SlideShare a Scribd company logo
1 of 49
Camera model 
2014/11/14 
ked
Outline 
 How to descript a camera 
 Camera calibration 
 A calibration tool 
 Examples
Outline 
 How to descript a camera 
 Camera calibration 
 A calibration tool 
 Examples
Intrinsic & extrinsic
Intrinsic & extrinsic
疑問 
 線性模型如何造成非線性結果
Outline 
 How to descript a camera 
 Camera calibration 
 A calibration tool 
 Examples
Hard to solve
Hard to solve
Nonlinear optimization 
 Model M: 
 
 Minimize
 Levenberg-Marquardt method
Solving methods 
 Steepest descent 
 Newton’s method
Jacobian matrix
Summary 
 Steepest descent 
 
 Gauss-Newton method 
 
 Levenberg-Marquardt method 

Outline 
 How to descript a camera 
 Camera calibration 
 A calibration tool 
 Examples
Outline 
 How to descript a camera 
 Camera calibration 
 A calibration tool 
 Examples
 https://www.youtube.com/watch?v=OlMzE4u3Pbw 
 https://www.youtube.com/watch? 
v=QU4pPnsqbeM

More Related Content

More from Su Yan-Jen

Captain america painting competition 9
Captain america painting competition 9Captain america painting competition 9
Captain america painting competition 9Su Yan-Jen
 
Captain america painting competition 8
 Captain america painting competition 8 Captain america painting competition 8
Captain america painting competition 8Su Yan-Jen
 
Captain america painting competition 7
 Captain america painting competition 7 Captain america painting competition 7
Captain america painting competition 7Su Yan-Jen
 
Captain america painting competition 6
 Captain america painting competition 6 Captain america painting competition 6
Captain america painting competition 6Su Yan-Jen
 
Captain america painting competition 5
Captain america painting competition 5Captain america painting competition 5
Captain america painting competition 5Su Yan-Jen
 
Captain america painting competition 4
Captain america  painting competition 4Captain america  painting competition 4
Captain america painting competition 4Su Yan-Jen
 
Captain america painting competition 3
Captain america painting competition 3Captain america painting competition 3
Captain america painting competition 3Su Yan-Jen
 
Captain america painting competition 2
Captain america painting competition 2Captain america painting competition 2
Captain america painting competition 2Su Yan-Jen
 
Captain America painting competition
Captain America painting competitionCaptain America painting competition
Captain America painting competitionSu Yan-Jen
 
PM2.5 visualization
PM2.5 visualizationPM2.5 visualization
PM2.5 visualizationSu Yan-Jen
 
Stereo matching
Stereo matchingStereo matching
Stereo matchingSu Yan-Jen
 
Face recognition
Face recognitionFace recognition
Face recognitionSu Yan-Jen
 
Data mining of commercial surveillance
Data mining of commercial surveillanceData mining of commercial surveillance
Data mining of commercial surveillanceSu Yan-Jen
 
Fundamental matrix
Fundamental matrixFundamental matrix
Fundamental matrixSu Yan-Jen
 
Pose normalization
Pose normalizationPose normalization
Pose normalizationSu Yan-Jen
 
Histogram of oriented gradients
Histogram of oriented gradientsHistogram of oriented gradients
Histogram of oriented gradientsSu Yan-Jen
 

More from Su Yan-Jen (20)

Captain america painting competition 9
Captain america painting competition 9Captain america painting competition 9
Captain america painting competition 9
 
Captain america painting competition 8
 Captain america painting competition 8 Captain america painting competition 8
Captain america painting competition 8
 
Captain america painting competition 7
 Captain america painting competition 7 Captain america painting competition 7
Captain america painting competition 7
 
Captain america painting competition 6
 Captain america painting competition 6 Captain america painting competition 6
Captain america painting competition 6
 
Captain america painting competition 5
Captain america painting competition 5Captain america painting competition 5
Captain america painting competition 5
 
Captain america painting competition 4
Captain america  painting competition 4Captain america  painting competition 4
Captain america painting competition 4
 
Captain america painting competition 3
Captain america painting competition 3Captain america painting competition 3
Captain america painting competition 3
 
Captain america painting competition 2
Captain america painting competition 2Captain america painting competition 2
Captain america painting competition 2
 
Captain America painting competition
Captain America painting competitionCaptain America painting competition
Captain America painting competition
 
PM2.5 visualization
PM2.5 visualizationPM2.5 visualization
PM2.5 visualization
 
Transformer 3
Transformer 3Transformer 3
Transformer 3
 
Transformer 2
Transformer 2Transformer 2
Transformer 2
 
Transformer
TransformerTransformer
Transformer
 
Stereo matching
Stereo matchingStereo matching
Stereo matching
 
Face recognition
Face recognitionFace recognition
Face recognition
 
Data mining of commercial surveillance
Data mining of commercial surveillanceData mining of commercial surveillance
Data mining of commercial surveillance
 
Fundamental matrix
Fundamental matrixFundamental matrix
Fundamental matrix
 
Pose normalization
Pose normalizationPose normalization
Pose normalization
 
SDM
SDMSDM
SDM
 
Histogram of oriented gradients
Histogram of oriented gradientsHistogram of oriented gradients
Histogram of oriented gradients
 

Recently uploaded

Scaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organizationScaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organizationRadu Cotescu
 
The Role of Taxonomy and Ontology in Semantic Layers - Heather Hedden.pdf
The Role of Taxonomy and Ontology in Semantic Layers - Heather Hedden.pdfThe Role of Taxonomy and Ontology in Semantic Layers - Heather Hedden.pdf
The Role of Taxonomy and Ontology in Semantic Layers - Heather Hedden.pdfEnterprise Knowledge
 
Finology Group – Insurtech Innovation Award 2024
Finology Group – Insurtech Innovation Award 2024Finology Group – Insurtech Innovation Award 2024
Finology Group – Insurtech Innovation Award 2024The Digital Insurer
 
The Codex of Business Writing Software for Real-World Solutions 2.pptx
The Codex of Business Writing Software for Real-World Solutions 2.pptxThe Codex of Business Writing Software for Real-World Solutions 2.pptx
The Codex of Business Writing Software for Real-World Solutions 2.pptxMalak Abu Hammad
 
08448380779 Call Girls In Civil Lines Women Seeking Men
08448380779 Call Girls In Civil Lines Women Seeking Men08448380779 Call Girls In Civil Lines Women Seeking Men
08448380779 Call Girls In Civil Lines Women Seeking MenDelhi Call girls
 
08448380779 Call Girls In Friends Colony Women Seeking Men
08448380779 Call Girls In Friends Colony Women Seeking Men08448380779 Call Girls In Friends Colony Women Seeking Men
08448380779 Call Girls In Friends Colony Women Seeking MenDelhi Call girls
 
The 7 Things I Know About Cyber Security After 25 Years | April 2024
The 7 Things I Know About Cyber Security After 25 Years | April 2024The 7 Things I Know About Cyber Security After 25 Years | April 2024
The 7 Things I Know About Cyber Security After 25 Years | April 2024Rafal Los
 
Unblocking The Main Thread Solving ANRs and Frozen Frames
Unblocking The Main Thread Solving ANRs and Frozen FramesUnblocking The Main Thread Solving ANRs and Frozen Frames
Unblocking The Main Thread Solving ANRs and Frozen FramesSinan KOZAK
 
Boost PC performance: How more available memory can improve productivity
Boost PC performance: How more available memory can improve productivityBoost PC performance: How more available memory can improve productivity
Boost PC performance: How more available memory can improve productivityPrincipled Technologies
 
Histor y of HAM Radio presentation slide
Histor y of HAM Radio presentation slideHistor y of HAM Radio presentation slide
Histor y of HAM Radio presentation slidevu2urc
 
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024BookNet Canada
 
CNv6 Instructor Chapter 6 Quality of Service
CNv6 Instructor Chapter 6 Quality of ServiceCNv6 Instructor Chapter 6 Quality of Service
CNv6 Instructor Chapter 6 Quality of Servicegiselly40
 
Swan(sea) Song – personal research during my six years at Swansea ... and bey...
Swan(sea) Song – personal research during my six years at Swansea ... and bey...Swan(sea) Song – personal research during my six years at Swansea ... and bey...
Swan(sea) Song – personal research during my six years at Swansea ... and bey...Alan Dix
 
Salesforce Community Group Quito, Salesforce 101
Salesforce Community Group Quito, Salesforce 101Salesforce Community Group Quito, Salesforce 101
Salesforce Community Group Quito, Salesforce 101Paola De la Torre
 
A Domino Admins Adventures (Engage 2024)
A Domino Admins Adventures (Engage 2024)A Domino Admins Adventures (Engage 2024)
A Domino Admins Adventures (Engage 2024)Gabriella Davis
 
SQL Database Design For Developers at php[tek] 2024
SQL Database Design For Developers at php[tek] 2024SQL Database Design For Developers at php[tek] 2024
SQL Database Design For Developers at php[tek] 2024Scott Keck-Warren
 
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...Neo4j
 
Raspberry Pi 5: Challenges and Solutions in Bringing up an OpenGL/Vulkan Driv...
Raspberry Pi 5: Challenges and Solutions in Bringing up an OpenGL/Vulkan Driv...Raspberry Pi 5: Challenges and Solutions in Bringing up an OpenGL/Vulkan Driv...
Raspberry Pi 5: Challenges and Solutions in Bringing up an OpenGL/Vulkan Driv...Igalia
 
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptxHampshireHUG
 
Data Cloud, More than a CDP by Matt Robison
Data Cloud, More than a CDP by Matt RobisonData Cloud, More than a CDP by Matt Robison
Data Cloud, More than a CDP by Matt RobisonAnna Loughnan Colquhoun
 

Recently uploaded (20)

Scaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organizationScaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organization
 
The Role of Taxonomy and Ontology in Semantic Layers - Heather Hedden.pdf
The Role of Taxonomy and Ontology in Semantic Layers - Heather Hedden.pdfThe Role of Taxonomy and Ontology in Semantic Layers - Heather Hedden.pdf
The Role of Taxonomy and Ontology in Semantic Layers - Heather Hedden.pdf
 
Finology Group – Insurtech Innovation Award 2024
Finology Group – Insurtech Innovation Award 2024Finology Group – Insurtech Innovation Award 2024
Finology Group – Insurtech Innovation Award 2024
 
The Codex of Business Writing Software for Real-World Solutions 2.pptx
The Codex of Business Writing Software for Real-World Solutions 2.pptxThe Codex of Business Writing Software for Real-World Solutions 2.pptx
The Codex of Business Writing Software for Real-World Solutions 2.pptx
 
08448380779 Call Girls In Civil Lines Women Seeking Men
08448380779 Call Girls In Civil Lines Women Seeking Men08448380779 Call Girls In Civil Lines Women Seeking Men
08448380779 Call Girls In Civil Lines Women Seeking Men
 
08448380779 Call Girls In Friends Colony Women Seeking Men
08448380779 Call Girls In Friends Colony Women Seeking Men08448380779 Call Girls In Friends Colony Women Seeking Men
08448380779 Call Girls In Friends Colony Women Seeking Men
 
The 7 Things I Know About Cyber Security After 25 Years | April 2024
The 7 Things I Know About Cyber Security After 25 Years | April 2024The 7 Things I Know About Cyber Security After 25 Years | April 2024
The 7 Things I Know About Cyber Security After 25 Years | April 2024
 
Unblocking The Main Thread Solving ANRs and Frozen Frames
Unblocking The Main Thread Solving ANRs and Frozen FramesUnblocking The Main Thread Solving ANRs and Frozen Frames
Unblocking The Main Thread Solving ANRs and Frozen Frames
 
Boost PC performance: How more available memory can improve productivity
Boost PC performance: How more available memory can improve productivityBoost PC performance: How more available memory can improve productivity
Boost PC performance: How more available memory can improve productivity
 
Histor y of HAM Radio presentation slide
Histor y of HAM Radio presentation slideHistor y of HAM Radio presentation slide
Histor y of HAM Radio presentation slide
 
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
 
CNv6 Instructor Chapter 6 Quality of Service
CNv6 Instructor Chapter 6 Quality of ServiceCNv6 Instructor Chapter 6 Quality of Service
CNv6 Instructor Chapter 6 Quality of Service
 
Swan(sea) Song – personal research during my six years at Swansea ... and bey...
Swan(sea) Song – personal research during my six years at Swansea ... and bey...Swan(sea) Song – personal research during my six years at Swansea ... and bey...
Swan(sea) Song – personal research during my six years at Swansea ... and bey...
 
Salesforce Community Group Quito, Salesforce 101
Salesforce Community Group Quito, Salesforce 101Salesforce Community Group Quito, Salesforce 101
Salesforce Community Group Quito, Salesforce 101
 
A Domino Admins Adventures (Engage 2024)
A Domino Admins Adventures (Engage 2024)A Domino Admins Adventures (Engage 2024)
A Domino Admins Adventures (Engage 2024)
 
SQL Database Design For Developers at php[tek] 2024
SQL Database Design For Developers at php[tek] 2024SQL Database Design For Developers at php[tek] 2024
SQL Database Design For Developers at php[tek] 2024
 
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
 
Raspberry Pi 5: Challenges and Solutions in Bringing up an OpenGL/Vulkan Driv...
Raspberry Pi 5: Challenges and Solutions in Bringing up an OpenGL/Vulkan Driv...Raspberry Pi 5: Challenges and Solutions in Bringing up an OpenGL/Vulkan Driv...
Raspberry Pi 5: Challenges and Solutions in Bringing up an OpenGL/Vulkan Driv...
 
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
 
Data Cloud, More than a CDP by Matt Robison
Data Cloud, More than a CDP by Matt RobisonData Cloud, More than a CDP by Matt Robison
Data Cloud, More than a CDP by Matt Robison
 

Camera model

Editor's Notes

  1. outline
  2. Pinhole camera,呈現倒影
  3. 描述的時候,把像平面移到前面
  4. 真實的(X, Y, Z),在像平面上變成(fX/Z, fY/Z)
  5. 對於相機的描述,可以將它拆解成intrinsic和extrinsic兩部分, Intrinsic是對於相機本身的描述,如focal length, optical center, 長寬比等, Extrinsic則是描述相機外在的動作
  6. Intrinsic matrix除了focal length, principal point之外,還可以描述很多東西, 以下這個寫法可以描述non-square pixel, skew, radial distortion等情況
  7. Distortion是相機一種常見的現象, Radial distortion描述的就是,離中心點越遠變形越嚴重的情況
  8. 相機校正
  9. 相機校正的目是要推算出camera model的參數, 估計的方法: 場景的幾何形狀是已知的;和未知的。
  10. 場景已知 -> 用設計過的幾何形狀物,來估算相機參數
  11. 計算方式: 線性、非線性
  12. 線性的估算
  13. 把整個 camera model看成11個變數的matrix
  14. 然後用least square method求解
  15. 最大缺點 相機移動後 整個model要重算
  16. 非線性的方式則是把各個參數分別算出
  17. 一樣是要最小化差距的平方和
  18. 不過要估算的參數可以是非線性的
  19. Function的Taylor expansion如下
  20. 如果該點是區域最小值,一次微分為0
  21. 但是這樣不夠,它也可能是最大值或saddle point
  22. 還要滿足另一個必要條件 二次微分是正定矩陣
  23. 常見的解法有兩種疊代方式
  24. Steepest descent是沿著gradient的方向走
  25. 他保證一定會收斂,但是越接近最小值的時候,收斂越慢
  26. 牛頓法收斂比較快,但是在不好的初始情況會有無法收斂的問題
  27. Gauss-Newton method是一種改進Newton method的方式 他不需要計算二次微分,而是以Jacobian matrix取代
  28. LM則是結合steepest descent和Newton method的好處
  29. 用/mu/來調節steepest descent和Newton method的比重
  30. 這是它們收斂行為的比較