image warping - taudcor/graphics/pdf.slides/... · 2017. 4. 24. · forward mapping -disadvantages....
TRANSCRIPT
![Page 1: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/1.jpg)
ImageWarping
![Page 2: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/2.jpg)
ImageMapping
![Page 3: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/3.jpg)
ImageMapping- Examples
![Page 4: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/4.jpg)
ForwardMapping
![Page 5: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/5.jpg)
ForwardMapping- Disadvantages
![Page 6: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/6.jpg)
Example– ForwardMappingOriginal Rotated
ZoomIn
![Page 7: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/7.jpg)
BackwardMapping
𝑓"#
TheProblem:(u,v)arenotintegers!
![Page 8: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/8.jpg)
![Page 9: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/9.jpg)
![Page 10: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/10.jpg)
NearestNeighbor
![Page 11: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/11.jpg)
![Page 12: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/12.jpg)
Example- NearestNeighborOriginal Rotated
ZoomIn
![Page 13: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/13.jpg)
Bi-linearInterpolation• Bi-linearinterpolatesfourclosestpixels.• Theweightforeachpixelisproportionaltoitsdistancefromthesamplingpoint(x,y)
![Page 14: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/14.jpg)
Bi-linearInterpolation
![Page 15: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/15.jpg)
Bi-linearInterpolation
![Page 16: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/16.jpg)
Bi-linearInterpolation
![Page 17: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/17.jpg)
Bi-linearInterpolation
![Page 18: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/18.jpg)
ExampleBi-linearOriginal Rotated
ZoomIn
![Page 19: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/19.jpg)
Bi-cubic
(u,v)
• Bicubic interpolates16closestneighbors(4x4neighborhood)• Theresultismuchmoresmooth
![Page 20: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/20.jpg)
Bi-cubicInterpolation
![Page 21: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/21.jpg)
Bi-cubicInterpolation
![Page 22: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/22.jpg)
Bi-cubicInterpolation
![Page 23: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/23.jpg)
ExampleBi-cubicOriginal Rotated
ZoomIn
![Page 24: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/24.jpg)
NearestNeighbor
![Page 25: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/25.jpg)
Bi-LinearInterpolation
![Page 26: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/26.jpg)
Bi-CubicInterpolation
![Page 27: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/27.jpg)
ComparisonNearestNeighbor Bi-linear Bi-cubic
![Page 28: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/28.jpg)
DirectRotation
![Page 29: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/29.jpg)
Shear
![Page 30: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/30.jpg)
Shear
![Page 31: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/31.jpg)
ShearandScaleOperatinglinebyline,fasterandsimplerfilters
![Page 32: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/32.jpg)
Shear
÷÷ø
öççè
æ=÷÷
ø
öççè
æyx
Avu
÷÷ø
öççè
æ=÷÷
ø
öççè
æ÷÷ø
öççè
æ=÷÷
ø
öççè
æ=÷÷
ø
öççè
æyx
Tyx
ABvu
Bsr
÷÷ø
öççè
æ+
=÷÷ø
öççè
æ=÷÷
ø
öççè
æaaaa
cosysinx siny -cosx
yx
Tsr
![Page 33: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/33.jpg)
Shear
÷÷ø
öççè
æ=÷÷
ø
öççè
æ=÷÷
ø
öççè
æy)f(x,x
yx
Avu
Apreservecolumns
÷÷ø
öççè
æ=÷÷
ø
öççè
æ=÷÷
ø
öççè
ævv)g(u,
vu
Bsr
Bpreserverows
![Page 34: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/34.jpg)
Shear
÷÷ø
öççè
æ=÷÷
ø
öççè
æ=÷÷
ø
öççè
æ÷÷ø
öççè
æ=÷÷
ø
öççè
æ=÷÷
ø
öççè
æy)f(x,y))f(x,g(x,
y)f(x,x
Byx
ABvu
Bsr
Wegetaa cosy sinx sy)f(x, +==
÷÷ø
öççè
æ+
=÷÷ø
öççè
æ=÷÷
ø
öççè
æaaaa
cosysinx siny -cosx
yx
Tsr
aa siny cosx v)g(u, -=
![Page 35: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/35.jpg)
Shear
Weneedtoexpressitintermsofu,vWeknowthatx=u,and
aa cosy sinx y)f(x,v +==
aa siny cosx v)g(u, -=
Weget
aa
aa
cossinu -v
cossinx -vy ==
![Page 36: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/36.jpg)
Shear
aaaaaa tanvsecu sin
cossinu -v-cosu v)g(u, -==
Weputitalltogetherandget
![Page 37: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/37.jpg)
Shear
Atlastweget
÷÷ø
öççè
æ+
=÷÷ø
öççè
æaa cosy sinx
xyx
A
÷÷ø
öççè
æ -=÷÷
ø
öççè
æv
tanvsecu vu
Baa
![Page 38: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/38.jpg)
Shear
Usingalargeangle(80degree)
![Page 39: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/39.jpg)
Shear
![Page 40: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/40.jpg)
Shear
![Page 41: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/41.jpg)
Shear
SecondpasswithBackwardMapping
![Page 42: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/42.jpg)
Shear
• Rotatein90degree,thenuseshearwithasmallangle
• Westillhaveascalefactorintheshearwhichcreateholes;onesolutionistousefilter
![Page 43: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/43.jpg)
Shear
÷÷ø
öççè
æ -÷÷ø
öççè
æ÷÷ø
öççè
æ -=÷÷
ø
öççè
æ -10
2/tan11sin01
102/tan1
cossinsincos a
aa
aaaa
Theothersolutionisbyusingthreesheartransformations
WeneedThreepassesinsteadofTwo.Butnoscale!Justshiftlines!
![Page 44: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/44.jpg)
Shear
Twofirstshears
![Page 45: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/45.jpg)
Shear
![Page 46: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/46.jpg)
Shear
![Page 47: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/47.jpg)
Shear
![Page 48: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/48.jpg)
Shear
![Page 49: Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages. Example –Forward Mapping Original Rotated Zoom In. Backward Mapping!"# The Problem:](https://reader036.vdocument.in/reader036/viewer/2022071507/61288f93918bba786e1a985f/html5/thumbnails/49.jpg)
Shear