Creases are a type of ridge/valley structures of an image characterized by local conditions. As creases tend to be at the center of anisotropic grey-level shapes, creaseness can be considered a measure of medialness, and therefore as useful in many image analysis problems. Among the several possibilities, a priori the creaseness based on the level-set extrinsic curvature (LSEC) is especially interesting due to its invariance properties. However, in practice, it produces a discontinuous response with a badly dynamic range. The same problems arise with other related creaseness measures proposed in the literature. In this paper, we argue that these problems are due to the very local definition of the LSEC. Therefore, rather than designing an ad hoc solution, we propose two new multilocal creaseness measures that we will show to be free of discontinuities and to have a meaningful dynamic range of response. Still, these measures are based on the LSEC idea, to preserve its invariance properties. We demonstrate the usefulness of the new creaseness measures in the context of two applications that we are currently developing in the field of 3D medical image analysis, the rigid registration of CT and MR head volumes and the orientation analysis of trabecular bone patterns.