A spatially regularized Gaussian mixture model, LapGM, is proposed for the bias field correction and magnetic resonance normalization problem. The proposed spatial regularizer gives practitioners fine-tuned control between balancing bias field removal and preserving image contrast preservation for multi-sequence, magnetic resonance images. The fitted Gaussian parameters of LapGM serve as control values which can be used to normalize image intensities across different patient scans. LapGM is compared to well-known debiasing algorithm N4ITK in both the single and multi-sequence setting. As a normalization procedure, LapGM is compared to known techniques such as: max normalization, Z-score normalization, and a water-masked region-of-interest normalization. Lastly a CUDA-accelerated Python package $\texttt{lapgm}$ is provided from the authors for use.