where $`N`$ is the number of pixels inside the ROI. As an example, the top-left figure below shows an experimental image for a disc under diametric loading and the lower-left figure below shows the $`G^2`$ image calculated based on the experimental image. Both figures are colormap images: red means large value and blue means small value. For the $`G^2`$ image, the value of each pixel is the gradient square $`\nabla I^2`$ of the experimental image. The $`G^2`$ value for this disc is calculated by averaging the $`\nabla I`$ values inside the disc, which is the ROI of the problem.
where $`N`$ is the number of pixels inside the ROI. As an example, the top-left figure below shows an experimental image for a disc under diametric loading and the lower-left figure below shows the $`G^2`$ image calculated based on the experimental image. Both figures are colormap images: red means large value and blue means small value. For the $`G^2`$ image, the value of each pixel is the gradient square $`|\nabla I|^2`$ of the experimental image. The $`G^2`$ value for this disc is calculated by averaging the $`\nabla I`$ values inside the disc, which is the ROI of the problem.
