Images and Filters CSE 576 Ali Farhadi Many slides from Steve - PowerPoint PPT Presentation

Images and Filters CSE 576 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick

Administrative Stuff • See the setup instructions on the course web page • Setup your environment • Project – Topic – Team up (discussion board) – The project proposal is due on 4/6 • Use the dropbox link on the course webpage to upload • HW1 – Due on 4/8 – Use the dropbox link on the course webpage to upload

What is an image?

P = f ( x , y ) f : R 2 ⇒ R

Image Operations (functions of functions) F( ) =

Image Operations (functions of functions) 0.1 0 0.8 0.9 0.9 0.9 0.2 F( ) = 0.4 0.3 0.6 0 0 0.1 0.5 0.9 0.9 0.2 0.4 0.3 0.6 0 0 0.1 0.9 0.9 0.2 0.4 0.3 0.6 0 0

Image Operations (functions of functions) F( , ) 0.23 =

Local image functions F( ) =

How can I get rid of the noise in this image?

Image filtering 1 1 1 g [ , ] ⋅ ⋅ 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = ∑ h [ m , n ] g [ k , l ] f [ m k , n l ] + + k , l Credit: S. Seitz

Image filtering 1 1 1 g [ , ] ⋅ ⋅ 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 0 0 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = ∑ h [ m , n ] g [ k , l ] f [ m k , n l ] + + k , l Credit: S. Seitz

Image filtering 1 1 1 g [ , ] ⋅ ⋅ 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 0 0 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = ∑ h [ m , n ] g [ k , l ] f [ m k , n l ] + + k , l Credit: S. Seitz

Image filtering 1 1 1 g [ , ] ⋅ ⋅ 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 0 0 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = ∑ h [ m , n ] g [ k , l ] f [ m k , n l ] + + k , l Credit: S. Seitz

Image filtering 1 1 1 g [ , ] ⋅ ⋅ 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = ∑ h [ m , n ] g [ k , l ] f [ m k , n l ] + + k , l Credit: S. Seitz

Image filtering 1 1 1 g [ , ] ⋅ ⋅ 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 ? 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = ∑ h [ m , n ] g [ k , l ] f [ m k , n l ] + + k , l Credit: S. Seitz

Image filtering 1 1 1 g [ , ] ⋅ ⋅ 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 ? 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 50 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = ∑ h [ m , n ] g [ k , l ] f [ m k , n l ] + + k , l Credit: S. Seitz

Image filtering g [ , ] 1 1 1 ⋅ ⋅ 1 1 1 1 1 1 h [.,.] f [.,.] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 30 20 10 0 0 0 90 90 90 90 90 0 0 0 20 40 60 60 60 40 20 0 0 0 90 90 90 90 90 0 0 0 30 60 90 90 90 60 30 0 0 0 90 90 90 90 90 0 0 0 30 50 80 80 90 60 30 0 0 0 90 0 90 90 90 0 0 0 30 50 80 80 90 60 30 0 20 30 50 50 60 40 20 0 0 0 90 90 90 90 90 0 0 10 20 30 30 30 30 20 10 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 10 10 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = ∑ h [ m , n ] g [ k , l ] f [ m k , n l ] + + k , l Credit: S. Seitz

Box Filter g [ , ] ⋅ ⋅ What does it do? • Replaces each pixel with 1 1 1 an average of its neighborhood 1 1 1 1 1 1 • Achieve smoothing effect (remove sharp features) Slide credit: David Lowe (UBC)

Smoothing with box filter

Practice with linear filters 0 0 0 ? 0 1 0 0 0 0 Original Source: D. Lowe

Practice with linear filters 0 0 0 0 1 0 0 0 0 Original Filtered (no change) Source: D. Lowe

Practice with linear filters 0 0 0 ? 0 0 1 0 0 0 Original Source: D. Lowe

Practice with linear filters 0 0 0 0 0 1 0 0 0 Original Shifted left By 1 pixel Source: D. Lowe

Practice with linear filters 0 0 0 1 1 1 - ? 0 2 0 1 1 1 0 0 0 1 1 1 (Note that filter sums to 1) Original Source: D. Lowe

Practice with linear filters 0 0 0 1 1 1 - 0 2 0 1 1 1 0 0 0 1 1 1 Original Sharpening filter - Accentuates differences with local average Source: D. Lowe

Sharpening Source: D. Lowe

Other filters 1 0 -1 2 0 -2 1 0 -1 Sobel Vertical Edge (absolute value)

Other filters 1 2 1 0 0 0 -1 -2 -1 Sobel Horizontal Edge (absolute value)

Basic gradient filters Horizontal Gradient Vertical Gradient -1 0 1 0 0 0 0 or 0 0 0 0 -1 0 1 1 0 -1 0 0 0 0 or -1 0 1

Gaussian filter Compute empirically = * Filter h Input image f Output image g

Gaussian vs. mean filters What does real blur look like?

Important filter: Gaussian • Spatially-weighted average 0.003 0.013 0.022 0.013 0.003 0.013 0.059 0.097 0.059 0.013 0.022 0.097 0.159 0.097 0.022 0.013 0.059 0.097 0.059 0.013 0.003 0.013 0.022 0.013 0.003 5 x 5, σ = 1 Slide credit: Christopher Rasmussen

Smoothing with Gaussian filter

Smoothing with box filter

Gaussian filters • What parameters matter here? • Variance of Gaussian: determines extent of smoothing Source: K. Grauman

Smoothing with a Gaussian Parameter σ is the “scale” / “width” / “spread” of the Gaussian kernel, and controls the amount of smoothing. … Source: K. Grauman

First and second derivatives = *

First and second derivatives What are these good for? Original First Derivative x Second Derivative x, y

Subtracting filters Original Second Derivative Sharpened

Combining filters for some 0 0 0 0 0 = * 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = 0 0 -1 0 0 * 0 -1 4 -1 0 0 0 -1 0 0 0 0 0 0 0 It’s also true:

Combining Gaussian filters = ? * More blur than either individually (but less than )

Images and Filters CSE 576 Ali Farhadi Many slides from Steve - PowerPoint PPT Presentation

Images and Filters CSE 576 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick Administrative Stuff See the setup instructions on the course web page Setup your environment Project Topic Team up (discussion board)

Images and Filters CSE 576 Ali Farhadi Many slides from

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