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Image warping using correspondences between sparse control points.

Apply a non-linear warp to the image, where the warp is specified by the source and destination locations of a (potentially small) number of control points. First, we use a polyharmonic spline (tf.contrib.image.interpolate_spline) to interpolate the displacements between the corresponding control points to a dense flow field. Then, we warp the image using this dense flow field (tf.contrib.image.dense_image_warp).

Let t index our control points. For regularization_weight=0, we have: warped_image[b, dest_control_point_locations[b, t, 0], dest_control_point_locations[b, t, 1], :] = image[b, source_control_point_locations[b, t, 0], source_control_point_locations[b, t, 1], :].

For regularization_weight > 0, this condition is met approximately, since regularized interpolation trades off smoothness of the interpolant vs. reconstruction of the interpolant at the control points. See tf.contrib.image.interpolate_spline for further documentation of the interpolation_order and regularization_weight arguments.

image [batch, height, width, channels] float Tensor
source_control_point_locations [batch, num_control_points, 2] float Tensor
dest_control_point_locations [batch, num_control_points, 2] float Tensor
interpolation_order polynomial order used by the spline interpolation
regularization_weight weight on smoothness regularizer in interpolation
num_boundary_points How many zero-flow boundary points to include at each image edge.Usage: num_boundary_points=0: don't add zero-flow points num_boundary_points=1: 4 corners of the image num_boundary_points=2: 4 corners and one in the middle of each edge (8 points total) num_boundary_points=n: 4 corners and n-1 along each edge
name A name for the operation (optional).

Note that image and offsets can be of type tf.half, tf.float32, or tf.float64, and do not necessarily have to be the same type.

warped_image [batch, height, width, channels] float Tensor with same type as input image.
flow_field [batch, height, width, 2] float Tensor containing the dense flow field produced by the interpolation.