We present a technique to perform nonlinear 3D pattern recognition, and we analyze the performance of the Fourier plane nonlinear filters in terms of signal-to-noise (SNR). Using in-line digital holography, the complex amplitude distribution generated by a 3D object at an arbitrary plane located in the Fresnel diffraction region is recorded by phase-shifting interferometry. Information about the 3D object shape, location and orientation is contained in the digital hologram. This allows us to perform 3D pattern- recognition techniques using non-linear correlation filters. Then we obtain a range non linearities for which the SNR is robust to the variations in input noise bandwidth, which keeps the output SNR of the filter stable relative to changes in the noise bandwidth, using Karhunen-Loeve series expansion of the noise process. This is shown both by analytical estimates of the SNR for nonlinear filters as well as by experimental simulations.