In this paper we present a novel method to implement the monogenic scale space on a rectangulardomain. The monogenic scale space is a vector valued scale space based on the Poisson scale space, which establishesa sophisticated alternative to the Gaussian scale space. Previous implementations of the monogenic scale space areFourier transform based, and therefore suffer from the implicit periodicity in case of finite domains.The features of the monogenic scale space, including local amplitude, local phase, local orientation, local frequency,and phase congruency, are much easier to interpret in terms of image features evolving through scale thanin the Gaussian case. Furthermore, applying results from harmonic analysis, relations between the features areobtained which improve the understanding of image analysis. As applications, we present a very simple but stillaccurate approach to image reconstruction from local amplitude and local phase and a method for extracting theevolution of lines and edges through scale.