Reconstruction: Why Undistort Image and Normalize Coordinates?
From the Tutorial: I Don't Understand Why They First Undistort the Images # Undistort the Images Self. Img1 = Cv2. Undistort(Self. Img1, Self. K, Self. D)...
From the Tutorial: I don't understand why they first undistort the images
# undistort the images
self.img1 = cv2.undistort(self.img1, self.K, self.d)
self.img2 = cv2.undistort(self.img2, self.K, self.d)
and: Compute the Essential Matrix
def _find_fundamental_matrix(self):
self.F, self.Fmask = cv2.findFundamentalMat(self.match_pts1,
self.match_pts2,
cv2.FM_RANSAC, 0.1,0.99)
def _find_essential_matrix(self):
self.E = self.K.T.dot(self.F).dot(self.K)
and also Normalize the coordinates:
first_inliers = []
second_inliers = []
for i in range(len(self.Fmask)):
if self.Fmask[i]:
# normalize and homogenize the image coordinates
first_inliers.append(self.K_inv.dot([self.match_pts1[i][0],
self.match_pts1[i][1], 1.0]))
second_inliers.append(self.K_inv.dot([self.match_pts2[i][0],
self.match_pts2[i][1], 1.0]))
Shouldn't it be either or? Or do I have some wrong understanding here? Can please somone help me on that?
2 Answers
The first step, undistort, does a number of things to reverse the typical warping caused by small camera lenses. See the Wikipedia article on distortion (optics) for more background.
The last step, homogenizing the coordinates, is a completely different thing. The Wikipedia article on homogenous coordinates explains it, but the basic idea is that you add in an extra fake axis that lets you do all affine and projective transformations with chained simple matrix multiplication and then just project back to 3D at the end. Normalizing is just a step you do to make that math easier—basically, you want your extra coordinate to start off as 1.0 (multiply by the inverse of the projective norm).
The requirement for normalization is explained at page-107 of Multi-View Geometry (Hartley and Zisserman). The normalization is required in addition to the un-distortion.
If are using raw pixel values in homogeneous coordinates, the Z-coordinate which is 1 will be small compared to the X and Y co-coordinates. Eg: (X=320, Y=220, Z=1).
But if the homogenized coordinates are the image pixel positions normalized to a standard range, ie -1.0 to 1.0, then we are talking about coordinate values all of whom are kind of in the same range , Eg: (0.75, -0.89, 1.0).
If the image coordinates are of dramatically different ranges(as in the unnormalized case), then the DLT matrix produced will have a bad condition number, and consequently small variations in input image pixel positions, could produce wide variations in the result.
Please see page 107 for a very good explanation.
Sarah Jenkins is a veteran tech journalist with over 12 years of experience covering artificial intelligence, mobile innovations, and digital ethics. Her insights have appeared in leading technology publications worldwide.
