Fig. 1. Schematic representation of the HEARTSVG.

a HEARTSVG utilizes the semi-pooling process to convert spatial gene expressions into marginal expressions ($\mathbf{r}$) and calculates autocorrelations ($\mathit{\rho }$) of marginal expressions. HEARTSVG calculates the sum of the squared autocorrelations (${\widehat{Q}}_m=T{\sum }_{l=1}^m{\widehat{\rho }}_l^2$) for each marginal expression series and obtains a p-value by testing ${\widehat{Q}}_m$. All these p-values are combined into a final p-value through the Stouffer combination ($z_s={\sum }_{i=1}^4\frac{z_i}{\sqrt{4}}~N\left(0,1\right)$, final $\mathrm{p}-\mathrm{value}=2\left(\right)1-\mathrm{\Phi }\left(\mid z_s\mid \right)$). HEARTSVG distinguishes between SVGs and non-SVGs by the final p-value. b The autocorrelations ($\mathit{\rho }$) of marginal expressions ($\mathbf{r}$) for the SVG and non-SVG exhibit different level scales. Representative autocorrelation estimator plots are plotted below the corresponding marginal expression plots for the SVG and non-SVG. The color depth represents the magnitude of autocorrelation.