I'm pretty sure the brightness gradient vector given by $$(E_x,E_y)^T = (sin\theta,-cos\theta)^T (B_2-B_1)\delta(xsin\theta-ycos\theta + \rho)$$ is a coordinate-system-independent vector. However, I am not sure how to prove it.

  • $\begingroup$ I'm not familiar with the "brightness gradient vector"--a quick Google search makes it seem like it's somehow related to neurons? Perhaps you could clarify that, and then people might be more able to answer your question. (Also, please clarify exactly what you're looking for in an answer. As it stands, there is no question in the above post. ;)) $\endgroup$ – apnorton Oct 3 '14 at 3:17
  • $\begingroup$ This may be helpful, but the question is unclear, esp. the rotationally symmetric part. $\endgroup$ – user147263 Oct 3 '14 at 4:15
  • $\begingroup$ Added an edit that should clarify a bit. $\endgroup$ – Tonyui Oct 3 '14 at 4:17

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