In this talk, we study the problem of extracting local scales of oscillatory patterns in images and on plane curves. In the first case, Given a multi-scale representation {u(t)} of an image f, we are interested in automatically picking out a few choices of t_i(x), which we call local scales, that better represent the multi-scale structure of f at x. We will characterize local scales coming from the Gaussian kernel. In the second case, we propose an approach to extracting local scales on curves to segment objects with irregular boundaries. Theory and experimental results will be presented with applications to image decomposition/denoising.