There is a constant need for improvement of lithium-ion batteries (LIB), in particular, charge/discharge time, capacity, and safety to fulfil the increasing performance requirements. The performance of LIB materials is heavily dependent on their 3D microstructural characteristics. Physics-based 3D microstructure models that resolve the microstructural characteristics of all phases in a porous electrode are critical for quantifying the interplay between battery microstructure and performance. In this work, we employed a machine-learning algorithm to segment the active particles from previously published tomographic data obtained for an inhomogeneous porous microstructure of the LIB cathode electrode. We performed geometric characterization analysis using the segmented data, extracting the particle size distribution, porosity, tortuosity, and the connectivity of the particle system. We also present a methodology for stochastic reconstruction of electrode microstructure which is statistically equivalent to the empirical microstructure in terms of geometric characteristics. We use spherical harmonics to accurately represent the non-spherical particle morphology and resolve the contact between the particles. The stochastic reconstruction technique proposed herein enables generation of virtual microstructure designs beyond the limitations of empirical datasets. The methods developed in this work are presented via open source.