BMT at TU München | Flashcards & Summaries

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# Lernmaterialien für BMT an der TU München

Greife auf kostenlose Karteikarten, Zusammenfassungen, Übungsaufgaben und Altklausuren für deinen BMT Kurs an der TU München zu.

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What does it mean that Transformation T is global?

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• Is the same for any point p
• Can be described by just a few numbers (parameters)
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2D Linear Transformations:

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• Identity
• Scaling
• Rotation
• Mirror
• Shear
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Transformations can be combined by ...?

What is important?

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Transformations can be combined by matrix multiplication (matrix composition).

The ordering here is IMPORTANT!

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Forward Warping

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Send each pixel f(x, y) to its corresponding location
(x', y')= T(x, y) in the second image.

And use Splatting to color the pixels

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Problem Forward Warping?

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Destination picture might have holes

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Inverse (Backward) Warping

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Get each pixel g(x', y') from its corresponding location
(x, y)= T^-1(x', y') in the ﬁrst image.

Use Interpolation to color the pixel.

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Pro and Con Inverse Warping

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+ ensures that no holes occur

- requires and invertible warp function

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Non-Parametric (Local) Image Warping

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Image Warping using Vector Fields

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Image Warping using Vector Fields

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• Let (vx, vy)= F(x, y) be an arbitrary vector ﬁeld and I an image.
• Question: How can we compute the value at I(x + vx, y + vy)?
• Answer: Use forward warping to propagate the pixels to a new
location.
• Problem: Same as before, resulting image will contain holes.

-> Solution:

• Answer 2: Use inverse warping with bilinear interpolation.
• Need to invert vector ﬁeld F(x, y)
• Look up source pixels using F(x', y')^-1
• Interpolate using one of the presented models, e.g. bilinear

-> Vector Fields transform each pixel separately

-> Inverse warping is better, but requires invertible vector field

Lösung ausblenden
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Good interpolation techniques attempt to find an optimal balance between three undesirable artifacts:

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edge halos

blurring

aliasing

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Bilinear Interpolation: Pros and Cons

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No jagged artifacts as in Nearest Neighbor

BUT blurry edges

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Transformation T is a coordinate-changing machine:

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p' = T(p) (p = 2D vector)

Lösung ausblenden
• 441980 Karteikarten
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## Beispielhafte Karteikarten für deinen BMT Kurs an der TU München - von Kommilitonen auf StudySmarter erstellt!

Q:

What does it mean that Transformation T is global?

A:
• Is the same for any point p
• Can be described by just a few numbers (parameters)
Q:

2D Linear Transformations:

A:
• Identity
• Scaling
• Rotation
• Mirror
• Shear
Q:

Transformations can be combined by ...?

What is important?

A:

Transformations can be combined by matrix multiplication (matrix composition).

The ordering here is IMPORTANT!

Q:

Forward Warping

A:

Send each pixel f(x, y) to its corresponding location
(x', y')= T(x, y) in the second image.

And use Splatting to color the pixels

Q:

Problem Forward Warping?

A:

Destination picture might have holes

Q:

Inverse (Backward) Warping

A:

Get each pixel g(x', y') from its corresponding location
(x, y)= T^-1(x', y') in the ﬁrst image.

Use Interpolation to color the pixel.

Q:

Pro and Con Inverse Warping

A:

+ ensures that no holes occur

- requires and invertible warp function

Q:

Non-Parametric (Local) Image Warping

A:

Image Warping using Vector Fields

Q:

Image Warping using Vector Fields

A:

• Let (vx, vy)= F(x, y) be an arbitrary vector ﬁeld and I an image.
• Question: How can we compute the value at I(x + vx, y + vy)?
• Answer: Use forward warping to propagate the pixels to a new
location.
• Problem: Same as before, resulting image will contain holes.

-> Solution:

• Answer 2: Use inverse warping with bilinear interpolation.
• Need to invert vector ﬁeld F(x, y)
• Look up source pixels using F(x', y')^-1
• Interpolate using one of the presented models, e.g. bilinear

-> Vector Fields transform each pixel separately

-> Inverse warping is better, but requires invertible vector field

Q:

Good interpolation techniques attempt to find an optimal balance between three undesirable artifacts:

A:

edge halos

blurring

aliasing

Q:

Bilinear Interpolation: Pros and Cons

A:

No jagged artifacts as in Nearest Neighbor

BUT blurry edges

Q:

Transformation T is a coordinate-changing machine:

A:

p' = T(p) (p = 2D vector)

### Erstelle und finde Lernmaterialien auf StudySmarter.

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## Das sind die beliebtesten StudySmarter Kurse für deinen Studiengang BMT an der TU München

Für deinen Studiengang BMT an der TU München gibt es bereits viele Kurse, die von deinen Kommilitonen auf StudySmarter erstellt wurden. Karteikarten, Zusammenfassungen, Altklausuren, Übungsaufgaben und mehr warten auf dich!

## Das sind die beliebtesten BMT Kurse im gesamten StudySmarter Universum

##### BMT 1

Leibniz Universität Hannover