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Assignment 1

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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

- Homographies describe image transformation of...
- Displaying tracking data on a map
- Image mosaic / stitch and Texture mapping
- Bilinear interpolation
- Image compositing

- Wii (optional)

- + + … +=

Goal: Stitch together several images into a seamless composite

- 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’)

- 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’)

- 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’)

- 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’)

- Possible interpolation filters:
- nearest neighbor
- bilinear
- bicubic (interpolating)

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

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

rotate 45±, scale 1.5

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

from Akenine-Möller & Haines

Vertical blend

Horizontal blend

- Idea: Blend four pixel values surrounding source, weighted by nearness
- (see MO chapter 5)

Blending eliminates abrupt color changes, reducing aliasing artifacts

rotate 45±, scale 1.5

- Stitch pairs together, blend, then crop

- With homography computed, how to render combined image?
- 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

courtesy of P. Haeberli

- 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)

+

=

1

0

1

0

0

1

0

1

left

right

0

1

0

1

0

1

- “Optimal” window: smooth but not ghosted
- Doesn’t always work...

- Idea: Use “hat” function w 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:

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

Demo

[Brown & Lowe, ICCV’03]