This research concerns compression of digital images consisting of smoothly colored regions separated from each other by smooth contours. Wavelet transforms combined with a nonlinear thresholding step are optimal when catching point singularities, however, when trying to capture smooth line singularities in a parsimonious manner they perform suboptimal. We propose a geometrical method to deal with these inherent defficiencies of wavelets. The proposed method using normal offsets transforms the input image nonlinearly using only a series of scalar values. Special attention is given on how to adapt the concept of normal offsets towards the digital setting. Moreover, a local adaptive triangulation is issued such that the method is able to sparsely represent higher dimensional singularities,
i.e., line singularities. The adaptive triangulation encourages the triangle edges to settle themselves parallel with respect to the contour. At the same time the locality of the triangulation method induces
hierarchical mesh structures which are well suited for compression methods.