The field of functional analysis has provided insight into function spaces not obtained through the lens of linear algebra. These spaces are characterized by defining a norm which allows for measuring distinct degrees of smoothness (scale) t, say for an image f. Historically, we have seen the development of H ̈older, Sobolev, and Hardy spaces culminate as special cases of Besov and Triebel-Lizorkin spaces. This work focuses on the latter space, F ̇ α p,∞, with a connection to the fields of neuroscience and computer vision. A definition for local scale selection of f is provided using both isotropic and anisotropic Gaussian kernels. Numerical results include applications related to image classification and kernel estimation for deblurring processes in the isotropic case. In the anisotropic case results are in accordance with image features related to scale and orientation.
