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CACI Geospatial Technologies

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he basis for the SIPHER algorithm was discovered within a U.S. Air Force Research Laboratory (AFRL)-sponsored imagery research project. It is based on the concept of objects being in or out of spatial intensity phase with one another. We first define this “spatial intensity phase” quantity mathematically, then compare it to conventional signal phase relationships, and finally apply it to some images to demonstrate its behavior and utility for discriminating objects. Applications include all forms of image interpretation, from airborne reconnaissance to medical image interpretation.

We define spatial intensity phase (fSI) as an independent variable which contributes, along with other independent variables, to producing an amplitude in image pixels. This is similar to phase relationships producing time-dependent and phase-dependent amplitudes in signal processing situations. Hence, our general equation for this behavior is:

A = f (fSI, V1, ... Vn)

Where: f is a function of this spatial intensity phase (fSI) and possibly other independent variables, V1, ... Vn

A is the amplitude

Analogously, in signal processing terms, for a simple sinusoid we can express some voltage amplitude, V, as a function of the independent variables phase, f, frequency, f, and time, t. Hence, a comparable signal equation is:

V = f ( f, f, t)

V = V0sin(2πft + f)

Where: V is time-varying signal amplitude in volts, f is frequency in Hz (constant if not frequency-modulated), t is time in seconds, f is phase in radians, and V0 is the peak or maximum voltage amplitude.