Sentence examples for by taking the gradient from inspiring English sources

From the motion history image, we can derive the direction by taking the gradient.

(2.10) By taking the gradient of both sides of (2.10) we can prove that (rho_{0}) satisfies the equilibrium equation (1.1).

The edge map is obtained by taking the gradient of the input data and limiting it to an available threshold value.

(2.10) By taking the gradient on both sides of (2.10), we can prove that (rho_{0}) satisfies the equilibrium equation (1.1).

The geocentric components of the geomagnetic field in the northward, eastward, and radially inwards directions (X, Y and Z) are obtained from the model coefficients using Equation 1 and by taking the gradient of V in spherical polar co-ordinates X={frac{1}{r}}{frac{partial V}{partial theta }},quad Y=-{frac{1}{ rsin theta }}{frac{partial V}{partial phi }},quad Z={frac{partial V }{partial r}}.

By taking the instantaneous gradient term of the Lagrangian expression derived in (9) with respect to the adjustable code matrix results in (20).

and a simple adaptive algorithm for determining the adjustable code matrices can be derived by taking the instantaneous gradient terms of the Lagrangian expression with respect to the scalar (phi ^_{{k_{j}}_{text {SAS}}}[i]) in ({boldsymbol {Phi }}_{{eq_{k}}_{text {SAS}}}[i]), which is (35).

The Lagrangian expression of the optimization problem in (7) is given by (9). and by taking the instantaneous gradient of with respect to the code matrix (left ({boldsymbol {Phi }}^{boldsymbol {Delta }}_{{eq_{k}}_{text {MAS}}}[i]right)^) we can obtain (10).

The amount of volume change was quantified by taking the determinant of the gradient of deformation at a single-voxel level (Jacobian determinant).

The changes could be understood by taking the observed orientation gradients and anisotropic movement of grain boundaries into account.

Therefore, we calculate only the gradient norm by taking the interaction among the channels into account in order to edit color images using the proposed methods.