Step 1. Gradient computation: The gradient of each pixel in the window is calculated using two filter kernels: [−1, 0, 1] and [−1, 0, 1] T. Let the magnitude and orientation of the gradient of the i th pixel (1 ≤ i ≤ 4096) be denoted by m i and φ i, respectively.
Using the facts that the state of stress is not uniform across an element and that the deformation gradient is a spatially continuous (and possibly non-differentiable) tensor, the proposed model uses a continuously modified deformation gradient to capture the location and orientation of wrinkles more precisely.
As previously underlined, in cancellous bone, more than in other tissues, the magnetic susceptibility mismatch between the solid matrix and interstitial water bone marrow generates internal gradients of magnitude depending on the geometry and orientation of the trabeculae with respect to the static magnetic field direction scaling with magnetic field strength.
Then the integration scale σ 2, at which the averages of the estimates of the image derivatives are computed, is the link between the classical representation of the local image orientations by the gradient and the representation of the local image textures by the structure tensor.
First, the gradient magnitude and orientation are computed at each point of the window using a standard operator (Sobel 3 × 3 masks are used in our implementation).
Low roughness emphasizes the smooth nature of the basins' topography, where surfaces of homogeneous slope gradient and orientation dominate.
The gradient orientation of each sample in the region is weighted by its gradient magnitude and by a Gaussian window function with before being added to the histogram.
However, in multimodal images, the gradient orientation of corresponding points may be in opposite directions [20].
Thus, cells in a cAMP gradient have a very strong persistence, which amplifies the small bias of pseudopod orientation towards the gradient, and stores this directional movement for prolonged periods of time.
The keypoint descriptor in the final stage is created by sampling the magnitudes and orientations of the image gradients in a neighborhood of each keypoint and building smoothed orientation histograms that contain the important aspect of the neighborhood.
