Mean Shift with Flatness Constraints

Mean shift still belongs to the intensively developed image-segmentation methods. Appropriately setting so called bandwidth, which is richly discussed in literature, seems to be one of its problems. If the bandwidth is too small, the results suffer from over-segmentation. If it is too big, the edges need not be preserved sufficiently and the details can be lost. In this paper, we address the problem of over-segmentation and preserving the edges in mean shift too. However, we do not aim at proposing a further method for determining the bandwidth. Instead, we modify the mean-shift method itself. We show that the problems with over-segmentation are inherent for mean shift and follow from its theoretical essence. We also show that the mean-shift process can be seen as a process of solving a certain Euler-Lagrange equation and as a process of maximising a certain functional. In contrast with other known functional approaches, however, only the fidelity term is present in it. Other usual terms, e.g., the term requiring a short length of boundaries between the segments or the term requiring the flatness (in intensity) of the corresponding filtered image are not present, which explains the behaviour of mean shift. On the basis of this knowledge, we solve the problems with mean shift by modifying the functional. We show how the new functional can be maximised in practice, and we also show that the usual mean-shift algorithm can be regarded as a special case of the method we propose. The experimental results are also presented.