224 lines
8.6 KiB
Python
224 lines
8.6 KiB
Python
import math
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import tensorflow as tf
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def euler_to_matrix(x, y, z):
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"""
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:param x: Tensor of shape (B, 1) - x axis rotation
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:param y: Tensor of shape (B, 1) - y axis rotation
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:param z: Tensor of shape (B, 1) - z axis rotation
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:return: Rotation matrix for the given euler anglers, in the order rotation(x) -> rotation(y) -> rotation(z)
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"""
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batch_size = tf.shape(z)[0]
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# Euler angles should be between -pi and pi, clip so the pose network is coerced to this range
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z = tf.clip_by_value(z, -math.pi, math.pi)
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y = tf.clip_by_value(y, -math.pi, math.pi)
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x = tf.clip_by_value(x, -math.pi, math.pi)
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cosx = tf.cos(x)
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sinx = tf.sin(x)
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cosy = tf.cos(y)
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siny = tf.sin(y)
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cosz = tf.cos(z)
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sinz = tf.sin(z)
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# Otherwise this will need to be reversed
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# Rotate about x, y then z. z goes first here as rotation is always left side of coordinates
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# R = Rz(φ)Ry(θ)Rx(ψ)
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# = | cos(θ)cos(φ) sin(ψ)sin(θ)cos(φ) − cos(ψ)sin(φ) cos(ψ)sin(θ)cos(φ) + sin(ψ)sin(φ) |
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# | cos(θ)sin(φ) sin(ψ)sin(θ)sin(φ) + cos(ψ)cos(φ) cos(ψ)sin(θ)sin(φ) − sin(ψ)cos(φ) |
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# | −sin(θ) sin(ψ)cos(θ) cos(ψ)cos(θ) |
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row_1 = tf.concat([cosy * cosz, sinx * siny * cosz - cosx * sinz, cosx * siny * cosz + sinx * sinz], 1)
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row_2 = tf.concat([cosy * sinz, sinx * siny * sinz + cosx * cosz, cosx * siny * sinz - sinx * cosz], 1)
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row_3 = tf.concat([-siny, sinx * cosy, cosx * cosy], 1)
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return tf.reshape(tf.concat([row_1, row_2, row_3], axis=1), [batch_size, 3, 3])
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def pose_vec2mat(vec):
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"""Converts 6DoF parameters to transformation matrix
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Args:
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vec: 6DoF parameters in the order of tx, ty, tz, rx, ry, rz -- [B, 6]
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Returns:
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A transformation matrix -- [B, 3, 4]
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"""
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batch_size, _ = vec.get_shape().as_list()
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translation = tf.slice(vec, [0, 0], [-1, 3])
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translation = tf.expand_dims(translation, -1)
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rx = tf.slice(vec, [0, 3], [-1, 1])
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ry = tf.slice(vec, [0, 4], [-1, 1])
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rz = tf.slice(vec, [0, 5], [-1, 1])
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rot_mat = euler_to_matrix(rx, ry, rz)
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transform_mat = tf.concat([rot_mat, translation], axis=2)
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return transform_mat
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def image_coordinate(batch, height, width):
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"""
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Construct a tensor for the given height/width with elements the homogenous coordinates for the pixel
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:param batch: Number of images in a batch
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:param height: Height of image
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:param width: Width of image
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:return: Tensor of shape (B, height, width, 3), homogenous coordinates for an image.
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Coordinates are in order [x, y, 1]
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"""
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x_coords = tf.range(width)
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y_coords = tf.range(height)
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x_mesh, y_mesh = tf.meshgrid(x_coords, y_coords)
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ones_mesh = tf.cast(tf.ones([height, width]), tf.int32)
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stacked = tf.stack([x_mesh, y_mesh, ones_mesh], axis=2)
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return tf.cast(tf.repeat(tf.expand_dims(stacked, axis=0), batch, axis=0), dtype=tf.float32)
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def projective_inverse_warp(source_img, depth, pose, intrinsics, coordinates):
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"""
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Calculate the reprojected image from the source to the target, based on the given depth, pose and intrinsics
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SFM Learner inverse warp step
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ps ~ K.T(t->s).Dt(pt)*K^-1.pt
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Note that the depth pixel Dt(pt) is multiplied by every coordinate value (just element-wise, not matrix multiplication)
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Idea is to map the pixel coordinates of the target image to 3d space (Dt(pt).K^-1.pt), then map these onto
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the source image in pixel coordinates (K.T(t->s).{3d coord}), then using the projected coordinates we sample
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the pixels in the source image (ps) to reconstruct the target image.
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:param source_img: Tensor (batch, height, width, 3)
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:param depth: Tensor, (batch, height, width)
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:param pose: (batch, 6)
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:param intrinsics: (batch, 3, 3) TODO: Intrinsics per image (per source/target image)?
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:param coordinates: (batch, 3, height * width) - coordinates for the image. Pass this in so it doesn't need to be
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calculated on every warp step
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:return: The source image reprojected to the target
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"""
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# Convert pose vector (output of pose net) to pose matrix (4x4)
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pose_3x4 = pose_vec2mat(pose)
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# Convert intrinsics matrix (3x3) to (4x4) so it can be multiplied by the pose net
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# intrinsics_4x4 =
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# Calculate inverse of the 4x4 intrinsics matrix
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intrinsics_inverse = tf.linalg.inv(intrinsics)
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depth_flat = tf.reshape(depth, [depth.shape[0], depth.shape[1] * depth.shape[2]])
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# Do the function
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sample_coordinates = tf.matmul(tf.matmul(intrinsics, pose_3x4),
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tf.concat([depth_flat * tf.matmul(intrinsics_inverse, coordinates),
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tf.ones([depth_flat.shape[0], 1, depth_flat.shape[1]])], axis=1))
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# Normalise the x/y axes (divide by z axis)
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sample_coordinates = sample_coordinates[:, 0:2] / sample_coordinates[:, 2]
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# Reshape back to image coordinates
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sample_coordinates = tf.reshape(tf.transpose(sample_coordinates, [0, 2, 1]),
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[depth.shape[0], depth.shape[1], depth.shape[2], 2])
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# sample from the source image using the coordinates applied by the function
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return bilinear_sampler(source_img, sample_coordinates)
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def bilinear_sampler(imgs, coords):
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"""Construct a new image by bilinear sampling from the input image.
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Points falling outside the source image boundary have value 0.
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Args:
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imgs: source image to be sampled from [batch, height_s, width_s, channels]
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coords: coordinates of source pixels to sample from [batch, height_t,
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width_t, 2]. height_t/width_t correspond to the dimensions of the output
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image (don't need to be the same as height_s/width_s). The two channels
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correspond to x and y coordinates respectively.
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Returns:
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A new sampled image [batch, height_t, width_t, channels]
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"""
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def _repeat(x, n_repeats):
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rep = tf.transpose(
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tf.expand_dims(tf.ones(shape=tf.stack([
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n_repeats,
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])), 1), [1, 0])
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rep = tf.cast(rep, 'float32')
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x = tf.matmul(tf.reshape(x, (-1, 1)), rep)
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return tf.reshape(x, [-1])
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coords_x, coords_y = tf.split(coords, [1, 1], axis=3)
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inp_size = imgs.get_shape()
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coord_size = coords.get_shape()
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out_size = coords.get_shape().as_list()
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out_size[3] = imgs.get_shape().as_list()[3]
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coords_x = tf.cast(coords_x, 'float32')
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coords_y = tf.cast(coords_y, 'float32')
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x0 = tf.floor(coords_x)
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x1 = x0 + 1
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y0 = tf.floor(coords_y)
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y1 = y0 + 1
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y_max = tf.cast(tf.shape(imgs)[1] - 1, 'float32')
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x_max = tf.cast(tf.shape(imgs)[2] - 1, 'float32')
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zero = tf.zeros([1], dtype='float32')
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x0_safe = tf.clip_by_value(x0, zero, x_max)
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y0_safe = tf.clip_by_value(y0, zero, y_max)
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x1_safe = tf.clip_by_value(x1, zero, x_max)
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y1_safe = tf.clip_by_value(y1, zero, y_max)
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# bilinear interp weights, with points outside the grid having weight 0
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# wt_x0 = (x1 - coords_x) * tf.cast(tf.equal(x0, x0_safe), 'float32')
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# wt_x1 = (coords_x - x0) * tf.cast(tf.equal(x1, x1_safe), 'float32')
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# wt_y0 = (y1 - coords_y) * tf.cast(tf.equal(y0, y0_safe), 'float32')
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# wt_y1 = (coords_y - y0) * tf.cast(tf.equal(y1, y1_safe), 'float32')
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wt_x0 = x1_safe - coords_x
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wt_x1 = coords_x - x0_safe
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wt_y0 = y1_safe - coords_y
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wt_y1 = coords_y - y0_safe
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# indices in the flat image to sample from
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dim2 = tf.cast(inp_size[2], 'float32')
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dim1 = tf.cast(inp_size[2] * inp_size[1], 'float32')
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base = tf.reshape(
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_repeat(
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tf.cast(tf.range(coord_size[0]), 'float32') * dim1,
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coord_size[1] * coord_size[2]),
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[out_size[0], out_size[1], out_size[2], 1])
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base_y0 = base + y0_safe * dim2
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base_y1 = base + y1_safe * dim2
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idx00 = tf.reshape(x0_safe + base_y0, [-1])
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idx01 = x0_safe + base_y1
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idx10 = x1_safe + base_y0
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idx11 = x1_safe + base_y1
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# sample from imgs
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imgs_flat = tf.reshape(imgs, tf.stack([-1, inp_size[3]]))
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imgs_flat = tf.cast(imgs_flat, 'float32')
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im00 = tf.reshape(
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tf.gather(imgs_flat, tf.cast(idx00, 'int32')), out_size)
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im01 = tf.reshape(
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tf.gather(imgs_flat, tf.cast(idx01, 'int32')), out_size)
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im10 = tf.reshape(
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tf.gather(imgs_flat, tf.cast(idx10, 'int32')), out_size)
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im11 = tf.reshape(
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tf.gather(imgs_flat, tf.cast(idx11, 'int32')), out_size)
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w00 = wt_x0 * wt_y0
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w01 = wt_x0 * wt_y1
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w10 = wt_x1 * wt_y0
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w11 = wt_x1 * wt_y1
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output = tf.add_n([
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w00 * im00, w01 * im01,
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w10 * im10, w11 * im11
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])
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return output
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