Evaluate image symmetry
A practical approach with centering, filtering, derivative, etc. may provide some results. Taking a step back on associated properties, for instance in the Fourier domain, may give you different insights, since symmetry is not well-defined per se (local or global, radial or axis, etc.). I am thinking specifically of the phase-based approach in Peter Kovesi, Symmetry and Asymmetry from Local Phase, 1997:


  Symmetry is an important mechanism by which we identify the structure
  of objects. Man-made objects, plants and animals are usually highly
  recognizable from the symmetry, or partial symmetries that they often
  exhibit. Two difficulties found in most symmetry detection algorithms
  are firstly, that they usually require objects to be segmented prior
  to any symmetry analysis, and secondly, that they do not provide any
  absolute measure of the degree of symmetry at any point in an image.
  This paper presents a new measure of symmetry that is based on the
  analysis of local frequency information. It is shown that points of
  symmetry and asymmetry give rise to easily recognized patterns of
  local phase. This phase information can be used to construct a
  contrast invariant measure of symmetry that does not require any prior
  recognition or segmentation of objects.


Here are examples for testing local symmetry:

 

And some Matlab code, for instance phasesym.m in Peter Kovesi Matlab functions.