[Multiple View Geometry] Single View Metrology

출처 : (4) 3D Computer Vision | Lecture 6 (Part 2): Single view metrology - YouTube

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Objective

• Compute the Homography Matrix which can map the image quadrilateral to a rectangle with the correct aspect ratio.
• Map the Source image to the Target image using the homography matrix.

• Implement Planar Mosaicing: Images acquired by a camera rotating about its center are related by a planar homography.
• For example, we could stitch the below 3 images to make the panoramic view.

All images can be warped into the reference image by computing Homography Matrices.

• In outline, the algorithm is:
  1. Choose one image as a reference.
  2. Compute the homography matrix which maps one of the other images to the reference image.
  3. Wrap the image with this homography (here, Augment the reference image with the non-overlapping part of the wrapped image).
  4. Repeat the last two steps for the remaining images.
• Note that the homography matrix could be only computed in the two images which share the overlapping view.
• Homography(3->5) = Homography(3->4) x Homography(3->5)

 

What does Calibration Give?

• Suppose Points on the ray are written as X = (x, y, z) in the camera Euclidean coordinate frame.
• Then these points map to the point x as below.

• In other words, we can obtain the direction d by given intrinsic parameter K.
• Furthermore, we can obtain the angle between two rays as below.

• In other words, the calibrated camera could be used like a direction sensor like a 2D protractor.

 

The Image of the Absolute Conic

• The absolute conic is defined in the plane of infinity.
• By knowing the intrinsic value,