Homographies image mosaics and tracking
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Homographies , Image Mosaics and Tracking. Assignment 1. Homography estimation from corresponding points Homographies describe image transformation of... General scene when camera motion is rotation about camera center Planar surfaces under general camera motion

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Homographies image mosaics and tracking

Homographies,

Image Mosaics and Tracking

Assignment 1


Key parts

  • Homography estimation from corresponding points

    • Homographies describe image transformation of...

      • General scene when camera motion is rotation about camera center

      • Planar surfaces under general camera motion

  • Displaying tracking data on a map

  • Image mosaic / stitch and Texture mapping

    • Bilinear interpolation

    • Image compositing

  • Wii (optional)

Key Parts


Goal image mosaics
Goal: Image Mosaics

  • + + … + =

Goal: Stitch together several images into a seamless composite






Image warping
Image Warping

  • Given a coordinate transform x’ = h(x) and a source image f(x), how do we compute a transformed image g(x’)=f(h(x))?

  • What about holes?

h(x)

x

x’

f(x)

g(x’)


Forward warping
Forward Warping

  • Send each pixel f(x) to its corresponding location x’=h(x) in g(x’)

  • What if pixel lands “between” two pixels?

  • Answer: add “contribution” to several pixels, normalize later (splatting)

h(x)

x

x’

f(x)

g(x’)


Inverse warping
Inverse Warping

  • Get each pixel g(x’) from its corresponding location x’=h(x) in f(x)

  • What if pixel comes from “between” two pixels?

h(x)

x

x’

f(x)

g(x’)


Inverse warping1
Inverse Warping

  • Get each pixel g(x’) from its corresponding location x’=h(x) in f(x)

  • What if pixel comes from “between” two pixels?

  • Answer: resample color value from interpolated (prefiltered) source image

x

x’

f(x)

g(x’)


Interpolation
Interpolation

  • Possible interpolation filters:

    • nearest neighbor

    • bilinear

    • bicubic (interpolating)


Nearest neighbor interpolation nn

Round-off idea: Just use closest integer-valued pixel

Nearest neighbor interpolation (NN)


Nn issues

Problem is that it can cause big aliasing effects

Why? Because the round() function causes discontinuous switches in which pixel is nearest and hence is the color drawn

NN issues


Nn aliasing
NN aliasing

rotate 45±, scale 1.5


Blending

t controls “blend”

of two endpoints

  • From parametric definition of a line segment:

    p(t) = p0 + t(p1 ¡ p0), wheret2[0, 1]

    = p0¡tp0 + tp1

    = (1 ¡ t)p0 + tp1

Blending

from Akenine-Möller & Haines


Bilinear interpolation bli

Vertical blend

Horizontal blend

  • Idea: Blend four pixel values surrounding source, weighted by nearness

  • (see MO chapter 5)

Bilinear Interpolation (BLI)


Bilinear interpolation

Blending eliminates abrupt color changes, reducing aliasing artifacts

Bilinear interpolation

rotate 45±, scale 1.5


Pixel interpolation approaches nn vs bli
Pixel Interpolation approaches: artifactsNN vs. BLI


Pixel interpolation approaches nn vs bli1
Pixel Interpolation approaches: artifactsNN vs. BLI


Image stitching
Image Stitching artifacts


Assembling the panorama
Assembling the panorama artifacts

  • Stitch pairs together, blend, then crop


Image compositing issues

  • With homography computed, how to render combined image? artifacts

  • Simply putting one image on top of the other, even with bilinear interpolation, may result in a “seam” due to different brightness levels

    • Auto-iris can change overall lightness of images

    • Vignetting can make image edges darker

Image Compositing Issues

courtesy of P. Haeberli


Image feathering
Image feathering artifacts

  • Weight each image proportional to its distance from the edge (distance map [Danielsson, CVGIP 1980]

  • 1. Generate weight map for each image

  • 2. Sum up all of the weights and divide by sum:weights sum up to 1: wi’ = wi / ( ∑iwi)


Image feathering1
Image Feathering artifacts


Feathering

+ artifacts

=

1

0

1

0

Feathering


Effect of window size

0 artifacts

1

0

1

Effect of window size

left

right


Effect of window size1

0 artifacts

1

0

1

Effect of window size


Good window size

0 artifacts

1

Good window size

  • “Optimal” window: smooth but not ghosted

    • Doesn’t always work...


Bilinear compositing

  • Idea: Use “hat” function artifactsw indicating weight of contributions of an image to the mosaic

    • w is 1 at source image center, falls linearly to 0 at image boundaries

    • Combination of horizontal and vertical hat functions:

  • Normalize hat weights to get blend factor in overlaping area:

Bilinear Compositing




Mosaics for video coding
Mosaics for Video artifactsCoding????

  • Convert masked images into a background sprite for content-based coding

  • + + +

    =



Recognizing panoramas
Recognizing Panoramas artifacts

[Brown & Lowe, ICCV’03]