analysis. For example, merged particles may artificially increase size-related descriptors, including area, perimeter, and diameter, whereas missed particles may alter the measured population distribution and potentially obscure minor nanostructure populations. Therefore, improving segmentation consistency is critical for generating reliable morphological feature spaces and subsequent analysis. These generated image masks were subsequently used to derive quantitative morphological descriptors associated with particle size and projected shape. These descriptors included size-related parameters, such as area, equivalent diameter, major axis length, maximum Feret diameter, maximum radius, mean radius, median radius, minimum Feret diameter, minor axis length, and perimeter, as well as shape-related parameters, including compactness, eccentricity, extent, form factor, and solidity. It is important to note that TEM provides two-dimensional projections of three-dimensional nanomaterials. Therefore, the extracted descriptors represent projected morphological features rather than complete three-dimensional structural parameters. Nevertheless, several characteristics relevant to anisotropic nanostructure morphology, including apparent branching architecture and projected aspect ratio, can be quantitatively evaluated from TEM images. Accordingly, the descriptors extracted herein should be interpreted as quantitative measurements of projected particle morphology. The extracted morphological feature space provides an interpretable representation of particle-to-particle variation within a nanostructure population. Such quantitative descriptors may facilitate identification of morphological diversity that is difficult to resolve through conventional qualitative TEM examination.

Quantitative assessment of different size-related features of Au nanorods revealed relatively broad distributions of area and perimeter (Figure b), indicating the presence of size heterogeneity within the synthesized nanorod population. Similarly, shape-related feature analysis showed a broad distribution of compactness values, ranging from slightly below 1 to above 2.5, with a median value of about 1.75 (Figure c). This suggests that Au nanorods exhibited variations in projected morphology, ranging from relatively circular or oval structures to elongated ellipsoidal structures. The elongated morphology of Au nanorods was further supported by their eccentricity distribution, where most particles exhibited the values close to 1. These observations demonstrate that although Au nanorods generally retained their expected anisotropic morphology, particle-to-particle variation existed in both size and projected shape. A similar trend in size heterogeneity was observed for Au nanobranches. Specifically, these anisotropic nanostructures exhibited broad distributions of area and perimeter (Figure d). However, compared with Au nanorods, Au nanobranches displayed narrower compactness distributions but broader eccentricity distributions (Figure e). The compactness values of Au nanobranches ranged from approximately 1 to slightly above 2, whereas eccentricity values ranged from approximately 0.2 to about 0.9, with a median value near 0.6. These results suggest that although Au nanobranches maintained their characteristic core-tip architecture, they exhibited greater projected shape diversity compared with Au nanorods.

To demonstrate the analytical advantages of the presented machine-learning-assisted workflow, its performance was compared with a conventional ImageJ-based image analysis approach (Supporting Figures S1 and S2). Representative TEM images of Au nanorods and Au nanobranches were analyzed using standard intensity thresholding procedures. Although the majority of Au nanorods could be identified under favorable contrast conditions using ImageJ, conventional threshold-based segmentation showed limitations when particles were merged, partially overlapping, or present in images with uneven illumination. In particular, Au nanobranches with complex branching architectures were more susceptible to segmentation errors (Supporting Figure S1). Furthermore, manual adjustment of threshold parameters and background correction could result in missing or merged particles, leading to user-dependent variability and incomplete morphology data sets (Supporting Figure S2). In comparison, the proposed machine-learning-assisted pipeline requires limited manual annotation during initial training and subsequently enables automated processing of comparable image data sets (Supporting Figures S1 and S2). This approach improves segmentation consistency across images containing different contrast conditions, particle morphologies, and moderately overlapping nanostructures, thereby facilitating more reliable extraction of quantitative morphological descriptors. Nonetheless, extremely dense aggregation or severe particle overlap may still introduce ambiguity because the analysis relies on two-dimensional TEM projections.

To summarize the relative advantages and limitations of the two approaches, a detailed comparison between conventional ImageJ-based analysis and the proposed machine-learning-assisted workflow is provided (Supporting Table S2). The comparison considers various factors, including segmentation principle, manual adjustment requirements, handling of uneven illumination, particle overlap, extracted feature complexity, and suitability for population-level morphological analysis.

2.3. Delineation of Anisotropic Nanostructure Morphological Heterogeneity through Unsupervised Clustering

To further characterize the morphological heterogeneity of anisotropic Au nanostructures, unsupervised clustering was adopted to group individual nanostructures based on similarities and differences within their quantitative morphological feature space (Figure ). Principal component analysis (PCA) was first employed to transform the high-dimensional data set containing 15 morphological descriptors into lower-dimensional representations. The resulting principal components were subsequently analyzed using two unsupervised clustering approaches, namely, k-means clustering and Louvain clustering, to identify putative Au nanorod and nanobranch morphology-based subpopulations. By transforming multiple morphological descriptors into reduced feature representations and identifying groups of particles with similar characteristics, this approach enables quantitative visualization of morphological diversity within a synthesized nanostructure population. Importantly, the resulting clusters should be interpreted as computationally identified morphology-based subpopulations rather than predefined synthetic or mechanistic categories.

4.

Unsupervised clustering of anisotropic Au nanostructures and feature importance analysis. (a, b) Delineation of the subpopulations of (a) Au nanorods and (b) Au nanobranches using unsupervised k-means clustering and Louvain clustering. (c, d) Quantitative scoring and ranking of the morphological features of the subpopulations of (c) Au nanorods and (d) Au nanobranches delineated through k-means clustering (left) and Louvain clustering (right).

For Au nanorods, three and five putative nanorod subpopulations were identified through k-means clustering and Louvain clustering, respectively (Figure a). The difference in cluster number reflects the distinct mathematical principles underlying these approaches, where k-means clustering uses centroid-based partitioning based on Euclidean distance, whereas Louvain clustering identifies communities within a similarity graph. Similarly, for Au nanobranches, k-means clustering identified two putative subpopulations, whereas Louvain clustering identified four putative subpopulations (Figure b). The difference between clustering approaches highlights the complexity of defining discrete groups within continuous morphology distributions. Rather than indicating disagreement between methods, these results suggest that heterogeneous nanostructure populations may contain multiple levels of morphological variation that can be resolved differently depending on clustering strategy. The first two principal components accounted for the majority of variance within the morphology data sets. However, the third principal component was retained to capture additional subtle variations. Importantly, clustering results obtained using three principal components were highly consistent with those obtained using only the first two principal components, indicating that the identified morphological patterns were not strongly dependent on dimensionality reduction (Supporting Figure S3).

To further evaluate clustering reliability, cluster separation was assessed across varying numbers of retained principal components (Supporting Figure S4). Although different clustering algorithms yielded different number of clusters, consistent morphological differences were observed among identified groups, suggesting that the detected clusters represent meaningful variations within heterogeneous nanostructure populations rather than purely random computational partitioning.

2.4. Morphological Descriptor Analysis of Nanostructure Populations

To determine whether specific morphological descriptors were associated with differences among identified nanostructure subpopulations, all extracted features were statistically scored and ranked using ANOVA-based analysis. A higher ANOVA value indicates stronger association between a descriptor and differences among morphology-based subpopulations. Because several extracted descriptors represent related geometric characteristics, feature rankings were interpreted as indicators of descriptor association instead of independent contributions. For example, area, equivalent diameter, and perimeter are inherently related measurements of overall particle dimensions. Therefore, high rankings among these parameters may reflect a common underlying morphological variation rather than independent effects. Correlation analysis of the extracted morphological descriptors confirmed expected relationships among related size parameters (Supporting Figures S5 and S6). Strong correlations were observed among descriptors, such as area, equivalent diameter, and perimeter, whereas shape descriptors exhibited relatively lower correlations.

Evaluation of feature importance for k-means-clustered Au nanorod subpopulations showed that eccentricity, maximum Feret diameter, and equivalent diameter were among the highest-ranked descriptors in terms of their association with cluster separation (Figure c). In contrast, extent, solidity, and compactness showed weaker associations. Notably, except for eccentricity, most highly ranked descriptors were related to particle dimensions rather than shape. For Louvain-clustered Au nanorod subpopulations, equivalent diameter, area, and perimeter were among the highest-ranked descriptors, whereas eccentricity, extent, and solidity showed lower associations. The variation in ranking between clustering approaches likely reflects differences in how each algorithm emphasizes relationships within the multidimensional morphology feature space. Specifically, centroid-based k-means clustering may emphasize dominant variance directions because clustering is based on Euclidean distance from cluster centers. Since eccentricity directly reflects projected aspect ratio, it may contribute strongly to separation in this feature space. In contrast, Louvain clustering incorporates graph-based similarity relationships among particles and may distribute importance more broadly among correlated morphological descriptors.

For Au nanobranches, similar trends were observed (Figure d). Regardless of clustering approach, size-related descriptors generally exhibited stronger associations with identified subpopulations than shape-related descriptors. These observations suggest that the synthesized Au nanobranches exhibited relatively consistent projected core-tip architectures while varying primarily in overall dimensions. Importantly, the dominance of size-related descriptors reflects the characteristics of the analyzed nanostructure populations rather than a limitation of the workflow. The proposed framework remains capable of identifying more complex morphology-associated variations in systems exhibiting greater structural diversity.

2.5. Statistical Validation and Population-Level Interpretation of Morphology-Based Clusters

The individual morphological descriptors of identified nanostructure subpopulations were further compared to determine similarities and differences among clusters (Figure and Supporting Figures S7 to S10). For Au nanorod subpopulations identified through k-means clustering, analysis of highly ranked descriptors revealed that eccentricity exhibited the least overlap among clusters (Figure a and Supporting Figure S7). While clusters C1 and C3 showed comparable eccentricity distributions, these values differed substantially from those of C2 (Figure a). In contrast, several lower-ranked descriptors, including solidity and extent, displayed greater overlap among clusters (Supporting Figure S7).

5.

Statistical analysis of the subpopulation-identifying morphological features. (a, c) Statistical analysis of the three highest ranked morphological features and (b, d) representative morphology of various Au nanorod clusters identified through (a, b) k-means clustering and (c, d) Louvain clustering. n = 107 for C1, 9 for C2, and 62 for C3 identified through k-means clustering. n = 48 for C1, 37 for C2, 36 for C3, 29 for C4, and 28 for C5 identified through Louvain clustering. (e, g) Statistical analysis of the three highest ranked morphological features and (f, h) representative morphology of various Au nanobranch clusters identified through (e, f) k-means clustering and (g, h) Louvain clustering. n = 61 for C1 and 90 for C2 identified through k-means clustering. n = 54 for C1, 43 for C2, 32 for C3, and 22 for C4 identified through Louvain clustering. * p < 0.05, ** p < 0.01, *** p < 0.001, and **** p < 0.0001 based on Mann–Whitney test for pairwise comparisons and either Brown-Forsythe and Welch ANOVA tests followed by Dunnett’s T3 multiple comparisons test or Kruskal–Wallis test followed by Dunn’s multiple comparisons test for multiple comparisons.

The representative morphology of each cluster supported these statistical observations. Clusters C1 and C3 exhibited elongated projected morphologies, whereas C2 displayed a relatively more oval morphology (Figure b). Although clusters shared certain morphological similarities, their quantitative descriptor distributions enabled differentiation within the morphology feature space. Similar trends were observed for Louvain-clustered Au nanorod subpopulations (Figure c,d and Supporting Figure S8). For Au nanobranch subpopulations identified through k-means and Louvain clustering, size-related descriptors generally showed greater separation among clusters than shape-related descriptors (Figure e–h and Supporting Figures S9 and S10). These results indicate that Au nanobranch subpopulations maintained similar projected core-tip architectures but differed in their overall dimensions. Together, these findings demonstrated that the identified clusters corresponded to distinguishable morphology-based subpopulations supported by quantitative descriptor differences and representative particle morphology.

Beyond identifying morphology-based subpopulations, the proposed workflow enables estimation of their relative abundance within synthesized nanostructure batches. By assigning individual particles to their corresponding clusters, the fraction of particles associated with each morphology-based subpopulation could be quantified (Supporting Tables S3 and S4). This additional analysis provides a potential metric for evaluating nanostructure synthesis outcomes by determining the relative prevalence of different morphology classes within a batch. Such population-level analysis may complement conventional characterization methods by providing quantitative information regarding batch heterogeneity.

3. Conclusion

Herein, an integrated approach combining electron microscopy imaging and machine learning to augment the analysis of the projected morphological heterogeneity of anisotropic Au nanostructures was presented. Coupling TEM imaging with supervised pixel classification and image thresholding, a series of quantitative projected size- and shape-related morphological descriptors of Au nanorods and Au nanobranches was derived. PCA and unsupervised clustering were subsequently utilized to identify putative morphology-based Au nanostructure subpopulations based on similarities and differences within their quantitative feature spaces. Finally, statistical analysis was adopted to evaluate descriptor associations with morphological variations among identified subpopulations.

While conventional image analysis methods can extract basic morphological parameters, these approaches typically rely on manual parameter adjustment and do not readily support high-dimensional population-level analysis. The integration of machine learning in this workflow enables more consistent image segmentation, automated feature extraction, and morphology-based population analysis, thereby enhancing analytical throughput and reproducibility. Importantly, the presented framework facilitates quantitative evaluation of projected morphological descriptors at the single-particle level, which remains challenging using conventional approaches.

Beyond descriptive characterization, the quantitative morphological feature space established in this work may provide a foundation for future investigation of synthesis–morphology relationships in anisotropic nanostructures. The formation of anisotropic Au nanostructures is governed by complex interactions among nucleation kinetics, facet stabilization, directional growth rates, and reaction conditions. Parameters including precursor concentration, surfactant composition, seed-to-growth solution ratio, temperature, and pH can influence resulting nanostructure dimensions and morphology distributions. The morphological descriptors extracted herein are relevant to these growth-associated characteristics. For example, eccentricity reflects projected anisotropic growth characteristics, while equivalent diameter and Feret diameters describe overall projected particle dimensions. Future studies integrating quantitative morphological descriptors with systematically collected synthesis metadata may enable establishment of relationships between processing conditions and resulting nanostructure morphology. Such integration could ultimately support predictive modeling approaches and facilitate more rational nanomaterial design.

Overall, the proposed framework provided a versatile approach for 1) quantitative morphology assessment by identifying and estimating the relative abundance of morphology-based subpopulations within a nanostructure batch, 2) future synthesis optimization by linking morphological descriptors with systematically collected synthesis parameters, and 3) structure–property analysis where morphology influences functional performance. It is important to emphasize that the present study demonstrated the workflow using representative data sets of Au nanorods and Au nanobranches as proof-of-concept examples. Future studies evaluating independently synthesized batches and systematically varied reaction conditions will be important to further assess reproducibility, generalizability, and potential predictive capability. Despite these

limitations, this work demonstrated the potential of integrating machine learning with conventional nanomaterial characterization approaches to achieve more quantitative, objective, and comprehensive assessment of anisotropic nanostructure heterogeneity.

4. Methods

4.1. Synthesis and Characterization of Anisotropic Au Nanostructures

The anisotropic Au nanostructures employed in this work were synthesized following the protocols described in previous studies. − The prepared nanomaterials were then characterized for hydrodynamic size and zeta-potential, optical absorbance, and surface morphology using Zetasizer (Malvern Panalytical Ltd., United States), UV–Vis-NIR spectrophotometer (Shimadzu Scientific Instruments Inc., United States), and TEM (JEOL USA, Inc., United States), respectively.

4.2. Pixel Classification, Probability Map Generation, Object Segmentation, and Feature Extraction

Based on the protocols described in previous studies, , all acquired TEM images were processed through user-annotated pixel classification using ilastik 1.4.0 (The ilastik Developers) to generate the corresponding probability maps. In brief, raw TEM images were first loaded, followed by the selection of all 37 predefined features describing object color/intensity, edge, and texture. In the classifier training phase, two object classes, i.e., nanostructures and background, were assigned. A supervised random forest classifier was then trained through iterative labeling of pixels corresponding to Au nanostructures and background. In parallel, the predicted output classes were validated in real time, and additional labels were introduced to regions of an image with less accurate prediction. The eventual predicted outputs were exported as probability maps, which explain the probabilities of pixels belonging to Au nanostructures and background. The probability maps were converted to the corresponding image masks comprising segmented Au nanostructures using CellProfiler 4.2.1 (Broad Institute of MIT and Harvard, USA). In brief, Au nanostructures were identified as the primary objects. Objects with sizes beyond the specified ranges and those touching the borders of images were not considered. Image thresholding was performed based on a global thresholding strategy, Otsu thresholding method, and two-class thresholding. After object segmentation, a total of 15 specific nanostructure size and shape features were obtained and measured, including area, equivalent diameter, major axis length, maximum Feret diameter, maximum radius, mean radius, median radius, minimum Feret diameter, minor axis length, perimeter, compactness, eccentricity, extent, form factor, and solidity.

4.3. Conventional Object Segmentation

Representative TEM images of Au nanostructures were processed using ImageJ 1.54p (National Institutes of Health, United States). Images were first converted to 8-bit grayscale prior to segmentation. Global thresholding was then applied using the Otsu thresholding method. For images exhibiting uneven illumination, background correction was performed using a rolling ball algorithm before image thresholding.

4.4. Principal Component Analysis, Unsupervised Clustering, and Feature Scoring and Ranking

PCA, unsupervised clustering, and feature scoring and ranking were conducted using Orange Data Mining software (University of Ljubljana, Slovenia). For PCA, three principal components were selected to achieve explained variance of at least 90%. For k-means clustering, the number of clusters was considered between two and eight and chosen based on the highest silhouette score. The reruns and maximum iterations were set to 10 and 300, respectively. For Louvain clustering, Euclidean distance was selected. The number of k-neighbors and resolution were set to 30 and 1, respectively. For feature scoring and ranking, ANOVA was selected as the evaluation metric.

4.5. Statistical Analysis

All statistical analysis were performed using GraphPad Prism 10.6.1 (GraphPad Software Inc., United States). Data was first assessed for its distribution using the Shapiro-Wilk normality test. For correlation analysis, correlation matrices were generated using Spearman’s rank correlation coefficients. Statistical significance was assessed using two-tailed p-values, and 95% confidence intervals were calculated for all correlation coefficients. For pairwise comparisons, parametric data was analyzed through Welch’s t test, while nonparametric data was analyzed through Mann–Whitney test. For multiple comparisons, parametric data was analyzed through Brown-Forsythe and Welch ANOVA tests followed by Dunnett’s T3 multiple comparisons test, while nonparametric data was analyzed through Kruskal–Wallis test followed by Dunn’s multiple comparisons test. Statistically significant differences were accepted for * p < 0.05, ** p < 0.01, *** p < 0.001, and **** p < 0.0001.

4.6. Quantification of Nanostructure Subpopulation Abundance

The relative fractions of the identified Au nanostructure subpopulations were quantified based on eq

$$\mathrm{Cluster}\mathrm{fraction}(\%)=\frac{\mathrm{Number}\mathrm{of}\mathrm{particles}\mathrm{assigned}\mathrm{to}\mathrm{cluster}}{\mathrm{Total}\mathrm{analyzed}\mathrm{particles}}\times 100$$ 1

The data that support the findings of this study are available in the Supporting Information of this article.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnanoscienceau.6c00084.

• Representative TEM images of Au nanostructures and the corresponding image masks; unsupervised clustering of Au nanostructures; correlation matrices showing the relationships among the morphological descriptors of Au nanostructures; statistical analysis of the morphological descriptors of Au nanostructure clusters; comparison of microscopy-based methods for particle analysis; comparison of conventional and proposed methods for microscopy image processing and quantitative morphology analysis; relative fractions of Au nanostructure clusters (PDF)

The author declares no competing financial interest.

Published as part of ACS Nanoscience Au special issue “2026 Rising Stars in Nanoscience”.