Reliable uncertainty model calculation in subsurface engineering from
pore- and grain-scale to field-scale relies on sufficient data, but
subsurface dataset acquisition remains a challenge, particularly in
domains where data collection is expensive or time-consuming, such as
Computed Topography (CT) imaging for digital rock images. While AI-based
data augmentation may assist the model training, it still requires many
training images as well as the quality assessment of generated data.
Yet, most data quantitative metrics flatten spatial data into vectors;
therefore, removing the essential spatial relationships within the data.
We evaluate topology-based metrics for quality assessment of AI-based
image augmentation, coupled with digital rocks augmentation practice
using the Single image Generative Adversarial Network (SinGAN) for
binarized (segmented) images. Compared to most traditional
dimensionality reduction methods that process images into a flattened
vector, we propose topological image analysis for dimensionality
reduction while preserving the essential geometric and topological
features of the high-dimensional data. To demonstrate our proposed
approach, we evaluate the generated images starting from four distinct
digital rock samples, sorted sandstone, synthetic sphere pack,
limestone, and poorly sorted sandstone, using Minkowski functionals,
image graph network-based measures, graph Laplacian-based measures,
local trend maps, and a homogeneity-heterogeneity classifier. Our
workflow suggests that AI-based digital rock augmentation, combined with
topological dimensionality reduction offers a powerful tool for enhanced
quality assessment and diagnostic of digital rock augmentation and
improved interpretation to support decision-making.