Definition of objects in medical images requires a multiscale approach because important structure appears across a wide range of scales. Object boundaries, when they are required, must be inferred from the multiscale structure of the image and a priori knowledge. For many objectbased tasks, explicit identification of boundaries is not necessary. Instead, it is possible to base object measures on medial axes and their radius functions obtained using statistical methods. A medial approach makes the easy decisions about the membership of pixels in the object first. The difficult decisions about the boundaries are made using a fuzzy measure of "objectness" that can account for edge uncertainty, partial volume effects, and a priori information. Objectness diffuses outward from the medial axis, and non-objectness diffuses inward from medial axes of surrounding regions. Their competition in boundary regions defines objectness even in the absence of an edge. The area of an object is the integral of objectness across space. Statistical pattern recognition methods (supervised and unsupervised classification; linear projections) are used to identiQy medial axes in a feature space defined by multiscale Gaussian filters. The pattern describing a pixel is formed from the response at that location and nearby locations to the filters. Approximations to derivatives of Gaussians are linear subspaces of this feature space.