A neural network approach has been applied to three-dimensional correction of the geometrical nonlinearities in scanning probe microscope images. Creep and hysteresis of the piezo scanner cause nonlinear trajectory of the sensor movements over the sample which results in geometrically distorted scanning probe microscope images. A calibration sample with regular structure has been used for collection of data for the geometrical distortions. The inverse neural network model has been trained with these data. A single hidden layer network was sufficient to obtain satisfactory accuracy of the corrections. Using the same training data set polynomial approximation models have been implemented also. The accuracy of the neural network approximations shows to be better than the accuracy of the polynomial one. Additionally neural network corrected images reveal no boundary distortions typical for the linear piecewise approximation. Using the neural network approach surface maps of different scanning probe microscope techniques scanning tunneling microscopy, atomic force microscopy, and scanning thermal microscope have been successfully corrected.