The data used in this study were obtained from Stereopy, a Python package developed by BGI Spatial for spatial transcriptomics analysis. The main dataset, the MouseBrain Demo, includes two GEF files: SS200000135TL_D1.cellbin.gef and SS200000135TL_D1.tissue.gef. GEF files provide spatial coordinates, gene expression data, and metadata crucial for understanding spatial gene expression. Cellbin data represent gene expression at the cell nucleus level, while tissue data include expression data for spots within the mouse brain tissue. The dataset can be downloaded from the following URL: http://upload.dcs.cloud:8090/share/bb6fab82-2c16-46b2-a95e-6931338f31bf .

The data used in this study were entirely obtained from publicly available resources. Specifically, we used the SS200000135TL_D1 dataset provided by BGI Research, which includes spatial transcriptomic data derived from mouse brain tissue. The dataset was generated and released independently by BGI, and is publicly accessible at: https://enfile.stomics.tech/SS200000135TL_D1.report.html . No new animal experiments or tissue collection were performed by the authors in the course of this study.

The Voronoi tessellation was implemented using the scipy.spatial.Voronoi code in Python, which computes partitions based on Euclidean distances from the nuclei seed points. To ensure that all Voronoi regions were properly closed within the tissue boundary, we applied a boundary extension procedure by introducing pseudo-random points at the periphery of the convex hull. This approach allowed the algorithm to generate bounded polygons for previously unbounded cells, resulting in a complete and biologically realistic segmentation of the tissue section.

The BGI process consists of Preprocessing, Embedding, and Clustering.

Preprocessing is crucial for ensuring data quality and preparing it for subsequent analysis. The preprocessing steps are shown as follows:

1) Data filtering: To ensure the accuracy and reliability of the analysis, we perform quality control: remove all missing values and outliers from the dataset, as well as cells having too many mitochondrial genes expressed, cells without enough genes expressed, and cells exceeding the count range. Here, we delete the cells whose number of genes that have non-zero counts is less than 3.

2) Normalization [30] : Scaling the data to ensure that all features contribute equally to the analysis. This involves adjusting the values measured on different scales to a common scale. Methods for normalization are normalize_total [31] and log1p [32] .

3) Filtering: Highly variable genes are then selected based on predefined criteria to focus the analysis on the most pertinent features. The steropy package provides preloaded tools to handle and preprocess such spatial datasets effectively.

Embedding refers to transforming high-dimensional data into a lower-dimensional space to facilitate visualization and analysis.

1) Dimensionality Reduction: Techniques such as PCA are applied to reduce the dimensionality of the data while preserving its intrinsic structure. Only highly variable genes are taken into consideration in this step. After that, we calculate the neighborhood graph [33] of cells and use the UMAP method [34] with the help of the PCA representation of the expression matrix.

2) Visualization: The lower-dimensional embeddings are visualized to observe patterns and relationships within the data. UMAP is used to help in understanding the data’s underlying structure and distribution.

Clustering is the process of grouping similar data points together based on their features:

1) Algorithm Selection: Leiden algorithm, which has been proven to fit spatial transcriptomics better than Louvain, is selected [35] .

2) Cluster Assignment: Each data point was assigned to a cluster, and the resulting clusters were analyzed to understand their characteristics. Clusters can be visualized in scatter plots, and clustering effects can be evaluated by UMAP.

The Silhouette Score measures the cohesion and separation of clusters. It quantifies how similar each data point is to its own cluster compared to other clusters. The score ranges from −1 to 1, where a higher value indicates better-defined and more distinct clusters.

The Silhouette Score for point $i$ is defined as: $s\left(i\right)=\frac{b\left(i\right)-a\left(i\right)}{\text{max}\left(a\left(i\right),b\left(i\right)\right)}$, where $a\left(i\right)$ is the average intra-cluster distance, $b\left(i\right)$ is the average nearest-cluster distance.

The Calinski-Harabasz Index, also known as the Variance Ratio Criterion, evaluates the ratio of between-cluster variance to within-cluster variance. Higher values indicate better-defined clusters.

Set $k$ as the number of clusters, $n$ as the total number of data points, $S_B$ be the between-cluster dispersion matrix, and $S_w$ be the within-cluster dispersion matrix.

The index is computed as: $CHIndex=\frac{tr\left(S_B\right)/\left(k-1\right)}{tr\left(S_W\right)/\left(n-k\right)}$.

Here, $tr\left(S_B\right)$ is the trace of the between-cluster dispersion matrix, and $tr\left(S_{\text{w}}\right)$ is the trace of the within-cluster dispersion matrix.

Single-cell transcriptomic data were analyzed using MapMyCell [29] , a comprehensive software suite designed for the integration, visualization, and interpretation of single-cell RNA sequencing (scRNA-seq) data. The software supports the integration of multiple datasets and allows for the comparison of cell populations across different conditions or treatments. Key features include customizable visualization options, such as t-SNE and UMAP plots, which facilitate the identification of distinct cell types and states.

The generation of the Voronoi diagram was a pivotal step in our analysis. By using the spatial coordinates of nuclei from the cellbin data, we defined the centers of each cell region, which the Voronoi method then used to delineate boundaries ( Figure 1(a) ). This approach ensured that each nucleus was assigned a unique region, thereby accurately representing individual cells. By using the Voronoi Segmentation method, we divided the mouse brain section into certain regions that have the same number as the number of nuclei (cells) based on the nuclear position, as shown in Figure 1(b) . Cartesian coordinates of vertices and boundaries can be obtained so that each region has its own range presented in Cartesian coordinates and is assigned a unique region index ( Figure 1(c) ).

Recognizing that cellbin data primarily includes information about the locations of cell nuclei as detected during staining, it represents only a small fraction of the spatial landscape within the tissue slice. This limitation restricts the comprehensive analysis of gene expression across the entire tissue. In contrast, tissue data encompasses the entire tissue slice, providing a broader and more detailed spatial transcriptomic profile. To overcome the spatial limitations of cellbin data, we integrated tissue data with the cellbin nuclei locations. Allocated by the spatial coordinate, we map the denser tissue data onto the regions defined by the cellbin nuclei and Voronoi boundary and effectively quadruple the total number of assigned transcripts per cell region and gene expression information within each region, resulting in a more complete dataset that captures gene expression across the entire tissue slice.

After integrating tissue data into each region using the Voronoi method, we created a new, enriched dataset—referred to as the “Voronoi dataset.” This dataset offers a more comprehensive view of gene expression across the entire tissue section. To understand the extent of the improvements introduced by the Voronoi method, we compared this new dataset with the original cellbin dataset, which we’ll refer to as “Original dataset”, and refer to the “Original Method” as the way we derive “Original Dataset.”

Both datasets maintain the same structural format: an information matrix where rows correspond to spatial positions and columns represent different gene types. To evaluate the impact of the Voronoi method, we used the BGI toolkit to process and analyze, aiming to objectively assess whether the Voronoi method enhances the clustering quality and spatial resolution of the resulting analysis.

Our analysis began with a 3000 × 3000 μm section of the mouse brain, carefully selected to test the method’s effectiveness in a complex tissue environment. As illustrated in Figure 2 , we compared the spatial distribution of clusters identified using the Leiden clustering method after PCA.

Figure 2(a) displays the clustering results from the Original dataset, with each color corresponding to a specific cell type as indicated in the legend. The clusters, while distinguishable, show some overlap and blurred boundaries, indicating challenges in accurately defining cell types. This limitation is particularly evident in the center of the tissue, where different cell types are densely packed. In contrast, Figure 2(b) shows the clustering results after applying the Voronoi method. These clusters are more refined and distinct, with clearer separation between different cell types.

Figure 3(a) and Figure 3(b) further highlight the method’s impact on specific clusters. In the original dataset, clusters appeared dispersed with indistinct boundaries, complicating conclusions about spatial organization. However, the Voronoi method significantly improved the clarity and concentration of clusters, aligning well with known anatomical structures in the mouse brain, underscoring its accuracy in cell classification.

Moving to a broader analysis, Figure 4 compares UMAP embeddings from both methods. The Voronoi method consistently outperforms the Original method, producing more distinct and less overlapping clusters. This result indicates more accurate identification of cellular identities, which is critical for understanding the complex spatial dynamics within tissues.

To quantify the improvements, we calculated the Silhouette Score and Calinski-Harabasz Index for both methods, where higher values in both indices denote more distinct and well-defined clusters. The Voronoi method achieved a significantly higher Silhouette Score (0.166) and Calinski-Harabasz Index (2474.823) compared to the Original method (0.113 and 1256.078, respectively). These enhancements confirm that the Voronoi method produces more coherent and distinct clusters, reflecting better spatial separation and cluster compactness.

Moreover, the Voronoi method captured a higher total count of genes and identified more non-zero gene counts within each cell, as shown in Table 1 . These comparisons suggest that the Voronoi method not only improves detection of gene expression diversity but also enhances spatial resolution and clustering results, offering a more detailed and precise view of the tissue’s molecular landscape.

In conclusion, the Voronoi segmentation method demonstrates substantial improvements in cell type classification and spatial analysis compared to traditional approaches. It provides a more accurate and clearer representation of spatial layers in transcriptomic data, aligning better with known anatomical structures. This method not only accurately delineates cortical layers (e.g., L1 and L5) and the boundary between the striatum and neocortex, consistent with the anatomical references provided by the Allen Brain Atlas [38] , but also facilitates studying layer-specific cell-cell interactions, e.g., excitatory/inhibitory balance across layers or differential expression of signaling ligands, paving the way for deeper insights into cellular function and tissue organization.

To further evaluate the effectiveness of the Voronoi method in analyzing spatial transcriptomics data, we employed the MapMyCells [29] tool. This tool is designed to map scRNA-seq and spatial transcriptomics data to cell types with bootstrapping probability, enabling scientists to compare their transcriptomics and spatial data against Allen Institute’s datasets. We analyzed both the original and Voronoi-processed datasets to evaluate how well each method captured the spatial distribution of cell types across a full brain tissue section.

Initially, a smaller slice (3000*3000 μm) was analyzed, but to better learn the distribution of cell types and capture more contextual information across the entire mouse brain (11,000 × 16,000 μm), the analysis was expanded to a full brain tissue section. The following Figure 5 shows scatter plots representing entire mouse brain data processed by MapMyCells and categorized by cell type. Each plot visualizes the distribution of cell class within the brain slice, with distinct colors indicating various cell types as indicated by the class number on the right. This figure allows for a comparison of the clustering quality between the original method and the Voronoi method.

Figure 5(a) shows the results from the Original dataset. Here, the scatter plot reveals some overlap between clusters, particularly in the central part, where different cell types are mixed. This overlap suggests that the Original method may struggle to clearly separate different cell types, leading to potential inaccuracies in cell type identification and spatial distribution analysis. In contrast, Figure 5(b) shows the Voronoi method, with less overlap and more distinct clusters, indicating improved clustering performance. The Voronoi method’s enhanced separation between clusters allows for a clearer and more accurate spatial representation, which is critical for understanding cell interactions and functions within the tissue.

Mouse brain’s cerebral cortex is divided into six layers, each serving distinct functions and composed of various cell subtypes based on their spatial positions [39] . To further evaluate clustering quality, we focused on Layer 2, which has a unique cellular composition. MapMyCells classified cells into specific subtypes, and the spatial distribution of these subtypes was compared against known anatomical references to assess dataset quality.

Figure 6 consists of two scatter plots illustrating the distribution of unique cell subtypes that belong to layer 2 with bootstrapping probability. The cell subtypes represented in the plots can be regarded as marker subtypes of layer 2 [40] .

Figure 6 illustrates the distribution of key marker subtypes for Layer 2 detected in both datasets. The Voronoi method ( Figure 6(b) ) displays a denser and more defined boundary for Layer 2 compared to the Original method ( Figure 6(a) ), which shows lighter and less distinct boundaries with significant noise. The improved clarity and boundary definition in the Voronoi dataset suggest higher confidence in subtype classification, reflected in the darker points indicating higher bootstrapping probabilities. The reduction of noise further supports the Voronoi method’s superior simulation of the ground truth distribution, reinforcing its effectiveness in accurately mapping cellular subtypes.

To further assess the sharp performance of the Voronoi method in comparison to the Original method, we conducted a detailed analysis on Layer 5 of the mouse brain. Instead of using the standard x-axis or y-axis for analysis since it cannot indicate the edge sharpness in the irregular layer pattern, we selected a custom axis because direct analysis along either axis fails to capture the true spatial distribution of cells, where the distance represents the depth of the cortex.

Using this custom axis, we measured the distribution of cells and evaluated the fit of the data to the custom line to quantify how well each method captured the non-linear spatial dynamics of cell distributions. Figure 7(a) and Figure 7(b) present scatter plots of the cells in Layer 5 using the Original and Voronoi methods, respectively, along with the custom line fitted to the data. This custom axis, shown in red, is represented by the equation $y=-0.85\text{x}+22400$, and serves as a reference for analyzing the spatial organization of the cells relative to this axis.

To quantify the differences between the two methods, we measured the distances of each cell from the custom line and performed a Gaussian fit on the distribution of these distances, as shown in Figure 7(c) . The frequency plot illustrates the distribution of distances for both methods, with the Original method represented by the blue curve and the Voronoi method by the orange curve.

The Gaussian fitting results reveal that the Voronoi method produces a narrower distribution, with a lower mean distance (1539.74) and a smaller standard deviation (1117.62), compared to the Original method (mean = 1961.87, std = 1562.78). This indicates that the Voronoi method aligns the cells more closely with the custom axis, further supporting its superior ability to capture the true spatial dynamics of the tissue.

Finally, Figure 7(d) presents a comparison of two key statistical metrics: the R² value and the Chi-square value, both of which assess the goodness-of-fit for the Gaussian distributions. The bar plots on the left side of the figure show that the Voronoi method achieves a significantly higher R² value (0.733) compared to the Original method (0.530), indicating a better fit to the custom line. On the right, the Chi-square test results also favor the Voronoi method, with a substantially lower Chi-square value (1748) compared to the Original method (29,822), further confirming the improved performance of the Voronoi method.