Moment noise sensitivity

Various invariant moment schemes have proved useful in recognition and reconstruction tests [1,4,6,17]. They have proved successful and have shown invariance properties for images containing very little or no noise. However in the presence of noise, the computed Hu invariant moments $M_{1-7}$, begin to degrade. One study [19] showed that higher order moments are more vulnerable to white noise, thus making their use undesirable for pattern recognition. A more recent study [13] compared the performance of the Hu invariant moments with a set of moments based on wavelet basis functions. This study showed that when using Hu's moments, even a slight discrepancy in the image can cause considerable confusion (i.e. minor shape deformation or digitisation errors) if trying to discriminate between two similar images. However, noise simulation (in terms of image analysis) is very involved, and is highly dependent on the type of noise being simulated, its distribution, how it is applied etc. It must be noted that while studies involving noise analyses may be correct for each specific test condition, care must be taken when generalising to alternative noise-related conditions.