Figure 3.

Local phase relies on the differential response of odd and even filters to odd and even symmetric features. A 1D signal (black line) is shown containing an odd feature (step function) and an even feature (triangle function). When an even 1D Difference of Gaussians filter is convolved with the signal, the output (blue dashed line) is stronger for the even feature. The Hilbert Transform is used to generate a quadrature odd filter from the initial even filter, and this yields a stronger response to the odd feature (red dashed line).