Phase congruency is a low-level invariant property of image features. Interest in low-level image invariants has been limited. This is surprising, considering the fundamental importance of being able to obtain reliable results from low-level image operations in order to successfully perform any higher level operations. However, an impediment to the use of phase congruency to detect features has been its sensitivity to noise. This paper extends the theory behind the calculation of phase congruency in a number of ways. An effective method of noise compensation is presented that only assumes that the noise power spectrum is approximately constant. Problems with the localization of features are addressed by introducing a new, more sensitive measure of phase congruency. The existing theory that has been developed for 1D signals is extended to allow the calculation of phase congruency in 2D images. Finally, it is argued that high-pass filtering should be used to obtain image information at different scales. With this approach, the choice of scale only affects the relative significance of features without degrading their localization.