There are many factors influencing the accuracy of surface topography measurement results: one of them is the vibrations caused by the high-frequency noise occurrence. It is extremely difficult to extract results defined as noise from the real measured data, especially the application of various methods requiring skilled users and, additionally, the improper use of software may cause errors in the data processing. Accordingly, various thresholding methods for the minimization of errors in the raw surface topography data processing were proposed and compared with commonly used (available in the commercial software) techniques. Applied procedures were used for the minimization of errors in the surface topography parameters (from ISO 25178 standard) calculation after the removal and reduction, respectively, of the high-frequency noise (S-filter). Methods were applied for analysis of the laser-textured surfaces with a comparison of many regular methods, proposed previously in the commercial measuring equipment. It was found that the application of commonly used algorithms can be suitable for the processing of the measured data when selected procedures are provided. Moreover, errors in both the measurement process and the data processing can be reduced when thresholding methods support regular algorithms and procedures. From applied, commonly used methods (regular Gaussian regression filter, robust Gaussian regression filter, spline filter and fast Fourier transform filter), the most encouraging results were obtained for high-frequency noise reduction in laser-textured details when the fast Fourier transform filter was supported by a thresholding approach.