In this paper, we describe a new vector similarity measure associated with a
convex cost function. Given two vectors, we determine the surface normals of
the convex function at the vectors. The angle between the two surface normals
is the similarity measure. Convex cost function can be the negative entropy
function, total variation (TV) function and filtered variation function. The
convex cost function need not be differentiable everywhere. In general, we need
to compute the gradient of the cost function to compute the surface normals. If
the gradient does not exist at a given vector, it is possible to use the
subgradients and the normal producing the smallest angle between the two
vectors is used to compute the similarity measure