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We present a geometric framework for surface denoising using graph signal processing, which is an emerging field that aims to develop new tools for processing and analyzing graph-structured data. The proposed approach is formulated as a constrained optimization problem whose objective function consists of a fidelity term specified by a noise model and a regularization term associated with prior data. Both terms are weighted by a normalized mesh Laplacian, which is defined in terms of a data-adaptive kernel similarity matrix in conjunction with matrix balancing. Minimizing the objective function reduces it to iteratively solve a sparse system of linear equations via the conjugate gradient method. Extensive experiments on noisy carpal bone surfaces demonstrate the effectiveness of our approach in comparison with existing methods. We perform both qualitative and quantitative comparisons using various evaluation metrics.

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