lecture 14 shape google rigid shape statistics
play

Lecture 14: Shape Google: Rigid Shape Statistics COMPSCI/MATH - PowerPoint PPT Presentation

Jan 03, 2024 •173 likes •876 views

Lecture 14: Shape Google: Rigid Shape Statistics COMPSCI/MATH 290-04 Chris Tralie, Duke University 3/1/2016 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics Announcements Group Assignment 1 Full Submission Due Tomorrow

  1. Lecture 14: Shape Google: Rigid Shape Statistics COMPSCI/MATH 290-04 Chris Tralie, Duke University 3/1/2016 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  2. Announcements ⊲ Group Assignment 1 Full Submission Due Tomorrow (Wednesday) 11:55 PM ⊲ Rank Top 3 Final Project Choices By Friday 3/5 (Groups of 3-4) ⊲ Attendance Policy Clarification ⊲ Midterm Next Thursday 3/10 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  3. Table of Contents ◮ Shape Statistics / Algorithms ⊲ Comparing Shape Statistics ⊲ Classification / Performance Evaluation COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  4. Random Sampling By Area Goal: Given a shape, return similar shapes in a database Tralie 2010 ⊲ Focus on point clouds ⊲ Focus on shapes similar under rigid motion COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  5. Random Sampling By Area COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  6. Centroid Centering / RMS Scaling x i } N For a point cloud { � i = 1 ⊲ Subtract off centroid ⊲ Root mean square scale. Want � N � � 1 � � x i || 2 = 1 || � N i = 1 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  7. Shape Matching Criteria ⊲ Concise To Store ⊲ Quick to compute ⊲ Efficient to match ⊲ Discerning ⊲ Noise tolerant ⊲ Rotation Invariant COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  8. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  9. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  10. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  11. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  12. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  13. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  14. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  15. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  16. Shape Histogram: Shells COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  17. Shape Histogram: Shells ⊲ Quick To Compute COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  18. Shape Histogram: Shells ⊲ Quick To Compute COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  19. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  20. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  21. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  22. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  23. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant ⊲ Discerning COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  24. Shape Histogram: Shells ⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant ⊲ Discerning COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  25. Shape Histogram: Shells What can’t it tell apart? SHOW VIDEO COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  26. Shape Histogram: Shells And Sectors SHOW VIDEO COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  27. Shape Histogram: Shells And Sectors Still Rotation Invariant? COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  28. Shape Histogram: Shells And Sectors ⊲ Sort sectors within each shell ⊲ Record PCA eigenvalues within each shell COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  29. Spin Images Johnson/Herbert 1999, Figure Huang 2010 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  30. Spin Images: Rubber Duck Johnson/Herbert 1999 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  31. Spin Images ⊲ Quick To Compute COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  32. Spin Images ⊲ Quick To Compute COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  33. Spin Images ⊲ Quick To Compute ⊲ Concise To Store COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  34. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  35. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  36. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability) COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  37. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability) ⊲ Discerning COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  38. Spin Images ⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability) ⊲ Discerning COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  39. D2: Distance Histograms Osada 2003, Figure from Huang 2010 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  40. D2: Primitive Examples Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  41. D2: Real Examples Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  42. D1: Randomly Sample Points Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  43. D3: Randomly Sample Areas Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  44. D4: Randomly Sample Volumes Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  45. A3: Randomly Sample Angles Osada 2003 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  46. Extended Gaussian Image Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  47. Extended Gaussian Image Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  48. Extended Gaussian Image Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  49. Extended Gaussian Image Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  50. Extended Gaussian Image ⊲ Efficient To Compute / Concise To Store Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  51. Extended Gaussian Image ⊲ Efficient To Compute / Concise To Store Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  52. Extended Gaussian Image ⊲ Discerning Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  53. Extended Gaussian Image ⊲ Discerning (Only fully describes convex objects) Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  54. Extended Gaussian Image ⊲ Rotation Invariant Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  55. Extended Gaussian Image ⊲ Rotation Invariant (Rotate To Align With PCA Axes) Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  56. Extended Gaussian Image ⊲ Robust To Noise? Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  57. Extended Gaussian Image ⊲ Not Robust To Noise! Funkhouser 2004 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  58. Table of Contents ⊲ Shape Statistics / Algorithms ◮ Comparing Shape Statistics ⊲ Classification / Performance Evaluation COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  59. Normalize Histograms By Mass h [ i ] h ′ [ i ] = � N k = 1 h [ k ] In other words, all bins should sum to 1 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  60. Histogram Euclidean Distance For histograms h 1 and h 2 � N � � � ( h 1 [ i ] − h 2 [ i ]) 2 d E ( h 1 , h 2 ) = � i = 1 Just thinking of h 1 and h 2 as high dimensional Euclidean vectors! Each histogram bin is a dimension COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

  61. Histogram Cosine Distance � � h 1 · � � h 2 d C ( h 1 , h 2 ) = cos − 1 || � h 1 |||| � h 2 || COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

Recommend

image appears like the pre-image that has been moved through a certain distance with the

image appears like the pre-image that has been moved through a certain distance with the

D AY 61 T RIANGLE CONGRUENCE IN TERMS OF RIGID MOTIONS I NTRODUCTION A rigid motion transforms a figure such that the shape and size remain the same. When two figures have the same size and shape, they are said to be congruent. In this

328 views • 12 slides
Statistical Geometry Processing Winter Semester 2011/2012 (Deformable) Shape Matching Rigid Shape

Statistical Geometry Processing Winter Semester 2011/2012 (Deformable) Shape Matching Rigid Shape

Statistical Geometry Processing Winter Semester 2011/2012 (Deformable) Shape Matching Rigid Shape Matching Iterated Closest Points (ICP) Part B (moves, rotation & translation) Part A (stays fixed) The main idea: Pairwise matching

956 views • 82 slides
Non-Rigid Registration Hao Li Local Shape Matching: Non-Rigid Registration Correspondence

Non-Rigid Registration Hao Li Local Shape Matching: Non-Rigid Registration Correspondence

Non-Rigid Registration Hao Li Local Shape Matching: Non-Rigid Registration Correspondence Problem Classification How many meshes? Two: Pairwise registration Initial registration available? Yes: Local optimization methods Class of

1.88k views • 144 slides
Shape Statistics for Image Segmentation with Prior Guillaume Charpiat PhD Defense - 2006,

Shape Statistics for Image Segmentation with Prior Guillaume Charpiat PhD Defense - 2006,

Introduction Shapes and Shape Metrics Variational Shape Warping Statistics Segmentation with prior Summary Shape Statistics for Image Segmentation with Prior Guillaume Charpiat PhD Defense - 2006, December 13 PhD Supervisor: Olivier

1.1k views • 84 slides
Computer Vision Statistical Shape Analysis Shape Shape is the geometric information that

Computer Vision Statistical Shape Analysis Shape Shape is the geometric information that

Computer Vision Statistical Shape Analysis Shape Shape is the geometric information that remains when translation, rotation, and scale are factored out. Landmark points. D'Arcy Thompson. David George Kendall Fred Bookstein.

248 views • 9 slides
Shape Features WangRuchen CVBIOUC http://vision.ouc.edu.cn/~zhenghaiyong How to Convex hull

Shape Features WangRuchen CVBIOUC http://vision.ouc.edu.cn/~zhenghaiyong How to Convex hull

Shape Similarity describe a shape? Matching with shape contexts Inner-distance shape context calculation Shape context Methods Hausdorfg distance Shape Features WangRuchen CVBIOUC http://vision.ouc.edu.cn/~zhenghaiyong How to

853 views • 59 slides
Statistical Shape Models Eigenpatches model regions Assume shape is fixed What if it

Statistical Shape Models Eigenpatches model regions Assume shape is fixed What if it

Statistical Shape Models Eigenpatches model regions Assume shape is fixed What if it isn t? Faces with expression changes, organs in medical images etc Need a method of modelling shape and shape variation Shape Models

271 views • 24 slides
3D Descriptor Design and Learning for Robust Non-rigid Shape Matching Jianwei Guo NLPR,

3D Descriptor Design and Learning for Robust Non-rigid Shape Matching Jianwei Guo NLPR,

3D Descriptor Design and Learning for Robust Non-rigid Shape Matching Jianwei Guo NLPR, Institute of Automation, Chinese Academy of Sciences Sept.17, 2020 GAMES Webinar 1 Team--3D Visual Computing [ACM TOG (SIGGRAPH Asia) 2012]

611 views • 46 slides
3. Congruent figures These are figures that have the same size and shape. They can be mapped onto

3. Congruent figures These are figures that have the same size and shape. They can be mapped onto

D AY 11 I MAGES UNDER RIGID MOTION I NTRODUCTION When a car moves from one place to another, its position changes but its size and shape remain unchanged. In a similar manner, when a plane figure undergoes a transformation such as a

346 views • 20 slides
Some recent methods in non-rigid shape matching, with and without learning GAMES 2019 webinar

Some recent methods in non-rigid shape matching, with and without learning GAMES 2019 webinar

Some recent methods in non-rigid shape matching, with and without learning GAMES 2019 webinar Maks Ovsjanikov Based on joint work with: E. Corman, Michael Bronstein, Emanuele Rodol, Justin Solomon, Adrien Butscher, Mirela Ben-Chen, Leonidas

1.27k views • 81 slides
Automated Inference of Shape Specifications L Q Loc, Gherghina (Google), Qin (Teesside), W-N Chin

Automated Inference of Shape Specifications L Q Loc, Gherghina (Google), Qin (Teesside), W-N Chin

Automated Inference of Shape Specifications L Q Loc, Gherghina (Google), Qin (Teesside), W-N Chin Dept of Computer Science - National University of Singapore December 16, 2014 Loc, Gherghina, Qin, Chin (NUS) Shape Inference Tut 2b 1 / 51

620 views • 51 slides
Shape Contexts Newton Petersen 4/25/2008 "Shape Matching and Object Recognition Using

Shape Contexts Newton Petersen 4/25/2008 "Shape Matching and Object Recognition Using

Shape Contexts Newton Petersen 4/25/2008 "Shape Matching and Object Recognition Using Shape Contexts", Belongie et al. PAMI April 2002 Agenda Study Matlab code for computing shape context Look at limitations of descriptor

615 views • 26 slides
Sparks CH301 WHY IS EVERYTHING SO DIFFERENT? Think About Shape UNIT 3 Day 2 What are we going

Sparks CH301 WHY IS EVERYTHING SO DIFFERENT? Think About Shape UNIT 3 Day 2 What are we going

Sparks CH301 WHY IS EVERYTHING SO DIFFERENT? Think About Shape UNIT 3 Day 2 What are we going to learn today? Molecular Shape is an Important Predictor of Physical and Chemical Properties Shape Predict Polarity Properties Determine

211 views • 20 slides
Shape Optimization Shape Optimization Using Reflection Lines Using Reflection Lines Elif Tosun

Shape Optimization Shape Optimization Using Reflection Lines Using Reflection Lines Elif Tosun

Shape Optimization Shape Optimization Using Reflection Lines Using Reflection Lines Elif Tosun Yotam I. Gingold Jason Reisman Denis Zorin New York University Reflections are sensitive to surface shape depend on local quantities

736 views • 49 slides
Shape Matching Shape-Based Recognition Intro Humans can recognize many objects based on

Shape Matching Shape-Based Recognition Intro Humans can recognize many objects based on

Shape Matching Shape-Based Recognition Intro Humans can recognize many objects based on shape alone Fundamental cue for many object categories Invariant to photometric variation. Slide from Pedro Felzenszwalb Shapes vs. Intensity

1.88k views • 92 slides
Millifluidics, 1. Surface Tension Shape of droplets by Dr Seuss The shape of me and other

Millifluidics, 1. Surface Tension Shape of droplets by Dr Seuss The shape of me and other

Millifluidics, 1. Surface Tension Shape of droplets by Dr Seuss The shape of me and other stuff Theres a wocket in my pocket by Curious Georges from Opposites Nasa version M. Weislogel,

457 views • 11 slides
Statistical Geometry Processing Winter Semester 2011/2012 Global Shape Matching Rigid Global

Statistical Geometry Processing Winter Semester 2011/2012 Global Shape Matching Rigid Global

Statistical Geometry Processing Winter Semester 2011/2012 Global Shape Matching Rigid Global Matching Iterated Closest Points (ICP) Part B (moves, rotation & translation) Part A (stays fixed) Problems Need good intialization

824 views • 66 slides
Shape Outlier Detection Using Pose Preserving Dynamic Shape Models Chan-Su Lee and Ahmed

Shape Outlier Detection Using Pose Preserving Dynamic Shape Models Chan-Su Lee and Ahmed

Shape Outlier Detection Using Pose Preserving Dynamic Shape Models Chan-Su Lee and Ahmed Elgammal Rutgers, The State University of New Jersey Department of Computer Science Outline Introduction Shape Outlier Detection for Visual

753 views • 32 slides
Information Evening We shape our lives, and we shape ourselves The choices we make are

Information Evening We shape our lives, and we shape ourselves The choices we make are

Year 8: Options Information Evening We shape our lives, and we shape ourselves The choices we make are ultimately our own responsibility . Eleanor Roosevelt Why Now? 3 year KS4 will give more time to their chosen subjects Courses

983 views • 76 slides
fitting and non-rigid registration Marcel Lthi, Christoph Jud and Thomas Vetter University of

fitting and non-rigid registration Marcel Lthi, Christoph Jud and Thomas Vetter University of

A unified approach to shape model fitting and non-rigid registration Marcel Lthi, Christoph Jud and Thomas Vetter University of Basel Shape modeling pipeline Acquisition Registration Modeling Fitting Correspondence Correspondence

667 views • 53 slides
Slicing Imagine we have a hierarchy of shape shapes with the following inherits members

Slicing Imagine we have a hierarchy of shape shapes with the following inherits members

Slicing Imagine we have a hierarchy of shape shapes with the following inherits members get_name(): circle triangle the name assigned to the shape get_area(): the area occupied by the shape We also provide swap(&,

1.42k views • 83 slides
SHAPE Spiritual Gifts (what I am gifted to do) God has given each of us a special SHAPE Heart

SHAPE Spiritual Gifts (what I am gifted to do) God has given each of us a special SHAPE Heart

2/15/2016 HEARING YOUR HEARTBEAT God has given each of us a special SHAPE Applying Your Abilities (SHAPE Sermon Series) Spiritual gifts - what I am gifted to do? Heart - what do I love to do? Abilities - what am I good at? Personality -

296 views • 8 slides
Problem Definition Using Shape Spaces for Structure from Motion Can we understand motion using a

Problem Definition Using Shape Spaces for Structure from Motion Can we understand motion using a

Motivation Factorization Non-Rigid Motion Occlusion Motivation Factorization Non-Rigid Motion Occlusion Problem Definition Using Shape Spaces for Structure from Motion Can we understand motion using a single camera? Sharat Chandran ViGIL

981 views • 28 slides
Non-Rigid Puzzles Or Litany Tel Aviv University Joint work with 1/36 Non-Rigid Puzzles and

Non-Rigid Puzzles Or Litany Tel Aviv University Joint work with 1/36 Non-Rigid Puzzles and

Non-Rigid Puzzles Or Litany Tel Aviv University Joint work with 1/36 Non-Rigid Puzzles and other stories Or Litany Tel Aviv University Joint work with 1/36 Shape correspondence problem Isometric 2/36 Shape correspondence problem

1.64k views • 79 slides

More recommend