The Complete Set of Independent Affine Moment Invariants of Color Images

Moment invariants of images are important features for pattern recognition and image processing. Many methods have been proposed to derive moment invariants of images under different group actions. However, the completeness and independence of a set of moment invariants are two open problems. In this paper, we use the moving frame method to derive affine moment invariants of color images. The moving frame for the normalized color moment space under the action of the affine group is presented. Using this moving frame, we obtain a complete and independent set of affine moment invariants of color images. This system of affine moment invariants is also invariant under diagonal photometric changes. Experimental results are provided to validate the correctness of the derivation.

High frequency microseismic noise as possible earthquake precursor

Before an earthquake occurs, microseismic noise in high frequency (HF) range, <em>i.e.</em> 2-25 Hz, is being generated during preparation process. These signals change the microseismic noise and, consequently, the spectrum of microseismic noise. Time variation of spectra recorded at the same seismological station could imply the change of the state of noise source. We propose the image moment analysis approach to objectively compare microseismic noise spectra. The result could be used for earthquake precursor identification. Expected spectra change is in HF range, so the analysis has been limited to the shallow tectonic earthquakes with epicenters close, up to 15 km, the seismological stations. The method has been tested post festum using four earthquakes in Dinarides which satisfied condition for epicentral distance. The spectra were calculated for noise recorded in time intervals of 10 days before and 6 to 10 days after the earthquakes. Affine moment invariants were calculated for noise spectra which were treated as the input objects. Spectra of the first five days in the series were referent spectra. The classification parameters were Euclidean distances between referent spectra and the spectra for all days in the series, including referent ones. The results have shown that the spectra of the microseismic noise become noticeably different than the other spectra in time intervals one or two days before an earthquake.