Distorting an image using a height map?

Question

I have a height map for an image, which tells me the offset of each pixel in the Z direction. My goal is to flatten a distorted image using only it's height map.

How would I go about doing this? I know the position of the camera, if that helps.

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To do this, I was thinking about assuming that each pixel was a point on a plane, and then to translate each of those points vertically according to the Z-value I get from the height map, and from that translation (imagine you are looking at the points from above; the shift will cause the point to move around from your perspective).

From that projected shift, I could extract X and Y-shift of each pixel, which I could feed into cv.Remap().

But I have no idea how I could get the projected 3D offset of a point with OpenCV, let alone construct a offset map out of it.

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Here are my reference images for what I'm doing:

I know the angle of the lasers (45 degrees), and from the calibration images, I can calculate the height of the book really easily:

h(x) = sin(theta) * abs(calibration(x) - actual(x))

I do this for both lines and linearly interpolate the two lines to generate a surface using this approach (Python code. It's inside a loop):

height_grid[x][y] = heights_top[x] * (cv.GetSize(image)[1] - y) + heights_bottom[x] * y

I hope this helps ;)

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Right now, this is what I have to dewarp the image. All that strange stuff in the middle projects a 3D coordinate onto the camera plane, given it's position (and the camera's location, rotation, etc.):

class Point:
  def __init__(self, x = 0, y = 0, z = 0):
    self.x = x
    self.y = y
    self.z = z

mapX = cv.CreateMat(cv.GetSize(image)[1], cv.GetSize(image)[0], cv.CV_32FC1)
mapY = cv.CreateMat(cv.GetSize(image)[1], cv.GetSize(image)[0], cv.CV_32FC1)

c = Point(CAMERA_POSITION[0], CAMERA_POSITION[1], CAMERA_POSITION[2])
theta = Point(CAMERA_ROTATION[0], CAMERA_ROTATION[1], CAMERA_ROTATION[2])
d = Point()
e = Point(0, 0, CAMERA_POSITION[2] + SENSOR_OFFSET)

costx = cos(theta.x)
costy = cos(theta.y)
costz = cos(theta.z)

sintx = sin(theta.x)
sinty = sin(theta.y)
sintz = sin(theta.z)


for x in xrange(cv.GetSize(image)[0]):
  for y in xrange(cv.GetSize(image)[1]):
    
    a = Point(x, y, heights_top[x / 2] * (cv.GetSize(image)[1] - y) + heights_bottom[x / 2] * y)
    b = Point()
    
    d.x = costy * (sintz * (a.y - c.y) + costz * (a.x - c.x)) - sinty * (a.z - c.z)
    d.y = sintx * (costy * (a.z - c.z) + sinty * (sintz * (a.y - c.y) + costz * (a.x - c.x))) + costx * (costz * (a.y - c.y) - sintz * (a.x - c.x))
    d.z = costx * (costy * (a.z - c.z) + sinty * (sintz * (a.y - c.y) + costz * (a.x - c.x))) - sintx * (costz * (a.y - c.y) - sintz * (a.x - c.x))
    
    mapX[y, x] = x + (d.x - e.x) * (e.z / d.z)
    mapY[y, x] = y + (d.y - e.y) * (e.z / d.z)
    

print
print 'Remapping original image using map...'

remapped = cv.CreateImage(cv.GetSize(image), 8, 3)
cv.Remap(image, remapped, mapX, mapY, cv.CV_INTER_LINEAR)

This is turning into a huge thread of images and code now... Anyways, this code chunk takes my 7 minutes to run on a 18MP camera image; that's way too long, and in the end, this approach does nothing to the image (the offset for each pixel is << 1).

Any ideas?

Answer 1

I ended up implementing my own solution:

for x in xrange(cv.GetSize(image)[0]):
  for y in xrange(cv.GetSize(image)[1]):

    a = Point(x, y, heights_top[x / 2] * (cv.GetSize(image)[1] - y) + heights_bottom[x / 2] * y)
    b = Point()

    d.x = costy * (sintz * (a.y - c.y) + costz * (a.x - c.x)) - sinty * (a.z - c.z)
    d.y = sintx * (costy * (a.z - c.z) + sinty * (sintz * (a.y - c.y) + costz * (a.x - c.x))) + costx * (costz * (a.y - c.y) - sintz * (a.x - c.x))
    d.z = costx * (costy * (a.z - c.z) + sinty * (sintz * (a.y - c.y) + costz * (a.x - c.x))) - sintx * (costz * (a.y - c.y) - sintz * (a.x - c.x))

    mapX[y, x] = x + 100.0 * (d.x - e.x) * (e.z / d.z)
    mapY[y, x] = y + 100.0 * (d.y - e.y) * (e.z / d.z)


print
print 'Remapping original image using map...'

remapped = cv.CreateImage(cv.GetSize(image), 8, 3)
cv.Remap(image, remapped, mapX, mapY, cv.CV_INTER_LINEAR)

This (slowly) remaps each pixel using the cv.Remap function, and this seems to kind of work...