Quantifying near-field displacements can help enable a better understanding of earthquake physics and hazards. To date, established remote sensing techniques have failed to recover sub-cm level near-field displacements at the scale and resolution required for shallow fault physical investigations. In this study, methods are developed to rapidly extract planar parameters, using fast parallel approaches and an alternative registration approach is employed to automatically match planes extracted from pairwise temporally spaced MLS and ALS datasets along the Napa fault. The features extracted from two temporally spaced point clouds are then used to calculate rigidbody transformation parameters. The production of robust and accurate deformation maps requires the selection of appropriate planar feature extraction and feature mapping criteria. Rigorously propagated point accuracy estimates are employed to produce realistic estimated errors for the transformation parameters. Displacements of each aggregate study area are computed separately from left and right sides of the fault and compared to be within 3 mm of alinement array displacements. Local differential displacements show distinct patterns which compared to alinement array measurements, were found to agree within the confidence bounds. The findings demonstrate the ability to accurately estimate near-field deformations from repeated MLS or ALS scans of earthquake-prone urban areas. ALS is also used in conjunction with the MLS datasets, illustrating the algorithm's ability to accommodate different LiDAR collection modalities at sub-cm level accuracy. The automated planar extraction and registration is an important contribution to the study of nearfield earthquake dynamics and can be used as input observations for future geological inversion models.