initial commit

core/utils/augmentor.py

@@ -0,0 +1,233 @@
+import numpy as np
+import random
+import math
+import cv2
+from PIL import Image
+
+import torch
+import torchvision
+import torch.nn.functional as F
+
+class FlowAugmentor:
+    def __init__(self, crop_size, min_scale=-0.2, max_scale=0.5):
+        self.crop_size = crop_size
+        self.augcolor = torchvision.transforms.ColorJitter(
+            brightness=0.4, 
+            contrast=0.4, 
+            saturation=0.4, 
+            hue=0.5/3.14)
+
+        self.asymmetric_color_aug_prob = 0.2
+        self.spatial_aug_prob = 0.8
+        self.eraser_aug_prob = 0.5
+
+        self.min_scale = min_scale
+        self.max_scale = max_scale
+        self.max_stretch = 0.2
+        self.stretch_prob = 0.8
+        self.margin = 20
+
+    def color_transform(self, img1, img2):
+
+        if np.random.rand() < self.asymmetric_color_aug_prob:
+            img1 = np.array(self.augcolor(Image.fromarray(img1)), dtype=np.uint8)
+            img2 = np.array(self.augcolor(Image.fromarray(img2)), dtype=np.uint8)
+
+        else:
+            image_stack = np.concatenate([img1, img2], axis=0)
+            image_stack = np.array(self.augcolor(Image.fromarray(image_stack)), dtype=np.uint8)
+            img1, img2 = np.split(image_stack, 2, axis=0)
+
+        return img1, img2
+
+    def eraser_transform(self, img1, img2, bounds=[50, 100]):
+        ht, wd = img1.shape[:2]
+        if np.random.rand() < self.eraser_aug_prob:
+            mean_color = np.mean(img2.reshape(-1, 3), axis=0)
+            for _ in range(np.random.randint(1, 3)):
+                x0 = np.random.randint(0, wd)
+                y0 = np.random.randint(0, ht)
+                dx = np.random.randint(bounds[0], bounds[1])
+                dy = np.random.randint(bounds[0], bounds[1])
+                img2[y0:y0+dy, x0:x0+dx, :] = mean_color
+
+        return img1, img2
+
+    def spatial_transform(self, img1, img2, flow):
+        # randomly sample scale
+
+        ht, wd = img1.shape[:2]
+        min_scale = np.maximum(
+            (self.crop_size[0] + 1) / float(ht), 
+            (self.crop_size[1] + 1) / float(wd))
+
+        max_scale = self.max_scale
+        min_scale = max(min_scale, self.min_scale)
+        
+        scale = 2 ** np.random.uniform(self.min_scale, self.max_scale)
+        scale_x = scale
+        scale_y = scale
+        if np.random.rand() < self.stretch_prob:
+            scale_x *= 2 ** np.random.uniform(-self.max_stretch, self.max_stretch)
+            scale_y *= 2 ** np.random.uniform(-self.max_stretch, self.max_stretch)
+            
+        scale_x = np.clip(scale_x, min_scale, None)
+        scale_y = np.clip(scale_y, min_scale, None)
+
+        if np.random.rand() < self.spatial_aug_prob:
+            # rescale the images
+            img1 = cv2.resize(img1, None, fx=scale_x, fy=scale_y, interpolation=cv2.INTER_LINEAR)
+            img2 = cv2.resize(img2, None, fx=scale_x, fy=scale_y, interpolation=cv2.INTER_LINEAR)
+            flow = cv2.resize(flow, None, fx=scale_x, fy=scale_y, interpolation=cv2.INTER_LINEAR)
+            flow = flow * [scale_x, scale_y]
+
+        if np.random.rand() < 0.5: # h-flip
+            img1 = img1[:, ::-1]
+            img2 = img2[:, ::-1]
+            flow = flow[:, ::-1] * [-1.0, 1.0]
+
+        if np.random.rand() < 0.1: # v-flip
+            img1 = img1[::-1, :]
+            img2 = img2[::-1, :]
+            flow = flow[::-1, :] * [1.0, -1.0]
+
+        y0 = np.random.randint(-self.margin, img1.shape[0] - self.crop_size[0] + self.margin)
+        x0 = np.random.randint(-self.margin, img1.shape[1] - self.crop_size[1] + self.margin)
+        
+        y0 = np.clip(y0, 0, img1.shape[0] - self.crop_size[0])
+        x0 = np.clip(x0, 0, img1.shape[1] - self.crop_size[1])
+
+        img1 = img1[y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]]
+        img2 = img2[y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]]
+        flow = flow[y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]]
+
+        return img1, img2, flow
+
+    def __call__(self, img1, img2, flow):
+        img1, img2 = self.color_transform(img1, img2)
+        img1, img2 = self.eraser_transform(img1, img2)
+        img1, img2, flow = self.spatial_transform(img1, img2, flow)
+
+        img1 = np.ascontiguousarray(img1)
+        img2 = np.ascontiguousarray(img2)
+        flow = np.ascontiguousarray(flow)
+
+        return img1, img2, flow
+
+
+class FlowAugmentorKITTI:
+    def __init__(self, crop_size, min_scale=-0.2, max_scale=0.5):
+        self.crop_size = crop_size
+        self.augcolor = torchvision.transforms.ColorJitter(
+            brightness=0.3, contrast=0.3, saturation=0.3, hue=0.3/3.14)
+
+        self.max_scale = max_scale
+        self.min_scale = min_scale
+
+        self.spatial_aug_prob = 0.8
+        self.eraser_aug_prob = 0.5
+        
+    def color_transform(self, img1, img2):
+        image_stack = np.concatenate([img1, img2], axis=0)
+        image_stack = np.array(self.augcolor(Image.fromarray(image_stack)), dtype=np.uint8)
+        img1, img2 = np.split(image_stack, 2, axis=0)
+        return img1, img2
+
+    def eraser_transform(self, img1, img2):
+        ht, wd = img1.shape[:2]
+        if np.random.rand() < self.eraser_aug_prob:
+            mean_color = np.mean(img2.reshape(-1, 3), axis=0)
+            for _ in range(np.random.randint(1, 3)):
+                x0 = np.random.randint(0, wd)
+                y0 = np.random.randint(0, ht)
+                dx = np.random.randint(50, 100)
+                dy = np.random.randint(50, 100)
+                img2[y0:y0+dy, x0:x0+dx, :] = mean_color
+
+        return img1, img2
+
+    def resize_sparse_flow_map(self, flow, valid, fx=1.0, fy=1.0):
+        ht, wd = flow.shape[:2]
+        coords = np.meshgrid(np.arange(wd), np.arange(ht))
+        coords = np.stack(coords, axis=-1)
+
+        coords = coords.reshape(-1, 2).astype(np.float32)
+        flow = flow.reshape(-1, 2).astype(np.float32)
+        valid = valid.reshape(-1).astype(np.float32)
+
+        coords0 = coords[valid>=1]
+        flow0 = flow[valid>=1]
+
+        ht1 = int(round(ht * fy))
+        wd1 = int(round(wd * fx))
+
+        coords1 = coords0 * [fx, fy]
+        flow1 = flow0 * [fx, fy]
+
+        xx = np.round(coords1[:,0]).astype(np.int32)
+        yy = np.round(coords1[:,1]).astype(np.int32)
+
+        v = (xx > 0) & (xx < wd1) & (yy > 0) & (yy < ht1)
+        xx = xx[v]
+        yy = yy[v]
+        flow1 = flow1[v]
+
+        flow_img = np.zeros([ht1, wd1, 2], dtype=np.float32)
+        valid_img = np.zeros([ht1, wd1], dtype=np.int32)
+
+        flow_img[yy, xx] = flow1
+        valid_img[yy, xx] = 1
+
+        return flow_img, valid_img
+
+    def spatial_transform(self, img1, img2, flow, valid):
+        # randomly sample scale
+
+        ht, wd = img1.shape[:2]
+        min_scale = np.maximum(
+            (self.crop_size[0] + 1) / float(ht), 
+            (self.crop_size[1] + 1) / float(wd))
+
+        scale = 2 ** np.random.uniform(self.min_scale, self.max_scale)
+        scale_x = np.clip(scale, min_scale, None)
+        scale_y = np.clip(scale, min_scale, None)
+
+        if np.random.rand() < self.spatial_aug_prob:
+            # rescale the images
+            img1 = cv2.resize(img1, None, fx=scale_x, fy=scale_y, interpolation=cv2.INTER_LINEAR)
+            img2 = cv2.resize(img2, None, fx=scale_x, fy=scale_y, interpolation=cv2.INTER_LINEAR)
+            flow, valid = self.resize_sparse_flow_map(flow, valid, fx=scale_x, fy=scale_y)
+
+        if np.random.rand() < 0.5: # h-flip
+            img1 = img1[:, ::-1]
+            img2 = img2[:, ::-1]
+            flow = flow[:, ::-1] * [-1.0, 1.0]
+            valid = valid[:, ::-1]
+
+        margin_y = 20
+        margin_x = 50
+
+        y0 = np.random.randint(0, img1.shape[0] - self.crop_size[0] + margin_y)
+        x0 = np.random.randint(-margin_x, img1.shape[1] - self.crop_size[1] + margin_x)
+
+        y0 = np.clip(y0, 0, img1.shape[0] - self.crop_size[0])
+        x0 = np.clip(x0, 0, img1.shape[1] - self.crop_size[1])
+
+        img1 = img1[y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]]
+        img2 = img2[y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]]
+        flow = flow[y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]]
+        valid = valid[y0:y0+self.crop_size[0], x0:x0+self.crop_size[1]]
+        return img1, img2, flow, valid
+
+
+    def __call__(self, img1, img2, flow, valid):
+        img1, img2 = self.color_transform(img1, img2)
+        img1, img2 = self.eraser_transform(img1, img2)
+        img1, img2, flow, valid = self.spatial_transform(img1, img2, flow, valid)
+
+        img1 = np.ascontiguousarray(img1)
+        img2 = np.ascontiguousarray(img2)
+        flow = np.ascontiguousarray(flow)
+        valid = np.ascontiguousarray(valid)
+
+        return img1, img2, flow, valid

core/utils/flow_viz.py

@@ -0,0 +1,275 @@
+# MIT License
+#
+# Copyright (c) 2018 Tom Runia
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to conditions.
+#
+# Author: Tom Runia
+# Date Created: 2018-08-03
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import numpy as np
+
+
+def make_colorwheel():
+    '''
+    Generates a color wheel for optical flow visualization as presented in:
+        Baker et al. "A Database and Evaluation Methodology for Optical Flow" (ICCV, 2007)
+        URL: http://vision.middlebury.edu/flow/flowEval-iccv07.pdf
+    According to the C++ source code of Daniel Scharstein
+    According to the Matlab source code of Deqing Sun
+    '''
+
+    RY = 15
+    YG = 6
+    GC = 4
+    CB = 11
+    BM = 13
+    MR = 6
+
+    ncols = RY + YG + GC + CB + BM + MR
+    colorwheel = np.zeros((ncols, 3))
+    col = 0
+
+    # RY
+    colorwheel[0:RY, 0] = 255
+    colorwheel[0:RY, 1] = np.floor(255*np.arange(0,RY)/RY)
+    col = col+RY
+    # YG
+    colorwheel[col:col+YG, 0] = 255 - np.floor(255*np.arange(0,YG)/YG)
+    colorwheel[col:col+YG, 1] = 255
+    col = col+YG
+    # GC
+    colorwheel[col:col+GC, 1] = 255
+    colorwheel[col:col+GC, 2] = np.floor(255*np.arange(0,GC)/GC)
+    col = col+GC
+    # CB
+    colorwheel[col:col+CB, 1] = 255 - np.floor(255*np.arange(CB)/CB)
+    colorwheel[col:col+CB, 2] = 255
+    col = col+CB
+    # BM
+    colorwheel[col:col+BM, 2] = 255
+    colorwheel[col:col+BM, 0] = np.floor(255*np.arange(0,BM)/BM)
+    col = col+BM
+    # MR
+    colorwheel[col:col+MR, 2] = 255 - np.floor(255*np.arange(MR)/MR)
+    colorwheel[col:col+MR, 0] = 255
+    return colorwheel
+
+
+def flow_compute_color(u, v, convert_to_bgr=False):
+    '''
+    Applies the flow color wheel to (possibly clipped) flow components u and v.
+    According to the C++ source code of Daniel Scharstein
+    According to the Matlab source code of Deqing Sun
+    :param u: np.ndarray, input horizontal flow
+    :param v: np.ndarray, input vertical flow
+    :param convert_to_bgr: bool, whether to change ordering and output BGR instead of RGB
+    :return:
+    '''
+
+    flow_image = np.zeros((u.shape[0], u.shape[1], 3), np.uint8)
+
+    colorwheel = make_colorwheel()  # shape [55x3]
+    ncols = colorwheel.shape[0]
+
+    rad = np.sqrt(np.square(u) + np.square(v))
+    a = np.arctan2(-v, -u)/np.pi
+
+    fk = (a+1) / 2*(ncols-1) + 1
+    k0 = np.floor(fk).astype(np.int32)
+    k1 = k0 + 1
+    k1[k1 == ncols] = 1
+    f = fk - k0
+
+    for i in range(colorwheel.shape[1]):
+
+        tmp = colorwheel[:,i]
+        col0 = tmp[k0] / 255.0
+        col1 = tmp[k1] / 255.0
+        col = (1-f)*col0 + f*col1
+
+        idx = (rad <= 1)
+        col[idx]  = 1 - rad[idx] * (1-col[idx])
+        col[~idx] = col[~idx] * 0.75   # out of range?
+
+        # Note the 2-i => BGR instead of RGB
+        ch_idx = 2-i if convert_to_bgr else i
+        flow_image[:,:,ch_idx] = np.floor(255 * col)
+
+    return flow_image
+
+
+def flow_to_color(flow_uv, clip_flow=None, convert_to_bgr=False):
+    '''
+    Expects a two dimensional flow image of shape [H,W,2]
+    According to the C++ source code of Daniel Scharstein
+    According to the Matlab source code of Deqing Sun
+    :param flow_uv: np.ndarray of shape [H,W,2]
+    :param clip_flow: float, maximum clipping value for flow
+    :return:
+    '''
+
+    assert flow_uv.ndim == 3, 'input flow must have three dimensions'
+    assert flow_uv.shape[2] == 2, 'input flow must have shape [H,W,2]'
+
+    if clip_flow is not None:
+        flow_uv = np.clip(flow_uv, 0, clip_flow)
+
+    u = flow_uv[:,:,0]
+    v = flow_uv[:,:,1]
+
+    rad = np.sqrt(np.square(u) + np.square(v))
+    rad_max = np.max(rad)
+
+    epsilon = 1e-5
+    u = u / (rad_max + epsilon)
+    v = v / (rad_max + epsilon)
+
+    return flow_compute_color(u, v, convert_to_bgr)
+
+
+
+UNKNOWN_FLOW_THRESH = 1e7
+SMALLFLOW = 0.0
+LARGEFLOW = 1e8
+
+def make_color_wheel():
+    """
+    Generate color wheel according Middlebury color code
+    :return: Color wheel
+    """
+    RY = 15
+    YG = 6
+    GC = 4
+    CB = 11
+    BM = 13
+    MR = 6
+
+    ncols = RY + YG + GC + CB + BM + MR
+
+    colorwheel = np.zeros([ncols, 3])
+
+    col = 0
+
+    # RY
+    colorwheel[0:RY, 0] = 255
+    colorwheel[0:RY, 1] = np.transpose(np.floor(255*np.arange(0, RY) / RY))
+    col += RY
+
+    # YG
+    colorwheel[col:col+YG, 0] = 255 - np.transpose(np.floor(255*np.arange(0, YG) / YG))
+    colorwheel[col:col+YG, 1] = 255
+    col += YG
+
+    # GC
+    colorwheel[col:col+GC, 1] = 255
+    colorwheel[col:col+GC, 2] = np.transpose(np.floor(255*np.arange(0, GC) / GC))
+    col += GC
+
+    # CB
+    colorwheel[col:col+CB, 1] = 255 - np.transpose(np.floor(255*np.arange(0, CB) / CB))
+    colorwheel[col:col+CB, 2] = 255
+    col += CB
+
+    # BM
+    colorwheel[col:col+BM, 2] = 255
+    colorwheel[col:col+BM, 0] = np.transpose(np.floor(255*np.arange(0, BM) / BM))
+    col += + BM
+
+    # MR
+    colorwheel[col:col+MR, 2] = 255 - np.transpose(np.floor(255 * np.arange(0, MR) / MR))
+    colorwheel[col:col+MR, 0] = 255
+
+    return colorwheel
+
+
+
+def compute_color(u, v):
+    """
+    compute optical flow color map
+    :param u: optical flow horizontal map
+    :param v: optical flow vertical map
+    :return: optical flow in color code
+    """
+    [h, w] = u.shape
+    img = np.zeros([h, w, 3])
+    nanIdx = np.isnan(u) | np.isnan(v)
+    u[nanIdx] = 0
+    v[nanIdx] = 0
+
+    colorwheel = make_color_wheel()
+    ncols = np.size(colorwheel, 0)
+
+    rad = np.sqrt(u**2+v**2)
+
+    a = np.arctan2(-v, -u) / np.pi
+
+    fk = (a+1) / 2 * (ncols - 1) + 1
+
+    k0 = np.floor(fk).astype(int)
+
+    k1 = k0 + 1
+    k1[k1 == ncols+1] = 1
+    f = fk - k0
+
+    for i in range(0, np.size(colorwheel,1)):
+        tmp = colorwheel[:, i]
+        col0 = tmp[k0-1] / 255
+        col1 = tmp[k1-1] / 255
+        col = (1-f) * col0 + f * col1
+
+        idx = rad <= 1
+        col[idx] = 1-rad[idx]*(1-col[idx])
+        notidx = np.logical_not(idx)
+
+        col[notidx] *= 0.75
+        img[:, :, i] = np.uint8(np.floor(255 * col*(1-nanIdx)))
+
+    return img
+
+# from https://github.com/gengshan-y/VCN
+def flow_to_image(flow):
+    """
+    Convert flow into middlebury color code image
+    :param flow: optical flow map
+    :return: optical flow image in middlebury color
+    """
+    u = flow[:, :, 0]
+    v = flow[:, :, 1]
+
+    maxu = -999.
+    maxv = -999.
+    minu = 999.
+    minv = 999.
+
+    idxUnknow = (abs(u) > UNKNOWN_FLOW_THRESH) | (abs(v) > UNKNOWN_FLOW_THRESH)
+    u[idxUnknow] = 0
+    v[idxUnknow] = 0
+
+    maxu = max(maxu, np.max(u))
+    minu = min(minu, np.min(u))
+
+    maxv = max(maxv, np.max(v))
+    minv = min(minv, np.min(v))
+
+    rad = np.sqrt(u ** 2 + v ** 2)
+    maxrad = max(-1, np.max(rad))
+
+    u = u/(maxrad + np.finfo(float).eps)
+    v = v/(maxrad + np.finfo(float).eps)
+
+    img = compute_color(u, v)
+
+    idx = np.repeat(idxUnknow[:, :, np.newaxis], 3, axis=2)
+    img[idx] = 0
+
+    return np.uint8(img)

core/utils/frame_utils.py

@@ -0,0 +1,124 @@
+import numpy as np
+from PIL import Image
+from os.path import *
+import re
+import cv2
+
+TAG_CHAR = np.array([202021.25], np.float32)
+
+def readFlow(fn):
+    """ Read .flo file in Middlebury format"""
+    # Code adapted from:
+    # http://stackoverflow.com/questions/28013200/reading-middlebury-flow-files-with-python-bytes-array-numpy
+
+    # WARNING: this will work on little-endian architectures (eg Intel x86) only!
+    # print 'fn = %s'%(fn)
+    with open(fn, 'rb') as f:
+        magic = np.fromfile(f, np.float32, count=1)
+        if 202021.25 != magic:
+            print('Magic number incorrect. Invalid .flo file')
+            return None
+        else:
+            w = np.fromfile(f, np.int32, count=1)
+            h = np.fromfile(f, np.int32, count=1)
+            # print 'Reading %d x %d flo file\n' % (w, h)
+            data = np.fromfile(f, np.float32, count=2*int(w)*int(h))
+            # Reshape data into 3D array (columns, rows, bands)
+            # The reshape here is for visualization, the original code is (w,h,2)
+            return np.resize(data, (int(h), int(w), 2))
+
+def readPFM(file):
+    file = open(file, 'rb')
+
+    color = None
+    width = None
+    height = None
+    scale = None
+    endian = None
+
+    header = file.readline().rstrip()
+    if header == b'PF':
+        color = True
+    elif header == b'Pf':
+        color = False
+    else:
+        raise Exception('Not a PFM file.')
+
+    dim_match = re.match(rb'^(\d+)\s(\d+)\s$', file.readline())
+    if dim_match:
+        width, height = map(int, dim_match.groups())
+    else:
+        raise Exception('Malformed PFM header.')
+
+    scale = float(file.readline().rstrip())
+    if scale < 0: # little-endian
+        endian = '<'
+        scale = -scale
+    else:
+        endian = '>' # big-endian
+
+    data = np.fromfile(file, endian + 'f')
+    shape = (height, width, 3) if color else (height, width)
+
+    data = np.reshape(data, shape)
+    data = np.flipud(data)
+    return data
+
+def writeFlow(filename,uv,v=None):
+    """ Write optical flow to file.
+    
+    If v is None, uv is assumed to contain both u and v channels,
+    stacked in depth.
+    Original code by Deqing Sun, adapted from Daniel Scharstein.
+    """
+    nBands = 2
+
+    if v is None:
+        assert(uv.ndim == 3)
+        assert(uv.shape[2] == 2)
+        u = uv[:,:,0]
+        v = uv[:,:,1]
+    else:
+        u = uv
+
+    assert(u.shape == v.shape)
+    height,width = u.shape
+    f = open(filename,'wb')
+    # write the header
+    f.write(TAG_CHAR)
+    np.array(width).astype(np.int32).tofile(f)
+    np.array(height).astype(np.int32).tofile(f)
+    # arrange into matrix form
+    tmp = np.zeros((height, width*nBands))
+    tmp[:,np.arange(width)*2] = u
+    tmp[:,np.arange(width)*2 + 1] = v
+    tmp.astype(np.float32).tofile(f)
+    f.close()
+
+
+def readFlowKITTI(filename):
+    flow = cv2.imread(filename, cv2.IMREAD_ANYDEPTH|cv2.IMREAD_COLOR)
+    flow = flow[:,:,::-1].astype(np.float32)
+    flow, valid = flow[:, :, :2], flow[:, :, 2]
+    flow = (flow - 2**15) / 64.0
+    return flow, valid
+
+def writeFlowKITTI(filename, uv):
+    uv = 64.0 * uv + 2**15
+    valid = np.ones([uv.shape[0], uv.shape[1], 1])
+    uv = np.concatenate([uv, valid], axis=-1).astype(np.uint16)
+    cv2.imwrite(filename, uv[..., ::-1])
+    
+
+def read_gen(file_name, pil=False):
+    ext = splitext(file_name)[-1]
+    if ext == '.png' or ext == '.jpeg' or ext == '.ppm' or ext == '.jpg':
+        return Image.open(file_name)
+    elif ext == '.bin' or ext == '.raw':
+        return np.load(file_name)
+    elif ext == '.flo':
+        return readFlow(file_name).astype(np.float32)
+    elif ext == '.pfm':
+        flow = readPFM(file_name).astype(np.float32)
+        return flow[:, :, :-1]
+    return []

core/utils/utils.py

@@ -0,0 +1,62 @@
+import torch
+import torch.nn.functional as F
+import numpy as np
+from scipy import interpolate
+
+
+def bilinear_sampler(img, coords, mode='bilinear', mask=False):
+    """ Wrapper for grid_sample, uses pixel coordinates """
+    H, W = img.shape[-2:]
+    xgrid, ygrid = coords.split([1,1], dim=-1)
+    xgrid = 2*xgrid/(W-1) - 1
+    ygrid = 2*ygrid/(H-1) - 1
+
+    grid = torch.cat([xgrid, ygrid], dim=-1)
+    img = F.grid_sample(img, grid, align_corners=True)
+
+    if mask:
+        mask = (xgrid > -1) & (ygrid > -1) & (xgrid < 1) & (ygrid < 1)
+        return img, mask.float()
+
+    return img
+
+def forward_interpolate(flow):
+    flow = flow.detach().cpu().numpy()
+    dx, dy = flow[0], flow[1]
+
+    ht, wd = dx.shape
+    x0, y0 = np.meshgrid(np.arange(wd), np.arange(ht))
+
+    x1 = x0 + dx
+    y1 = y0 + dy
+    
+    x1 = x1.reshape(-1)
+    y1 = y1.reshape(-1)
+    dx = dx.reshape(-1)
+    dy = dy.reshape(-1)
+
+    valid = (x1 > 0) & (x1 < wd) & (y1 > 0) & (y1 < ht)
+    x1 = x1[valid]
+    y1 = y1[valid]
+    dx = dx[valid]
+    dy = dy[valid]
+
+    flow_x = interpolate.griddata(
+        (x1, y1), dx, (x0, y0), method='nearest')
+
+    flow_y = interpolate.griddata(
+        (x1, y1), dy, (x0, y0), method='nearest')
+
+    flow = np.stack([flow_x, flow_y], axis=0)
+    return torch.from_numpy(flow).float()
+
+
+def coords_grid(batch, ht, wd):
+    coords = torch.meshgrid(torch.arange(ht), torch.arange(wd))
+    coords = torch.stack(coords[::-1], dim=0).float()
+    return coords[None].repeat(batch, 1, 1, 1)
+
+
+def upflow8(flow, mode='bilinear'):
+    new_size = (8 * flow.shape[2], 8 * flow.shape[3])
+    return  8 * F.interpolate(flow, size=new_size, mode=mode, align_corners=True)