Magnetic resonance imaging (MRI) has become an important imaging technique for quantifying the spatial location and magnitude/direction of longitudinal cartilage morphology changes in patients with osteoarthritis (OA). Although several analytical methods, such as subregion-based analysis, have been developed to refine and improve quantitative cartilage analyses, they can be suboptimal due to two major issues: the lack of spatial correspondence across subjects and time and the spatial heterogeneity of cartilage progression across subjects. The aim of this paper is to present a statistical method for longitudinal cartilage quantification in OA patients, while addressing these two issues. The 3D knee image data is preprocessed to establish spatial correspondence across subjects and/or time. Then, a Gaussian hidden Markov model (GHMM) is proposed to deal with the spatial heterogeneity of cartilage progression across both time and OA subjects. To estimate unknown parameters in GHMM, we employ a pseudo-likelihood function and optimize it by using an expectation-maximization (EM) algorithm. The proposed model can effectively detect diseased regions in each OA subject and present a localized analysis of longitudinal cartilage thickness within each latent subpopulation. Our GHMM integrates the strengths of two standard statistical methods including the local subregion-based analysis and the ordered value approach. We use simulation studies and the Pfizer longitudinal knee MRI dataset to evaluate the finite sample performance of GHMM in the quantification of longitudinal cartilage morphology changes. Our results indicate that GHMM significantly outperforms several standard analytical methods.