A different approach to fitting transformations in the presence of outliers is to model the uncertainty as a mixture of two Gaussians. The first Gaussian models the image noise, and the sec- ond Gaussian, which has a very large variance, accounts for the outliers. For example, for the affine transformation we would have Pr ( x | w ) = λ Norm x f aff [ w , Φ , τ ] , σ 2 I + (1 − λ ) Norm x f aff [ w , Φ , τ ] , σ 2 0 I + where λ is the probability of being an inlier, σ 2 is the image noise, and σ 2 is the large variance that accounts for the outliers. Sketch an approach to learning the parameters σ 2 , Φ , τ , and λ of this model. You may assume that σ 2 is fixed. Identify a possible weakness of this model. 0 0

A different approach to fitting transformations in the presence of outliers is to model the uncertainty as a mixture of two Gaussians. The first Gaussian models the image noise, and the sec- ond...

A different approach to fitting transformations in the presence of outliers is to model the uncertainty as a mixture of two Gaussians. The first Gaussian models the image noise, and the sec- ond Gaussian, which has a very large variance, accounts for the outliers. For example, for the affine transformation we would have

^Pr
⁽
^x
^|
^w
⁾

⁼

^λ
^Norm

x

^f
^aff
^[
^w
^,

^Φ
^,

^τ

^]
^,

^σ
²
^I

⁺

⁽¹

⁻

^λ
⁾
^Norm

x

^f
^aff
^[
^w
^,

^Φ
^,

^τ

^]
^,

^σ
²

₀

I

+

where

λ

is the probability of being an inlier,

σ

²

is the image noise, and

σ

²

is the large variance that accounts for the outliers. Sketch an approach to learning the parameters

σ

²

,

Φ

,

τ

, and

λ

of this model. You may assume that

σ

²
is fixed. Identify a possible weakness of this model.

May 12, 2022

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A different approach to fitting transformations in the presence of outliers is to model the uncertainty as a mixture of two Gaussians. The first Gaussian models the image noise, and the sec- ond...

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