This paper introduces a novel approach for image analysis based on the notion of multiscale connectivity. We use the proposed approach to design several novel tools for object-based image representation and analysis which exploit the connectivity structure of images in a multiscale fashion. More specifically, we propose a nonlinear pyramidal image representation scheme, which decomposes an image at different scales by means of multiscale grain filters. These filters gradually remove connected components from an image that fail to satisfy a given criterion. We also use the concept of multiscale connectivity to design a hierarchical data partitioning tool. We employ this tool to construct another image representation scheme, based on the concept of component trees, which organizes partitions of an image in a hierarchical multiscale fashion. In addition, we propose a geometrically-oriented hierarchical clustering algorithm which generalizes the classical single-linkage algorithm. Finally, we propose two object-based multiscale image summaries, reminiscent of the well-known (morphological) pattern spectrum, which can be useful in image analysis and image understanding applications.