Transcript
Page 1: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

CS559: Computer Graphics

Lecture 6: Edge Detection, Image Compositing, and WarpingLi Zhang

Spring 2010

Page 2: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Last time: Image Resampling and Painterly Rendering

Page 3: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Last time: Image Resampling and Painterly Rendering

Page 4: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Properties of Kernels

• Filter, Impulse Response, or kernel function, same concept but different names

• Degrees of continuity• Interpolating or no• Ringing or overshooting

Interpolating filter for reconstruction

Page 5: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010
Page 6: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010
Page 7: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Reconstruction filter Examples in 2D

)1()1(],[),(

,

yxmngyxf

myynxx

otherwise 0

1,1 )1()1(),(2

yxyxyxk D

g[n,m] g[n+1,m]

g[n,m+1] g[n+1,m+1]

(x,y)

2D example:

)1(],1[ yxmng yxmng )1(]1,[

yxmng ]1,1[

How to simplify the calculation?

Page 8: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010
Page 9: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Image Downsampling

Throw away every other row and column to create a 1/2 size image

- called image sub-sampling

1/4

1/8

Page 10: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Image sub-sampling

1/4 (2x zoom) 1/8 (4x zoom)

Why does this look so crufty?

1/2

Minimum Sampling requirement is not satisfied – resulting in Aliasing effect

Page 11: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Subsampling with Gaussian pre-filtering

G 1/4 G 1/8Gaussian 1/2

• Solution: filter the image, then subsample

Page 12: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Results in the paper

Original Biggest brush

Medium brush added Finest brush added

Page 13: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Changing Parameters

Page 14: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Changing Parameters

Impressionist, normal painting style Expressionist, elongated stroke

Colorist wash, semitransparent stroke with color jitter Densely-placed circles with random hue and saturation

Page 15: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Another type of painterly rendering• Line Drawing

http://www.cs.rutgers.edu/~decarlo/abstract.html

Page 16: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Another type of painterly rendering• Line Drawing

http://www.cs.rutgers.edu/~decarlo/abstract.html

Page 17: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Another type of painterly rendering• Line Drawing

http://www.cs.rutgers.edu/~decarlo/abstract.html

Page 18: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Another type of painterly rendering• Line Drawing

http://www.cs.rutgers.edu/~decarlo/abstract.html

Page 19: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Edge Detection

• Convert a 2D image into a set of curves– Extracts salient features of the scene

Page 20: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Edge detection• One of the most important uses of image

processing is edge detection:– Really easy for humans– Not that easy for computers

– Fundamental in computer vision– Important in many graphics applications

Page 21: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

What is an edge?

• Q: How might you detect an edge in 1D?

Page 22: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Image gradient• The gradient of an image:

• The gradient direction is given by:

• The gradient points in the direction of most rapid change in intensity

– how does the gradient relate to the direction of the edge?

• The edge strength is given by the gradient magnitude

Page 23: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Gradients• How can we approximate the gradient in a

discrete image?

gx[i,j] = f[i+1,j] – f[i,j] and gy[i,j]=f[i,j+1]-f[i,j]Can write as mask [-1 1] and [1 –1]’

Page 24: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Less than ideal edges

Page 25: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Results of Sobel edge detection

Page 26: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Edge enhancement• A popular gradient magnitude computation is

the Sobel operator:

• We can then compute the magnitude of the vector (sx, sy).

1 0 1

2 0 2

1 0 1

1 2 1

0 0 0

1 2 1

x

y

s

s

Page 27: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Results of Sobel edge detection

Page 28: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Results of Sobel edge detection

Page 29: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Non-maximum Suppression

• Check if pixel is local maximum along gradient direction– requires checking interpolated pixels p and r

The Canny Edge Detector

Page 30: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Steps in edge detection• Edge detection algorithms typically proceed in

three or four steps:– Filtering: cut down on noise– Enhancement: amplify the difference between

edges and non-edges– Detection: use a threshold operation– Localization (optional): estimate geometry of

edges, which generally pass between pixels

Page 31: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

The Canny Edge Detector

original image (Lena)

Page 32: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

The Canny Edge Detector

magnitude of the gradient

Page 33: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

The Canny Edge Detector

After non-maximum suppression

Page 34: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Canny Edge Detector

Canny with Canny with original

• The choice of depends on desired behavior

– large detects large scale edges– small detects fine features

: Gaussian filter parameter

Page 35: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Compositing• Compositing combines components from two or

more images to make a new image– Special effects are easier to control when done in

isolation– Even many all live-action sequences are more safely

shot in different layers

Page 36: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Compositing• Compositing combines components from two or

more images to make a new image– Special effects are easier to control when done in

isolation– Even many all live-action sequences are more safely

shot in different layers

Page 37: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Perfect Storm

Page 38: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Animated Example

over =

Page 39: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Mattes

• A matte is an image that shows which parts of another image are foreground objects

• Term dates from film editing and cartoon production

• How would I use a matte to insert an object into a background?

• How are mattes usually generated for television?

Page 40: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Working with Mattes• To insert an object into a background

– Call the image of the object the source– Put the background into the destination– For all the source pixels, if the matte is white, copy the

pixel, otherwise leave it unchanged

Page 41: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Working with Mattes• To insert an object into a background

– Call the image of the object the source– Put the background into the destination– For all the source pixels, if the matte is white, copy the

pixel, otherwise leave it unchanged• To generate mattes:

– Use smart selection tools in Photoshop or similar• They outline the object and convert the outline to a

matte– Blue Screen: Photograph/film the object in front of a blue

background, then consider all the blue pixels in the image to be the background

Page 42: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Compositing

• Compositing is the term for combining images, one over the other– Used to put special effects into live action

• Or live action into special effects

Page 43: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Alpha• Basic idea: Encode opacity information in the image• Add an extra channel, the alpha channel, to each image

– For each pixel, store R, G, B and Alpha– alpha = 1 implies full opacity at a pixel– alpha = 0 implies completely clear pixels

• Images are now in RGBA format, and typically 32 bits per pixel (8 bits for alpha)

• All images in the project are in this format

Page 44: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Pre-Multiplied Alpha• Instead of storing (R,G,B,), store (R,G,B,)• The compositing operations in the next several

slides are easier with pre-multiplied alpha• To display and do color conversions, must

extract RGB by dividing out – =0 is always black– Some loss of precision as gets small, but generally

not a big problem

Page 45: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Why do we need pre-multiplied alpha?

gffo ccc )1(1

gfff

o

RR

c

)1(

“Over” Operator

1g

g

g

g B

G

R

c

f

f

f

f

f B

G

R

c

Page 46: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Why do we need pre-multiplied alpha?

gffo ccc )1(1

gfff

gfff

gfff

o BB

GG

RR

c)1(

)1(

)1(

“Over” Operator

1g

g

g

g B

G

R

c

f

f

f

f

f B

G

R

c

Page 47: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Why do we need pre-multiplied alpha?

gffo ccc )1(1

1

)1(

)1(

)1(

gfff

gfff

gfff

o BB

GG

RR

c

“Over” Operator

1g

g

g

g B

G

R

c

f

f

f

f

f B

G

R

c

Page 48: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Why do we need pre-multiplied alpha?

gffo ccc )1(1

1

)1(

)1(

)1(

gfff

gfff

gfff

o BB

GG

RR

c

“Over” Operator

g

g

g

g

g B

G

R

c

f

f

f

f

g B

G

R

c

Page 49: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Why do we need pre-multiplied alpha?

gffo ccc )1(1

ggfff

ggfff

ggfff

o BB

GG

RR

c

)1(

)1(

)1(

“Over” Operator

g

g

g

g

g B

G

R

c

f

f

f

f

g B

G

R

c

Page 50: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Why do we need pre-multiplied alpha?

gffo ccc )1(1

gff

ggfff

ggfff

ggfff

o BB

GG

RR

c

)1(

)1(

)1(

)1(

“Over” Operator

g

g

g

g

g B

G

R

c

f

f

f

f

g B

G

R

c

g

gg

gg

gg

f

f

ff

ff

ff

B

G

R

B

G

R

)1(

Page 51: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Basic Compositing Operation• At each pixel, combine the pixel data from f and

the pixel data from g with the equation:

gffo ccc )1(1

],,,[ ffffffff BGRc

],,,[ gggggggg BGRc

“Over” Operator

Page 52: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

• Changing pixel values

• Moving pixels around

Image Manipulation

hf

g

h([x,y])=[x,y/2]

Page 53: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Parametric (global) warping

translation rotation aspect

affineperspective

cylindrical

Examples of parametric warps:

Page 54: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Application of Image Warp

Creating virtual wide-angle camera

Mosaics: stitching images together

Page 55: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Application of Image Warp

Creating realistic surface appearance

Texture mapping

http://www.futuretech.blinkenlights.nl/tex.html

Page 56: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Application of Image Warp• Morphing

morphingimage #1 image #2

Page 57: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Parametric (global) warping

• Transformation T is a coordinate-changing machine: p’ = T(p)

• What does it mean that T is global?– can be described by just a few numbers (parameters)– the parameters are the same for any point p

• Represent T as a matrix: p’ = Mp

T

p = (x,y) p’ = (x’,y’)

y

x

y

xM

'

'

h([x,y])=[x,y/2]

Page 58: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Scaling• Scaling a coordinate means multiplying each of

its components by a scalar• Uniform scaling means this scalar is the same for

all components:

2

f g

y

x

y

x

2

2

'

'

y

x

Page 59: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

• Non-uniform scaling: different scalars per component:

Scaling

x 2,y 0.5

y

x

y

x

5.0

2

'

'

Page 60: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

Scaling

• Scaling operation:

• Or, in matrix form:

byy

axx

'

'

y

x

b

a

y

x

0

0

'

'

scaling matrix S

What’s inverse of S?

b

aS

/10

0/11

Page 61: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

2-D Rotation

(x, y)

(x’, y’)

x’ = x cos() - y sin()y’ = x sin() + y cos()

Page 62: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

2-D Rotation• This is easy to capture in matrix form:

• How can I remember this? • Even though sin() and cos() are nonlinear to ,

– x’ is a linear combination of x and y– y’ is a linear combination of x and y

• What is the inverse transformation?– Rotation by –– For rotation matrices, det(R) = 1

y

x

y

x

cossin

sincos

'

'

TRR 1

R

x’ = x cos() - y sin()y’ = x sin() + y cos()

Page 63: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

2x2 Matrices• What types of transformations can be

represented with a 2x2 matrix?

2D Identity?

yyxx

''

yx

yx

1001

''

2D Scale around (0,0)?

ysy

xsx

y

x

*'

*'

y

x

s

s

y

x

y

x

0

0

'

'

Page 64: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

2x2 Matrices• What types of transformations can be

represented with a 2x2 matrix?

2D Rotate around (0,0)?

yxy

yxx

*cos*sin'

*sin*cos'

y

x

y

x

cossin

sincos

'

'

2D Shear?

yxshy

yshxx

y

x

*'

*'

y

x

sh

sh

y

x

y

x

1

1

'

'

Page 65: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

• What types of transformations can be represented with a 2x2 matrix?

2x2 Matrices

2D Shear?

yxshy

yshxx

y

x

*'

*'

y

x

sh

sh

y

x

y

x

1

1

'

'

(1,1)

1

1

0 x

y

1

1

0 x’

y’

shy

shx

Page 66: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

2x2 Matrices• What types of transformations can be

represented with a 2x2 matrix?

2D Mirror about Y axis?

yyxx

''

yx

yx

1001

''

2D Mirror over (0,0)?

yyxx

''

yx

yx

1001

''

Page 67: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

• Linear transformations are combinations of …– Scale,– Rotation,– Shear, and– Mirror

• Any 2D transform can be decomposed into the product of a rotation, scale, and a rotation

All 2D Linear Transformations

y

x

dc

ba

y

x

'

'

)3.58()618.0,618.1()7.31(10

11

rotatescalerotate

Page 68: CS559: Computer Graphics Lecture 6: Edge Detection, Image Compositing, and Warping Li Zhang Spring 2010

• Linear transformations are combinations of …– Scale,– Rotation,– Shear, and– Mirror

• A symmetric 2D transform can be decomposed into the product of a rotation, scale, and the inverse rotation

All 2D Linear Transformations

y

x

dc

ba

y

x

'

'

)7.31()382.0,618.2()7.31(11

12

rotatescalerotate


Top Related