This paper aims at acquiring robust rotation, scale, and translation-invariant feature from a space-variant image by a fovea sensor. A proposed model of eccentricity compensator corrects deformation that occurs in a log-polar image when the fovea sensor is not centered at a target, that is, when eccentricity exists. An image simulator in discrete space remaps a compensated log-polar image using this model. This paper proposes Unreliable Feature Omission (UFO) that reduces local high frequency noise in the space-variant image using Discrete Wavelet Transform. It discards coefficients when they are regarded as unreliable based on digitized errors of the input image. The first simulation mainly tests geometric performance of the compensator, in case without noise. This result shows the compensator performs well and its root mean square error (RMSE) changes only by up to 2.54[%] in condition of eccentricity within 34.08[°]. The second simulation applies UFO to the log-polar image remapped by the compensator, taking its space-variant resolution into account. The result draws a conclusion that UFO performs better in case with more white Gaussian noise (WGN), even if the resolution of the compensated log-polar image is not isotropic.