Surface Curvature as a Measure of Image Texture

Methods from the theory of surfaces in differential geometry are applied to the gray tone intensity and absorbance surfaces defined by a digital image. In particular, the first fundamental form, the second fundamental form, the two principal curvatures, the Gaussian curvature, and mean curvature from classical differential geometry are presented. New curvatures are introduced which appear to be more appropriate for the purposes of image texture. For each curvature, a texture feature is generated. These features are applied to biological cell nuclei and it is found that they are useful for purposes of discrimination.