The image foresting transform (IFT) reduces optimal image partition problems into a shortest-path forest problem in a graph, whose solution can be obtained in linear time. Such a strategy has allowed a unified and effective approach to the design of image processing operators, such as edge detection, region growing, watershed transforms, distance transforms, and connected filters. This paper presents a fast and simple IFT-based approach to multiscale shape representation with applications to medical imaging. Given an image with multiple contours, each contour pixel defines a seed with a contour label and a pixel label. The IFT computes the Euclidean distance transform, propagating both types of labels to other pixels in the image. A difference image is created from the propagated labels. The skeleton by influence zone (SKIZ) and multiscale skeletons are produced by thresholding the difference image. As compared to other approaches, including multiscale skeletonization based on the Voronoi diagram, the presented method can generate high-quality one-pixel-wide connected skeletons and SKIZ for objects of arbitrary topologies, simultaneously. Multiscale shape reconstructions can then be obtained by considering the SKIZ, the skeletons and the Euclidean distance values. The method allows non-linear multiscale shape filtering without border shifting, as illustrated with medical images.