Generalised Hilbert Transforms for the Estimation of Growth Direction in Coral Cores

Measuring coral growth rate is essential for monitoring coral reef health, and part of the process involves directional analysis of x-ray images of coral sections. The monogenic signal is useful for this application as it represents an image in terms of intrinsically-1D feature type (phase), strength (amplitude) and orientation. At certain locations the monogenic signal may give orientation errors, however these can be resolved using higher order generalised Hilbert transforms. We follow this approach, but combine components using a double angle representation as well as the sign of the phase. The improved algorithm is then applied to estimation of growth direction in coral x-ray images. An objective estimation of major growth axis, growth band location, and off axis extension compensation is now possible, and shows the usefulness of 2D analytic signal based image analysis.