Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages....

49
Image Warping

Transcript of Image Warping - TAUdcor/Graphics/pdf.slides/... · 2017. 4. 24. · Forward Mapping -Disadvantages....

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:

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:

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:

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:

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:

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:

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:

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:
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:
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:

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:
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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

Shear


Mapping Empires, Mapping Bodies: Reflections on … · Mapping Empires, Mapping Bodies: ... Mapping Empires, Mapping Bodies: Reflections on the Use and Abuse of ... cartographer draw

Mapping Empires, Mapping Bodies: Reflections on … · Mapping Empires, Mapping Bodies: ... Mapping Empires, Mapping Bodies: Reflections on the Use and Abuse of ... cartographer draw

Concept mapping, mind mapping and argument mapping: what are the

Concept mapping, mind mapping and argument mapping: what are the

Acceleration Data Structures for Ray Tracingdcor/Graphics/pdf.slides/RT... · 2016. 4. 15. · –Partition the 5D space of rays into a collection of 5D hypercubes, each containing

Acceleration Data Structures for Ray Tracingdcor/Graphics/pdf.slides/RT... · 2016. 4. 15. · –Partition the 5D space of rays into a collection of 5D hypercubes, each containing

Every image tells a story - TAUdcor/Graphics/pdf.slides/intro2.pdf · Every image tells a story •Goal of computer vision: perceive the “story” behind the picture •Compute

Every image tells a story - TAUdcor/Graphics/pdf.slides/intro2.pdf · Every image tells a story •Goal of computer vision: perceive the “story” behind the picture •Compute

Concept mapping, mind mapping and argument mapping: what ... · concept mapping has been developed to address these limitations of mind mapping. Concept mapping Concept mapping is

Concept mapping, mind mapping and argument mapping: what ... · concept mapping has been developed to address these limitations of mind mapping. Concept mapping Concept mapping is

3D Polygon Rendering Pipelinedcor/Graphics/pdf.slides/...Cohen-Sutherland Line Clipping Use simple tests to classify easy cases first Clipping is performed by the computation of the

3D Polygon Rendering Pipelinedcor/Graphics/pdf.slides/...Cohen-Sutherland Line Clipping Use simple tests to classify easy cases first Clipping is performed by the computation of the

Mapping and association mapping

Mapping and association mapping

Mapping Communities, Mapping Rights: Participatory ...€¦ · Theme II: Initiatives of Rights-holders 156 Mapping Communities, Mapping Rights: Participatory Community Mapping as

Mapping Communities, Mapping Rights: Participatory ...€¦ · Theme II: Initiatives of Rights-holders 156 Mapping Communities, Mapping Rights: Participatory Community Mapping as

Concept Mapping, Mind Mapping and Argument Mapping: What ... · PDF fileConcept Mapping, Mind Mapping and Argument Mapping: ... a number of education-related purposes. ... Novakian

Concept Mapping, Mind Mapping and Argument Mapping: What ... · PDF fileConcept Mapping, Mind Mapping and Argument Mapping: ... a number of education-related purposes. ... Novakian

Concept mapping, mind mapping and argument mapping: …fbe.unimelb.edu.au/__data/.../632516/mind_concept_argument_mappi… · Concept mapping, mind mapping and argument ... academics

Concept mapping, mind mapping and argument mapping: …fbe.unimelb.edu.au/__data/.../632516/mind_concept_argument_mappi… · Concept mapping, mind mapping and argument ... academics

Mapping Prejudice: Social Justice Mapping

Mapping Prejudice: Social Justice Mapping

Concept Mapping, Mind Mapping and Argument Mapping: What are ...

Concept Mapping, Mind Mapping and Argument Mapping: What are ...

מצגת של PowerPoint - TAUdcor/Graphics/cg-slides/rotation...• Precompute a set of prefiltered textures (essentially an image pyramid). • Based on the area of the pre-image

מצגת של PowerPoint - TAUdcor/Graphics/cg-slides/rotation...• Precompute a set of prefiltered textures (essentially an image pyramid). • Based on the area of the pre-image

Image Space Occlusion Culling - TAUdcor/Graphics/adv-slides/short-image-based-cullin… · occlusion map. • The occlusion map is a z-pyramid… 17 The Z-Pyramid Objects are. rendered.

Image Space Occlusion Culling - TAUdcor/Graphics/adv-slides/short-image-based-cullin… · occlusion map. • The occlusion map is a z-pyramid… 17 The Z-Pyramid Objects are. rendered.

Chapter 4 Spectral transform - TAUdcor/courses/exercise/spectral_v5.pdf · chapter where we present tools for spectral transform of 3D geometric data. Before going into 3D data, we

Chapter 4 Spectral transform - TAUdcor/courses/exercise/spectral_v5.pdf · chapter where we present tools for spectral transform of 3D geometric data. Before going into 3D data, we

Ray Tracing - TAUdcor/Graphics/adv-slides/ray-tracing06.pdf · 2008. 11. 25. · 2 7 Backward Tracing 8 Overview of today • Shadows • Reflection • Refraction • Recursive Ray

Ray Tracing - TAUdcor/Graphics/adv-slides/ray-tracing06.pdf · 2008. 11. 25. · 2 7 Backward Tracing 8 Overview of today • Shadows • Reflection • Refraction • Recursive Ray

Concept mapping, mind mapping and argument mapping: what are

Concept mapping, mind mapping and argument mapping: what are

Shape Co-analysisdcor/Graphics/pdf.slides/co-analysis.pdf · SIGGRAPH ASIA 2012. Active Co-Analysis •A semi-supervised method for co-segmentation with minimal user input 51 . Automatically

Shape Co-analysisdcor/Graphics/pdf.slides/co-analysis.pdf · SIGGRAPH ASIA 2012. Active Co-Analysis •A semi-supervised method for co-segmentation with minimal user input 51 . Automatically

Colorization by Example - TAUdcor/online_papers/papers/colorization... · 2005-06-06 · Colorization by Example R. Irony1, D. Cohen-Or1, and D. Lischinski2 1 Tel-Aviv University

Colorization by Example - TAUdcor/online_papers/papers/colorization... · 2005-06-06 · Colorization by Example R. Irony1, D. Cohen-Or1, and D. Lischinski2 1 Tel-Aviv University

Concept mapping, mind mapping and argument mapping: what ...

Concept mapping, mind mapping and argument mapping: what ...