Magnification of label maps with a topology-preserving level-set method

Image segmentation aims at partitioning an image into multiple segments. The application of this procedure produces a label map (also referred to as segmentation map) that classifies the pixels of the original image. In contrast to "natural" images, label maps are nominal-scale images, typically represented as integer-valued images. Nominal-scaled label maps can also appear as a representation of the raw data in areas, such as in geostatistics. In some applications, the original resolution of a label map does not suffice and a larger size map has to be generated. In this paper, we present a magnification algorithm for label maps and nominal images. The main property of our method is that it preserves the topology during the magnification process, which means that no isolated pixel vanishes. To the best of our knowledge, apart from nearest-neighbor interpolation, the problem of label map magnification has not previously been addressed in the literature. The main idea of the proposed method is to accomplish a boundary refinement by smoothing the regions' boundaries on a finer grid. The method relies on well known methods, namely, the fundamental operations of morphological image processing-erosion and dilation-and the level-set method. The level-set method is well suited for our purposes since it does not depend on a parametrization and it is numerically stable. The topological flexibility of the level-set method-often found to be an advantage in applications-is a drawback here, since the topology of the original label map should be preserved. However, using the so-called simple point criterion from digital topology, one can adapt the conventional level-set method so that the topology will not be modified throughout the magnification procedure.