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• Mathematical and quantitative methods were used to describe the damaged shape repair and provide the restoration results in the form of a probability distribution. • A specialized triangle mesh topology for Buddha statue head registration was designed, and a semi-automated registration strategy was developed to achieve high-quality shape registration. • Using the deformation field and interpolator, we defined the Gaussian process model, in which every shape sampling from the model is a function defined on the reference shape. • A set of kernel functions was designed to extend the flexibility of the learned model. • A series of experiments was conducted to investigate the effectiveness of our method, and we applied the methods to an actual damaged Buddha statue head repair project. Buddha statues are distributed worldwide, and each piece reflects the aesthetic fashion of a particular region and historical era. Therefore, these sculptures have important cultural, aesthetic, and historical value. Owing to natural or artificial destruction, several Buddha statues have been damaged, with head or facial damage being the most prominent damage type. Because Buddha statue heads exhibit intricate variations in facial expressions and proportions, restoring head or facial damage is the most challenging aspect of damaged sculpture restoration projects. This study provides a new method for the restoration of damaged statues based on a Gaussian process model. The Gaussian process model entails a type of statistical shape modeling that allows it to learn shape distribution properties from a training dataset. During the restoration process, we used the residual parts of the damaged shape for the observations and added them to a Bayesian inference system to obtain the possible restoration result in the form of a posterior distribution. Therefore, the proposed method can be regarded as a quantitative mathematical representation of the subjective deduction process. Compared to those of the traditional manual restoration method, our results were more repeatable and stable, and the restoration process was automatic and rigorous, which reduced the requirements for professional knowledge and experience. Based on the learned model information, the proposed method exhibits strong robustness and anti-noise properties. In contrast to the optimization method, our final restoration result is a probability distribution, applicable to the repair of cultural relics. As our method make the missing shape inference using residual shape information and the regularity learned from training dataset, it is suitable for the restoration of damaged parts with no direct shape evidence. Finally, our model is generative; in other words, we can generate shapes on the posterior distribution and provide the corresponding probability. To demonstrate the effectiveness of our method, a series of experiments were conducted to restore damaged parts under different parameters and damage type settings. Subsequently, a quantitative analysis was performed. Finally, we applied this method to the virtual restoration of a damaged Buddha statue head in Xi 'an Museum. [Display omitted] [ABSTRACT FROM AUTHOR]