Image Processing and Morphing

Vision for GraphicsCSE 590SS, Winter 2001

Richard Szeliski

Image Pyramids

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Image Pyramids

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Pyramid Creation

“Laplacian” Pyramid• Created from Gaussian

pyramid by subtractionLl = Gl – expand(Gl+1)

filter mask

“Gaussian” Pyramid

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Octaves in the Spatial Domain

Bandpass Images

Lowpass Images

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PyramidsAdvantages of pyramids

• Faster than Fourier transform• Avoids “ringing” artifacts

Many applications• small images faster to process• good for multiresolution processing• compression• progressive transmission

Known as “mip-maps” in graphics communityPrecursor to wavelets

• Wavelets also have these advantages

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laplacianlevel

4

laplacianlevel

2

laplacianlevel

0

left pyramid right pyramid blended pyramid

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Pyramid Blending

Image Warping

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Image Warpingimage filtering: change range of image

g(x) = h(f(x))

image warping: change domain of imageg(x) = f(h(x))

f

x

hf

x

f

x

hf

x

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Image Warpingimage filtering: change range of image

g(x) = h(f(x))

image warping: change domain of imageg(x) = f(h(x))

h

h

f

f g

g

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Parametric (global) warping

Examples of parametric warps:

translation rotation aspect

affineperspective

cylindrical

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2D coordinate transformations

translation: x’ = x + t x = (x,y)rotation: x’ = R x + tsimilarity: x’ = s R x + taffine: x’ = A x + tperspective: x’ H x x = (x,y,1)

(x is a homogeneous coordinate)

These all form a nested group (closed w/ inv.)

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Image Warping

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))?

f(x) g(x’)x x’

h(x)

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Forward Warping

Send each pixel f(x) to its corresponding location x’ = h(x) in g(x’)

f(x) g(x’)x x’

h(x)

• What if pixel lands “between” two pixels?

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Forward Warping

Send each pixel f(x) to its corresponding location x’ = h(x) in g(x’)

f(x) g(x’)x x’

h(x)

• What if pixel lands “between” two pixels?• Answer: add “contribution” to several pixels,

normalize later (splatting)

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Inverse Warping

Get each pixel g(x’) from its corresponding location x = h-1(x’) in f(x)

f(x) g(x’)x x’

h-1(x’)

• What if pixel comes from “between” two pixels?

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Inverse Warping

Get each pixel g(x’) from its corresponding location x = h-1(x’) in f(x)

• What if pixel comes from “between” two pixels?• Answer: resample color value from

interpolated (prefiltered) source image

f(x) g(x’)x x’

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Interpolation

Possible interpolation filters:• nearest neighbor• bilinear• bicubic (interpolating)• sinc / FIR

Needed to prevent “jaggies” and “texture crawl” (see demo)

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Prefiltering

Essential for downsampling (decimation) to prevent aliasing

MIP-mapping [Williams’83]:1. build pyramid (but what decimation filter?):

– block averaging– Burt & Adelson (5-tap binomial)– 7-tap wavelet-based filter (better)

2. trilinear interpolation– bilinear within each 2 adjacent levels– linear blend between levels (determined by pixel size)

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Prefiltering

Essential for downsampling (decimation) to prevent aliasing

Other possibilities:• summed area tables• elliptically weighted Gaussians (EWA)

[Heckbert’86]

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Image Warping – non-parametric

Specify more detailed warp function

Examples: • splines• triangles• optical flow (per-pixel motion)

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Image Warping – non-parametric

Move control points to specify spline warp

Image Morphing

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Image Morphing

How can we in-between two images?1. Cross-dissolve

(all examples from [Gomes et al.’99])

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Image Morphing

How can we in-between two images?2. Warp then cross-dissolve = morph

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Warp specification

How can we specify the warp?1. Specify corresponding points

• interpolate to a complete warping function

• Nielson, Scattered Data Modeling, IEEE CG&A’93]

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Warp specification

How can we specify the warp?2. Specify corresponding vectors

• interpolate to a complete warping function

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Warp specification

How can we specify the warp?2. Specify corresponding vectors

• interpolate [Beier & Neely, SIGGRAPH’92]

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Warp specification

How can we specify the warp?3. Specify corresponding spline control points

• interpolate to a complete warping function

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Final Morph Result

Image Mosaics

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Image Mosaics (stitching)

Blend together several overlapping images into one seamless mosaic (composite)

+ + … +=

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Mosaics for Video CodingConvert masked images into a background sprite

for content-based coding

+ + +

=

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f = 180 (pixels)

Cylindrical Panoramas

Map image to cylindrical or spherical coordinates• need known focal length

Image 384x300 f = 380f = 280

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Cylindrical warpingGiven focal length f and image center (xc,yc)

X

YZ

(X,Y,Z)

(sin,h,cos)

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Radial distortion

Correct for “bending” in wide field of view lenses

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Image Stitching

1. Align the images over each other2. Blend the images together (demo)

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Image Stitching Assignment

1. Take pictures on a tripod (or handheld)2. Warp to cylindrical coordinates3. Automatically compute pairwise alignments4. Fix up the end-to-end alignment5. Blend the images together6. Crop the result and import into a viewer

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Image registration (preview)

How do we determine alignment between images?

• One possible answer: block matching (correlation),

i.e., find minimum squared error

2),(

01 ),(),(),( yx

yxIvyuxIvuE

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Image registration (preview)

How do we determine alignment between images?

• Another possible answer: Fourier-domain correlation

[Brown’92] or phase correlation [Kuglin & Hines’75]

• <…discuss Fourier-domain convolution formulas…>

• More on alignment/registration on Wednesday

[Anandan]

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Full-view Panorama

++

++

++

++

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Texture Mapped Model

Image Enhancement

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Image Enhancement

Noise removal:• low-pass filtering

g(x) = h(x) f(x) = ih(-i) f(x+i)

• median filtering• anisotropic diffusion

– iteratively smooth with similar neighbors [Perona & Malik’90]

Sharpening:• “unsharp masking”

– remove a little bit of blurred image from original(darkroom trick)

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Image Enhancement

Super-resolution:• hallucinate more detail from

single low-res image[Freeman & Pasztor,ICCV’99]

– “learn” mapping between levels

• combine several low-res images using known (linear) formation model [Irani’91;Mann’94]

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Image Enhancement

Super-resolution:• [Freeman &

Pasztor,ICCV’99]– mapping between

levels depends on “training data”

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Image Enhancement

Brightness and gamma correction• linearize input brightness

Histogram equalization• balance (“flatten”) distribution

of brightness values

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Image Enhancement

High dynamic range photography[Debevec et al.’97; Mitsunaga & Nayar’99]• combine several different exposures together

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BibliographyL. Williams. Pyramidal parametrics.Computer Graphics, 17(3):1--11, July 1983.

L. G. Brown. A survey of image registration techniques.Computing Surveys, 24(4):325--376, December 1992.

C. D. Kuglin and D. C. Hines. The phase correlation image alignment method.In IEEE 1975 Conference on Cybernetics and Society, pages 163--165, New York, September 1975.

J. Gomes, L. Darsa, B. Costa, and L. Velho. Warping and Morphing of Graphical Objects.

Morgan Kaufmann Publishers, San Francisco Altos, California, 1999.

G. M. Nielson. Scattered data modeling.IEEE Computer Graphics and Applications, 13(1):60--70, January 1993.

T. Beier and S. Neely. Feature-based image metamorphosis.Computer Graphics (SIGGRAPH'92), 26(2):35--42, July 1992.

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BibliographyL. Williams. Performace driven facial animation.Computer Graphics, 24(4):235--242, 1990.

P. Perona and J. Malik. Scale space and edge detection using anisotropic diffusion.IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):629--639, July 1990.

W. T. Freeman and E. C. Pasztor. Learning low-level vision.In Seventh International Conference on Computer Vision (ICCV'99), pages 1182--1189, Kerkyra, Greece, September 1999.

M. Irani and S. Peleg. Improving resolution by image registration.Graphical Models and Image Processing, 53(3):231--239, May 1991.

S. Mann and R. W. Picard. Virtual bellows: Constructing high-quality images from video.

In First IEEE International Conference on Image Processing (ICIP-94), volume I, pages 363--367, Austin, Texas, November 1994.

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BibliographyPaul E. Debevec and Jitendra Malik.Recovering high dynamic range radiance maps from photographs.Proceedings of SIGGRAPH 97, pages 369--378, August 1997.ISBN 0-89791-896-7. Held in Los Angeles, California.

T. Mitsunaga and S. K. Nayar.Radiometric self calibration.In IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'99), volume 1, pages 374--380, Fort Collins, June 1999.