pivuq.warping

pivuq.warping.interpolate_to_pixel(U, imshape, kind='linear') → ndarray[source]

Interpolate velocity field to pixel level.

Parameters:

  • U (np.ndarray) – Sparse 2D velocity field.

  • imshape (tuple) – Image frame dimension (rows, cols).

  • kind ({"linear", "cubic", "quintic"}, default: "linear") – The kind of spline interpolation for scipy.interpolation.interp2d.

Returns:

Pixel-wise 2D velocity field.

Return type:

np.ndarray

pivuq.warping.warp(image_pair, U, velocity_upsample_kind='linear', direction='center', nsteps=1, order=-1, radius=2) → ndarray[source]

Warp image pair pixel-wise to each other using skimage.transform.warp.

Parameters:

  • image_pair (np.ndarray) – Image pairs \(\mathbf{I} = (I_0, I_1)^{\top}\) of size \(2 \times N \times M\).

  • U (np.ndarray) – Sparse or dense 2D velocity field \(\mathbf{U} = (u, v)^{\top}\) of size \(2 \times U_N \times U_M\).

  • warp_direction ({"forward", "center", "backward"}, default: "center") – Warping warp_direction.

  • velocity_upsample_kind ({"linear", "cubic", "quintic"}, default: "linear") – Velocity upsampling kind for spline interpolation scipy.interpolation.interp2d.

  • nsteps (int, default: 1) – Number of sub-steps to use for warping to improve accuracy. Although, the original flow estimator (e.g. PIV) most likely uses \(n_{\mathrm{steps}}=1\).

  • order (-1, 1, 2 (bug), 3, default: -1) – The order of interpolation for skimage.transform.warp. If order is negative, using Whittaker-Shannon interpolation.

  • radius (int, default: 3) – Radius of the Whittaker-Shannon interpolation stencil.

Returns:

Warped image pair \(\hat{\mathbf{I}} = (\hat{I}_0, \hat{I}_1)^{\top}\) of size \(2 \times N \times M\).

Return type:

np.ndarray

pivuq.warping.warp_skimage(frame, U, coords, order=1, mode='edge') → ndarray[source]

Warp image frame pixel-wise using skimage.transform.warp.

Parameters:

  • frame (np.ndarray) – image frame.

  • U (np.ndarray) – pixel-wise 2D velocity field.

  • coords (np.ndarray) – 2D image coordinates (row, cols).

  • order (1-5, default: 1) – The order of interpolation for skimage.transform.warp.

  • mode ({"constant", "edge", "symmetric", "reflect", "wrap"}, default: "edge") – Points outside the boundaries of the input are filled according to the given mode.

Returns:

Warped image frame

Return type:

np.ndarray

See also

skimage.transform.warp

Warp an image according to a given coordinate transformation.

pivuq.warping.warp_whittaker(frame, U, coords, radius=3) → ndarray[source]

Warp image using Whittaker-Shannon interpolation

Parameters:

  • frame (np.ndarray) – image frame.

  • U (np.ndarray) – pixel-wise 2D velocity field.

  • coords (np.ndarray) – 2D image coordinates (row, cols).

  • radius (int, default: 3) – Radius of the interpolation stencil.

Returns:

Warped image frame

Return type:

np.ndarray

See also

whittaker_interpolation

Whittaker-Shannon interpolation.

pivuq.warping.whittaker_interpolation(im, xi, yi, r=3)[source]

Whittaker-Shannon interpolation [1].

Parameters:

  • im (np.ndarray) – Image frame of shape (rows, cols).

  • xi (np.ndarray) – The x and y-coordinates at which to evaluate the interpolated values of shape (rows, cols).

  • yi (np.ndarray) – The x and y-coordinates at which to evaluate the interpolated values of shape (rows, cols).

  • r (int, default: 3) – Radius of the interpolation stencil.

Returns:

Interpolated image frame.

Return type:

np.ndarray

References