Geometric explanation of a methodology in the article about Image Denoising In article Ghimpeteanu G., et al. - A Decomposition Framework for Image Denoising Algorithms, I found as below:


  Let $\displaystyle I : \Omega \subset \mathbb{R}^2\mapsto \mathbb{R}$ be a gray-level image, and $(x, y)$ be the standard coordinate system of $\mathbb{R}^2$.We denote by $Ix
 \hspace{.2cm}resp.Iy$ the derivative of $I$ with respect to $x
 \hspace{.2cm}resp. y$, and by $\nabla I$ the gradient of $I$ . Our
  image decomposition model for $I$ is a two-stages approach: first, we
  construct an orthonormal moving frame $(Z_1, Z_2, N)$ of $(\mathbb{R}^3,\|
\|_2)$ over $\Omega$ that encodes the local geometry of $I$ . Then, we
  compute the components $(J^1, J^2, J^3)$ of the $\mathbb{R}^3-$valued function
  $(0, 0, I )$ in that moving frame. More precisely, we consider a
  scaled version $\mu I$ of $I$ , for $\mu \in ]0, 1]$, and its graph,
  which is the surface $S$ in $\mathbb{R}^3$ parametrized by $\psi : (x, y)
\mapsto (x, y,μ I (x, y))$


See snapshot-



Please someone explain (possibly visualize geometrically) 4th and 5th line of the excerpt. i.e 


  Our image decomposition model for $I$ is a two-stages approach: first, we construct an orthonormal moving frame $(Z_1, Z_2, N)$ of $(\mathbb{R}^3,\| \|_2)$ over $\Omega$ that encodes the local geometry of $I$ . Then, we compute the components $(J^1, J^2, J^3)$ of the $\mathbb{R}^3-$valued function $(0, 0, I )$ in that moving frame.
The explanation below the section you quote seems to be clear to me:



It's forming a vector field made up of the largest gradient direction, smallest gradient direction, and the normal to them both.