  Automated image processing algorithms can improve the quality, efficiency,
and consistency of classifying the morphology of heterogeneous carbonate rock
and can deal with a massive amount of data and images seamlessly. Geoscientists
face difficulties in setting the direction of the optimum method for
determining petrophysical properties from rock images, Micro-Computed
Tomography (uCT), or Magnetic Resonance Imaging (MRI). Most of the successful
work is from the homogeneous rocks focusing on 2D images with less focus on 3D
and requiring numerical simulation. Currently, image analysis methods converge
to three approaches: image processing, artificial intelligence, and combined
image processing with artificial intelligence. In this work, we propose two
methods to determine the porosity from 3D uCT and MRI images: an image
processing method with Image Resolution Optimized Gaussian Algorithm (IROGA);
advanced image recognition method enabled by Machine Learning Difference of
Gaussian Random Forest (MLDGRF). We have built reference 3D micro models and
collected images for calibration of IROGA and MLDGRF methods. To evaluate the
predictive capability of these calibrated approaches, we ran them on 3D uCT and
MRI images of natural heterogeneous carbonate rock. We measured the porosity
and lithology of the carbonate rock using three and two industry-standard ways,
respectively, as reference values. Notably, IROGA and MLDGRF have produced
porosity results with an accuracy of 96.2% and 97.1% on the training set and
91.7% and 94.4% on blind test validation, respectively, in comparison with the
three experimental measurements. We measured limestone and pyrite reference
values using two methods, X-ray powder diffraction, and grain density
measurements. MLDGRF has produced lithology (limestone and Pyrite) volumes with
97.7% accuracy.
