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Shape-Representation

Shape-Representation. and. Shape Similarity. Part 1: Shapes. Dr. Rolf Lakaemper. May I introduce myself…. Rolf Lakaemper PhD (Doctorate Degree) 2000 Hamburg University, Germany Currently Assist. Professor at Department of Computer and Information Sciences,

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Shape-Representation

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  1. Shape-Representation and Shape Similarity Part 1: Shapes Dr. Rolf Lakaemper

  2. May I introduce myself… • Rolf Lakaemper • PhD (Doctorate Degree) 2000 • Hamburg University, Germany • Currently Assist. Professor at Department • of Computer and Information Sciences, • Temple University, Philadelphia, USA • Main Research Area: Computer Vision

  3. Motivation WHY SHAPE ?

  4. Motivation These objects are recognized by…

  5. Motivation These objects are recognized by…

  6. Why Shape ? Several applications in computer vision use shape processing: • Object recognition • Image retrieval • Processing of pictorial information • Video compression (eg. MPEG-7) … This presentation focuses on object recognition and image retrieval.

  7. Motivation Typical Application: Multimedia: Image Database Query by Shape / Texture / …(Color / Keyword)

  8. Blobworld Example 1: Blobworld http://elib.cs.berkeley.edu/photos/blobworld/start.html BLOB = “Binary Large Object”, “an indistinct shapeless (really ?) form”

  9. Blobworld Blobworld: Query by Shape / Texture / Location / Color Selected Blob Query: by Color and Texture of Blob Result: Blobs with similar Color and Texture Satisfying ?

  10. Blobworld Blobworld: Query by Shape / Texture / Location / Color Selected Blob Query: by Shape of Blob Result: …are these shapes similar ? Satisfying ?

  11. Blobworld Result: SHAPE recognition seems to be necessary but not easy !

  12. ISS Database Example 2: ISS-Database http://knight.cis.temple.edu/~shape

  13. The Interface (JAVA – Applet)

  14. The Sketchpad: Query by Shape

  15. The First Guess: Different Shape - Classes

  16. Selected shape defines query by shape – class

  17. Result

  18. ISS Database ISS: Query by Shape / Texture Sketch of Shape Query: by Shape only Result: Satisfying ?

  19. ISS Database SHAPE recognition seems to be possible and leads to satisfying results !

  20. ISS Database The ISS-Database will be topic of part IV of this tutorial …so stay alert !

  21. Overview • Overview Part 1 • Why shape ? • What is shape ? • Shape similarity • Metrices • Classes of similarity measures • Feature Based Coding • Examples for global similarity

  22. Why Shape ? Why Shape ? • Shape is probably the most important property that is perceived about objects. It allows to predict more facts about an object than other features, e.g. color (Palmer 1999) • Thus, recognizing shape is crucial for object recognition. In some applications it may be the only feature present, e.g. logo recognition

  23. Why Shape ? • Shape is not only perceived by visual means: • tactical sensors can also provide shape information that are processed in a similar way. • robots’ range sensor provide shape information, too.

  24. Shape • Typical problems: • • How to describe shape ? • What is the matching transformation? • No one-to-one correspondence • • Occlusion • • Noise

  25. Shape • Partial match: only part of query appears in part of database shape

  26. What is Shape ? • What is Shape ? • Plato, "Meno", 380 BC: • "figure is the only existing thing that is found always following color“ • "figure is limit of solid"

  27. What is Shape ? … let’s start with some properties easier to agree on: • Shape describes a spatial region Shape is a (the ?) specific part of spatial cognition • Typically addresses 2D space why ?

  28. What is Shape ? • 3D => 2D projection

  29. What is Shape ? • the original 3D (?) object

  30. What is Shape ? Moving on from the naive understanding, some questions arise: • Is there a maximum size for a shape to be a shape? • Can a shape have holes? • Does shape always describe a connected region? • How to deal with/represent partial shapes (occlusion / partial match) ?

  31. What is Shape ? Shape or Not ? Continuous transformation from shape to no shape: Is there a point when it stops being a shape?

  32. What is Shape ? Shape or Not ? Continuous transformation from shape to two shapes: Is there a point when it stops being a single shape?

  33. What is Shape ? But there’s no doubt that a single, connected region is a shape. Right ?

  34. What is Shape ? A single, connected region. But a shape ? A question of scale !

  35. What is Shape ? • There’s no easy, single definition of shape • In difference to geometry, arbitrary shape is not covered by an axiomatic system • Different applications in object recognition focus on different shape related features • Special shapes can be handled • Typically, applications in object recognition employ a similarity measure to determine a plausibility that two shapes correspond to each other

  36. Similarity So the new question is: What is Shape Similarity ? or How to Define a Similarity Measure

  37. Similarity Again: it’s not so simple (sorry). There’s nothing like THE similarity measure

  38. Similarity which similarity measure, depends on which required properties, depends on which particular matching problem, depends on which application

  39. Similarity …which application Simple Recognition (yes / no) ... robustness Common Rating (best of ...) Analytical Rating (best of, but...) ... invariance to basic transformations

  40. Similarity …which problem • computation problem: d(A,B) • decision problem: d(A,B) <e ? • decision problem: is there g: d(g(A),B) <e ? • optimization problem: find g: min d(g(A),B)

  41. Similarity …which properties: We concentrate here on the computational problem d(A,B)

  42. Similarity Measure • Requirements to a similarity measure • Should not incorporate context knowledge (no AI), thus computes generic shape similarity

  43. Similarity Measure • Requirements to a similarity measure • Must be able to deal with noise • Must be invariant with respect to basic transformations Next: Strategy Scaling (or resolution) Rotation Rigid / non-rigid deformation

  44. Similarity Measure • Requirements to a similarity measure • Must be able to deal with noise • Must be invariant with respect to basic transformations • Must be in accord with human perception

  45. Similarity Measure Some other aspects worth consideration: • Similarity of structure • Similarity of area Can all these aspects be expressed by a single number?

  46. Similarity Measure • Desired Properties of a Similarity Function C • (Basri et al. 1998) • C should be a metric • C should be continous • C should be invariant (to…)

  47. Properties Metric Properties S set of patterns Metric: d: S ´ S ® R satisfying 1. Self-identity: " xÎS, d(x,x)=0 2. Positivity: " x ¹yÎS, d(x,y)>0 3. Symmetry: " x, yÎS, d(x,y)= d(y,x) 4. Triangle inequality: " x, y, zÎS, d(x,z)£d(x,y)+d(y,z) • Semi-metric: 1, 2, 3 • Pseudo-metric: 1, 3, 4 • S with fixed metric d is called metric space

  48. Properties • Self-identity: " xÎS, d(x,x)=0 • Positivity: " x ¹yÎS, d(x,y)>0 • …surely makes sense

  49. Properties

  50. Properties

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