Hypercomplex Fourier transforms applied to detection for side-scan sonar

This research addresses the problem of image processing for the detection of mine-like targets from sonar data. This is a challenging problem because of the large variability in both background clutter and object appearance. Bülow and Sommer (2001) use hypercomplex numbers to obtain local phase information, which reveals the intrinsic dimensionality of the signal. The three local phase components are indicative of the local texture within an image. We use these texture components to identify anomalies on the sea floor. First we generate the quaternion signal of real 2D input using Hilbert transforms (a 2D equivalent of the complex signal of real ID input). Three phase angles and a magnitude are obtained from this quaternion. The magnitude is the square root of the sum of the squares of the quaternion coefficients. The first phase angle, theta, is equivalent to the linear phase in the x-direction. The second phase angle, phi, is equivalent to the linear phase in the y-direction. The third phase angle, psi, is related to the two-dimensional texture. A very random texture produces random values for the phases. An anomaly in a given texture region maps to related values in the phase components in that region. We explore the effectiveness of this approach to texture anomaly detection with real data. Anomalous textures, such as man-made objects in images of the sea floor, appear as spatially predictable regions of extreme values in the phase components. We have shown that the phase components are of some value in identifying regions of a sonar image that contain unusual texture when compared to the rest of the image. This method could be used in a real system as a practical human decision support, identifying regions of interest (detections) in images where simple thresholding is ineffective.