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How to do it?

  • Basic Procedure

    • Take a sequence of images from the same position

      • Rotate the camera about its optical center

    • Compute transformation between second image and first

  • Transform the second image to overlap with the first

  • Blend the two together to create a mosaic

  • If there are more images, repeat

  • but wait, why should this work at all?

  • What about the 3D geometry of the scene?

  • Why aren’t we using it?

Aligning images: translation

left on top

right on top

Translations are not enough to align the images

Image reprojection

  • Basic question

    • How to relate 2 images from same camera center?

      • how to map a pixel from PP1 to PP2

    • Answer

      • Cast a ray through each pixel in PP1

      • Draw the pixel where that ray intersects PP2

But don’t we need to know the geometry of the two planes in respect to the eye?

PP1

PP2

Observation: Rather than thinking of this as a 3D reprojection, think of it as a 2D image warp from one image to another

real

synthetic

camera

camera

A pencil of rays contains all views

Can generate any synthetic camera view as long as it has the same center of projection!

Image reprojection

mosaic PP

  • The mosaic has a natural interpretation in 3D

    • The images are reprojected onto a common plane

    • The mosaic is formed on this plane

    • Mosaic is a synthetic wide-angle camera

Back to Image Warping

Which t-form is the right one for warping PP1 into PP2? e.g. translation, Euclidean, affine, projective

Translation

Affine

Perspective

2 unknowns

6 unknowns

8 unknowns

2

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