A multiresolution approach to curve extraction in images is described. Based on a piecewise linear representation of curves, the scheme combines an efficient method of extracting line segments with a grouping process to identify curve traces. The line segments correspond to linear features defined at appropriate spatial resolutions within a quadtree structure and are extracted using a hierarchical decision process based on frequency domain properties. Implementation is achieved through the use of the multiresolution Fourier transform (MFT), a linear transform providing spatially localised estimates of the frequency spectrum over multiple scales. The scheme is simple to implement, computationally inexpensive, and results of experiments performed on natural images demonstrate that its performance compares favourably with that of existing methods.