In this paper, we delve into the intricate task of registering 3D point clouds of plants over time and space, a pivotal step in advancing phenotyping applications focused on tracking plant traits over time. We introduce a novel methodology integrating tailored data association techniques with a refined non-rigid registration approach, overcoming challenges such as anisotropic growth, changing topology, and non-rigid motion during measurements. This innovative approach enables precise point cloud time series data analysis, facilitating comprehensive insights into plant dynamics. Utilizing iterative beam search for correspondence matching ensures computational efficiency and robustness, which is particularly advantageous for handling large graphs. Moreover, we refine the Hidden Markov Model (HMM) and spatio-temporal registration to integrate geometric constraints, enhancing the accuracy and reliability of trait analysis. Employing HMM, a widely adopted technique for modeling sequential data, enables accurate tracking of plant growth dynamics over time, facilitating precise assessments of phenotypic traits crucial for crop science and agriculture.