ABSTRACT
This chapter discusses the outlandish to the unenlightened/unaware reader. However, weighted manifolds in fact commonly encountered for instance, in Imaging, and none the less than in modeling the commonest, simplest and most natural example of image, namely grayscale images. In addition, such measures represent useful tools in many concrete settings, as ad hoc tools employed at various stages of the implementation of a variety of tasks, such as smoothing, registration, warping, and segmentation, etc. In addition, such measures represent useful tools in many concrete settings, as ad hoc tools employed at various stages of the implementation of a variety of tasks, such as smoothing, registration, warping, segmentation, etc. The importance of manifolds with densities and their Ricci curvature was first emphasized by Gromov, partly motivated by the connection between Ricci curvature and volume growth and collapse under the Ricci flow.
