Scale is a widely used notion in image analysis that evolved in the form of scale-space theory whose key idea is to represent and analyze an image at various resolutions. Recently, the notion of space-variant scale has drawn significant research interest. Previously, we introduced local morphometric scale using a spherical model whose major limitation was that it ignored orientation and anisotrophy making is suboptimal in many biomedical imaging applications where structures are inherently anisotropic and have mixed orientations. Here, we introduce a new idea of local scale, called tensor scale, which, at any image location, is the parametric representation of the largest ellipse (in 2D) or ellipsoid (in 3D) centered at that location that is contained in the same homogeneous region. Tensor scale is useful in spatially adapting neighborhood and controlling parameters in a space-variant and anisotropic fashion complying with orientation, anisotrophy, and thickness of local structures. Results of the method on several 2D images are presented and a few experiments are conducted to examine its behavior under rotation, varying pixel size, background inhomogeneity, and noise and blurring. Similarity of tensor scale images computed from multi-protocol images is studied.