def compute_IPM(pts_pix, pts_world):
""" Computes the homography that maps four points in pixel coords
to four points in world coords.
This is known as the 'Inverse Perspective Map' (IPM), as it can
be used to undo perspective effects in an image if you can
identify four points in the image that correspond to a rectangle
with known metric lengths.
Note: for pts_world, you don't have to input exactly the metrix
lengths: instead, you should scale the dimensions to achieve
an output image of desired size. For instance, if you input:
# A rectangle that is (1.2 meters x 1.4 meters):
pts_world = [[0.0, 1.2],
[1.4, 0.0],
[0.0, 1.2],
[1.4, 1.2]]
You'll get an output image where the selected region is of
size (1.2 x 1.4) pixels, which is probably not what you
wanted! Instead, you can scale the dimensions:
pts_world *= 100 # Now, region is (120 x 140) pix!
Input:
nparray pts_pix: N x 2
nparray pts_world: N x 2
Output:
(nparray IPM0, nparray IPM1)
Here, IPM0 is the computed that results in the pts_pix as the new
image origin. This will result in the rest of the image being
omitted. If you wish to apply the IPM such that the entire image
is displayed, use IPM1.
"""
pts_pix = pts_pix.copy().astype('float32')
pts_world = pts_world.copy().astype('float32')
IPM0 = cv2.getPerspectiveTransform(pts_pix, pts_world)
# Determine where (0,0) lands in IPM0's image, and do an offset
# to ensure that the entire image is displayed with IPM1
origin_new = homo2pt(np.dot(IPM0, pt2homo([0.0, 0.0])))
if origin_new[0] < 0:
pts_world[:, 0] += abs(origin_new[0])
if origin_new[1] < 0:
pts_world[:, 1] += abs(origin_new[1])
IPM1 = cv2.getPerspectiveTransform(pts_pix, pts_world)
return IPM0, IPM1
def compute_IPM(pts_pix, pts_world):
""" Computes the homography that maps four points in pixel coords
to four points in world coords.
This is known as the 'Inverse Perspective Map' (IPM), as it can
be used to undo perspective effects in an image if you can
identify four points in the image that correspond to a rectangle
with known metric lengths.
Note: for pts_world, you don't have to input exactly the metrix
lengths: instead, you should scale the dimensions to achieve
an output image of desired size. For instance, if you input:
# A rectangle that is (1.2 meters x 1.4 meters):
pts_world = [[0.0, 1.2],
[1.4, 0.0],
[0.0, 1.2],
[1.4, 1.2]]
You'll get an output image where the selected region is of
size (1.2 x 1.4) pixels, which is probably not what you
wanted! Instead, you can scale the dimensions:
pts_world *= 100 # Now, region is (120 x 140) pix!
Input:
nparray pts_pix: N x 2
nparray pts_world: N x 2
Output:
(nparray IPM0, nparray IPM1)
Here, IPM0 is the computed that results in the pts_pix as the new
image origin. This will result in the rest of the image being
omitted. If you wish to apply the IPM such that the entire image
is displayed, use IPM1.
"""
pts_pix = pts_pix.copy().astype('float32')
pts_world = pts_world.copy().astype('float32')
IPM0 = cv2.getPerspectiveTransform(pts_pix, pts_world)
# Determine where (0,0) lands in IPM0's image, and do an offset
# to ensure that the entire image is displayed with IPM1
origin_new = homo2pt(np.dot(IPM0, pt2homo([0.0, 0.0])))
if origin_new[0] < 0:
pts_world[:, 0] += abs(origin_new[0])
if origin_new[1] < 0:
pts_world[:, 1] += abs(origin_new[1])
IPM1 = cv2.getPerspectiveTransform(pts_pix, pts_world)
return IPM0, IPM1
def test_koopa_singleimage(SHOW_EPIPOLAR=False):
""" Here, I want to do "undo" the perspective distortion in the
image, based on the fact that I know:
- The camera matrix K
- The scene is planar
- The location of four points in the image that create a
rectangle in the world plane with known metric lengths
Note: I don't have to necessarily know the metric lengths,
but at least I need to know length ratios to construct
a corrected image with length ratios preserved.
In the literature, this is also known as: perspective rectification,
perspective correction.
"""
imgpath = os.path.join(IMGSDIR_KOOPA_MED, 'DSCN0643.png')
pts1 = np.array([
[373.0, 97.0], # A (upper-left red corner)
[650.0, 95.0], # B (upper-right red corner)
[674.0, 215.0], # C (lower-right red corner)
[503.0, 322.0], # D (lower-left green corner)
[494.0, 322.0], # E (lower-right blue corner)
[303.0, 321.0], # F (lower-left blue corner)
[332.0, 225.0], # G (upper-left blue corner)
[335.0, 215.0], # H (lower-left red corner)
[475.0, 135.0], # K (tip of pen)
[507.0, 225.0], # L (upper-left green corner)
[362.0, 248.0], # M (tip of glue bottle)
])
worldpts = get_worldplane_coords()
assert len(pts1) == len(worldpts)
calib_imgpaths = util.get_imgpaths(IMGSDIR_CALIB_MED)
print "(Calibrating camera...)"
if True:
print "(Using pre-computed camera matrix K!)"
K = np.array([[158.23796519, 0.0, 482.07814366],
[0., 28.53758493, 333.32239125], [0., 0., 1.]])
else:
K = calibrate_camera.calibrate_camera(calib_imgpaths, 9, 6, 0.023)
print "Finished calibrating camera, K is:"
print K
Kinv = np.linalg.inv(K)
pts1_norm = normalize_coords(pts1, K)
HL = estimate_planar_homography(pts1_norm, worldpts)
print "Estimated homography, H is:"
print HL
print "rank(H):", np.linalg.matrix_rank(HL)
if np.linalg.matrix_rank(HL) != 3:
print " Oh no! H is not full rank!"
#### Normalize H := H / sigma_2(H_)
U, S, V = np.linalg.svd(HL)
H = HL / S[1]
#### Enforce positive depth constraint
flag_flipped = False
for i, pt1 in enumerate(pts1_norm):
pt2 = worldpts[i]
val = np.dot(np.hstack((pt2, [1.0])), np.dot(H, np.hstack(
(pt1, [1.0]))))
if val < 0:
if flag_flipped:
print "WOAH, flipping twice?!"
pdb.set_trace()
print "FLIP IT! val_{0} was: {1}".format(i, val)
H = H * -1
flag_flipped = True
# (Sanity check positive depth constraint)
for i, pt1 in enumerate(pts1_norm):
pt2 = worldpts[i]
val = np.dot(np.hstack((pt2, [1.0])), np.dot(H, np.hstack(
(pt1, [1.0]))))
if val < 0:
print "WOAH, positive depth constraint violated!?"
pdb.set_trace()
#### Check projection error from I1 -> I2.
errs = []
for i, pt1 in enumerate(pts1_norm):
pt1_h = np.hstack((pt1, np.array([1.0])))
pt2_h = np.hstack((worldpts[i], np.array([1.0])))
pt2_pred = np.dot(H, pt1_h)
pt2_pred = pt2_pred / pt2_pred[2]
errs.append(np.linalg.norm(pt2_h - pt2_pred))
print "Projection error: {0} (Mean: {1} std: {2})".format(
sum(errs), np.mean(errs), np.std(errs))
#### Check if planar epipolar constraint is satisfied:
#### x2_hat * H * x1 = 0.0
errs = []
for i, pt1 in enumerate(pts1_norm):
pt1_h = np.hstack((pt1, [1.0]))
pt2_hat = util_camera.make_crossprod_mat(worldpts[i])
errs.append(np.linalg.norm(np.dot(pt2_hat, np.dot(H, pt1_h))))
print "Epipolar constraint error: {0} (Mean: {1} std: {2})".format(
sum(errs), np.mean(errs), np.std(errs))
#### Sanity-check that world points project to pixel points
Hinv = np.linalg.inv(H)
errs = []
for i, worldpt in enumerate(worldpts):
pt_img = np.hstack((pts1[i], [1.0]))
p = np.dot(Hinv, np.hstack((worldpt, [1.0])))
p /= p[2]
p = np.dot(K, p)
errs.append(np.linalg.norm(pt_img - p))
print "world2img errors (in pixels): {0} (mean={1} std={2})".format(
sum(errs), np.mean(errs), np.std(errs))
#### Perform Inverse Perspective Mapping (undo perspective effects)
## Pixel coordinates of a region of the image known to:
## a.) Lie on the plane
## b.) Has known metric lengths
Hinv = np.linalg.inv(H)
# Define hardcoded pixel/world coordinates on the poster plane
# TODO: We could try generalizing this to new images by:
# a.) Asking the user to choose four image points, and enter
# in metric length information (simplest)
# b.) Automatically detect four corner points that correspond
# to a world rectangle (somehow). If there are no
# reference lengths, then I believe the best thing we can
# do is do a perspective-correction up to an affine
# transformation (since we don't know the correct X/Y
# lengths).
pts_pix = np.array(
[
[372.0, 97.0], # Upperleft of redbox (x,y)
[651.0, 95.0], # Upperright of redbox (x,y)
[303.0, 321.0], # Lowerleft of bluebox (x,y)
[695.0, 324.0]
], # Lowerright of greenbox (x,y)
)
pts_world = np.zeros([0, 2])
# Populate pts_world via H (maps image plane -> world plane)
for pt_pix in pts_pix:
pt_world = homo2pt(np.dot(H, np.dot(Kinv, pt2homo(pt_pix))))
pts_world = np.vstack((pts_world, pt_world))
pts_world *= 1000.0 # Let's get a reasonable-sized image please!
# These are hardcoded world coords, but, we can auto-gen them via
# H, Kinv as above. Isn't geometry nice?
#pts_world = np.array([[0.0, 0.0],
# [175.0, 0.0],
# [0.0, 134.0],
# [175.0, 134.0]])
IPM0, IPM1 = compute_IPM(pts_pix, pts_world)
print 'IPM0 is:'
print IPM0
print 'IPM1 is:'
print IPM1
I = cv2.imread(imgpath, cv.CV_LOAD_IMAGE_COLOR).astype('float64')
I = (2.0 * I) + 40 # Up that contrast! Orig. images are super dark.
h, w = I.shape[0:2]
# Determine bounding box of IPM-corrected image
a = homo2pt(np.dot(IPM1, pt2homo([0.0, 0.0]))) # upper-left corner
b = homo2pt(np.dot(IPM1, pt2homo([w - 1, 0.0]))) # upper-right corner
c = homo2pt(np.dot(IPM1, pt2homo([0.0, h - 1]))) # lower-left corner
d = homo2pt(np.dot(IPM1, pt2homo([w - 1, h - 1]))) # lower-right corner
w_out = intrnd(max(b[0] - a[0], d[0] - c[0]))
h_out = intrnd(max(c[1] - a[1], d[1] - b[1]))
print "New image dimensions: ({0} x {1}) (Orig: {2} x {3})".format(
w_out, h_out, w, h)
# Warp the entire image I with the homography IPM1
Iwarp = cv2.warpPerspective(I, IPM1, (w_out, h_out))
# Draw selected points on I
for pt in pts_pix:
cv2.circle(I, tupint(pt), 5, (0, 255, 0))
# Draw rectified-rectangle in Iwarp
a = homo2pt(np.dot(IPM1, pt2homo(pts_pix[0])))
b = homo2pt(np.dot(IPM1, pt2homo(pts_pix[3])))
cv2.rectangle(Iwarp, tupint(a), tupint(b), (0, 255, 0))
#Iwarp = transform_image.transform_image_forward(I, IPM)
print "(Displaying before/after images, press <any key> to exit.)"
cv2.namedWindow('original')
cv2.imshow('original', I.astype('uint8'))
cv2.namedWindow('corrected')
cv2.imshow('corrected', Iwarp.astype('uint8'))
cv2.waitKey(0)
def test_koopa_singleimage(SHOW_EPIPOLAR=False):
""" Here, I want to do "undo" the perspective distortion in the
image, based on the fact that I know:
- The camera matrix K
- The scene is planar
- The location of four points in the image that create a
rectangle in the world plane with known metric lengths
Note: I don't have to necessarily know the metric lengths,
but at least I need to know length ratios to construct
a corrected image with length ratios preserved.
In the literature, this is also known as: perspective rectification,
perspective correction.
"""
imgpath = os.path.join(IMGSDIR_KOOPA_MED, 'DSCN0643.png')
pts1 = np.array([[373.0, 97.0], # A (upper-left red corner)
[650.0, 95.0], # B (upper-right red corner)
[674.0, 215.0], # C (lower-right red corner)
[503.0, 322.0], # D (lower-left green corner)
[494.0, 322.0], # E (lower-right blue corner)
[303.0, 321.0], # F (lower-left blue corner)
[332.0, 225.0], # G (upper-left blue corner)
[335.0, 215.0], # H (lower-left red corner)
[475.0, 135.0], # K (tip of pen)
[507.0, 225.0], # L (upper-left green corner)
[362.0, 248.0], # M (tip of glue bottle)
])
worldpts = get_worldplane_coords()
assert len(pts1) == len(worldpts)
calib_imgpaths = util.get_imgpaths(IMGSDIR_CALIB_MED)
print "(Calibrating camera...)"
if True:
print "(Using pre-computed camera matrix K!)"
K = np.array([[ 158.23796519, 0.0, 482.07814366],
[ 0., 28.53758493, 333.32239125],
[ 0., 0., 1. ]])
else:
K = calibrate_camera.calibrate_camera(calib_imgpaths, 9, 6, 0.023)
print "Finished calibrating camera, K is:"
print K
Kinv = np.linalg.inv(K)
pts1_norm = normalize_coords(pts1, K)
HL = estimate_planar_homography(pts1_norm, worldpts)
print "Estimated homography, H is:"
print HL
print "rank(H):", np.linalg.matrix_rank(HL)
if np.linalg.matrix_rank(HL) != 3:
print " Oh no! H is not full rank!"
#### Normalize H := H / sigma_2(H_)
U, S, V = np.linalg.svd(HL)
H = HL / S[1]
#### Enforce positive depth constraint
flag_flipped = False
for i, pt1 in enumerate(pts1_norm):
pt2 = worldpts[i]
val = np.dot(np.hstack((pt2, [1.0])), np.dot(H, np.hstack((pt1, [1.0]))))
if val < 0:
if flag_flipped:
print "WOAH, flipping twice?!"
pdb.set_trace()
print "FLIP IT! val_{0} was: {1}".format(i, val)
H = H * -1
flag_flipped = True
# (Sanity check positive depth constraint)
for i, pt1 in enumerate(pts1_norm):
pt2 = worldpts[i]
val = np.dot(np.hstack((pt2, [1.0])), np.dot(H, np.hstack((pt1, [1.0]))))
if val < 0:
print "WOAH, positive depth constraint violated!?"
pdb.set_trace()
#### Check projection error from I1 -> I2.
errs = []
for i, pt1 in enumerate(pts1_norm):
pt1_h = np.hstack((pt1, np.array([1.0])))
pt2_h = np.hstack((worldpts[i], np.array([1.0])))
pt2_pred = np.dot(H, pt1_h)
pt2_pred = pt2_pred / pt2_pred[2]
errs.append(np.linalg.norm(pt2_h - pt2_pred))
print "Projection error: {0} (Mean: {1} std: {2})".format(sum(errs), np.mean(errs), np.std(errs))
#### Check if planar epipolar constraint is satisfied:
#### x2_hat * H * x1 = 0.0
errs = []
for i, pt1 in enumerate(pts1_norm):
pt1_h = np.hstack((pt1, [1.0]))
pt2_hat = util_camera.make_crossprod_mat(worldpts[i])
errs.append(np.linalg.norm(np.dot(pt2_hat, np.dot(H, pt1_h))))
print "Epipolar constraint error: {0} (Mean: {1} std: {2})".format(sum(errs), np.mean(errs), np.std(errs))
#### Sanity-check that world points project to pixel points
Hinv = np.linalg.inv(H)
errs = []
for i, worldpt in enumerate(worldpts):
pt_img = np.hstack((pts1[i], [1.0]))
p = np.dot(Hinv, np.hstack((worldpt, [1.0])))
p /= p[2]
p = np.dot(K, p)
errs.append(np.linalg.norm(pt_img - p))
print "world2img errors (in pixels): {0} (mean={1} std={2})".format(sum(errs), np.mean(errs), np.std(errs))
#### Perform Inverse Perspective Mapping (undo perspective effects)
## Pixel coordinates of a region of the image known to:
## a.) Lie on the plane
## b.) Has known metric lengths
Hinv = np.linalg.inv(H)
# Define hardcoded pixel/world coordinates on the poster plane
# TODO: We could try generalizing this to new images by:
# a.) Asking the user to choose four image points, and enter
# in metric length information (simplest)
# b.) Automatically detect four corner points that correspond
# to a world rectangle (somehow). If there are no
# reference lengths, then I believe the best thing we can
# do is do a perspective-correction up to an affine
# transformation (since we don't know the correct X/Y
# lengths).
pts_pix = np.array([[372.0, 97.0], # Upperleft of redbox (x,y)
[651.0, 95.0], # Upperright of redbox (x,y)
[303.0, 321.0], # Lowerleft of bluebox (x,y)
[695.0, 324.0]], # Lowerright of greenbox (x,y)
)
pts_world = np.zeros([0, 2])
# Populate pts_world via H (maps image plane -> world plane)
for pt_pix in pts_pix:
pt_world = homo2pt(np.dot(H, np.dot(Kinv, pt2homo(pt_pix))))
pts_world = np.vstack((pts_world, pt_world))
pts_world *= 1000.0 # Let's get a reasonable-sized image please!
# These are hardcoded world coords, but, we can auto-gen them via
# H, Kinv as above. Isn't geometry nice?
#pts_world = np.array([[0.0, 0.0],
# [175.0, 0.0],
# [0.0, 134.0],
# [175.0, 134.0]])
IPM0, IPM1 = compute_IPM(pts_pix, pts_world)
print 'IPM0 is:'
print IPM0
print 'IPM1 is:'
print IPM1
I = cv2.imread(imgpath, cv.CV_LOAD_IMAGE_COLOR).astype('float64')
I = (2.0*I) + 40 # Up that contrast! Orig. images are super dark.
h, w = I.shape[0:2]
# Determine bounding box of IPM-corrected image
a = homo2pt(np.dot(IPM1, pt2homo([0.0, 0.0]))) # upper-left corner
b = homo2pt(np.dot(IPM1, pt2homo([w-1, 0.0]))) # upper-right corner
c = homo2pt(np.dot(IPM1, pt2homo([0.0, h-1]))) # lower-left corner
d = homo2pt(np.dot(IPM1, pt2homo([w-1, h-1]))) # lower-right corner
w_out = intrnd(max(b[0] - a[0], d[0] - c[0]))
h_out = intrnd(max(c[1] - a[1], d[1] - b[1]))
print "New image dimensions: ({0} x {1}) (Orig: {2} x {3})".format(w_out, h_out, w, h)
# Warp the entire image I with the homography IPM1
Iwarp = cv2.warpPerspective(I, IPM1, (w_out, h_out))
# Draw selected points on I
for pt in pts_pix:
cv2.circle(I, tupint(pt), 5, (0, 255, 0))
# Draw rectified-rectangle in Iwarp
a = homo2pt(np.dot(IPM1, pt2homo(pts_pix[0])))
b = homo2pt(np.dot(IPM1, pt2homo(pts_pix[3])))
cv2.rectangle(Iwarp, tupint(a), tupint(b), (0, 255, 0))
#Iwarp = transform_image.transform_image_forward(I, IPM)
print "(Displaying before/after images, press <any key> to exit.)"
cv2.namedWindow('original')
cv2.imshow('original', I.astype('uint8'))
cv2.namedWindow('corrected')
cv2.imshow('corrected', Iwarp.astype('uint8'))
cv2.waitKey(0)
