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Affine invariance of interest points

This overview delves into the concept of affine invariance of interest points in computer vision, highlighting the limitations of scale invariance, advancements in affine invariant points/regions, applications in recognition, multi-scale extraction of Harris interest points, selection of characteristic scale points, and more.

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Affine invariance of interest points

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  1. Affine invariance of interest points

  2. Overview • Scale invariance is not sufficient for large baseline changes • State of the art on affine invariant points/regions • Affine invariant interest points • Application to recognition

  3. Scale invariant Harris points • Multi-scale extraction of Harris interest points • Selection of points at characteristic scale in scale space Chacteristic scale : - maximum in scale space - scale invariant Laplacian

  4. Scale invariant interest points invariant points + associated regions [Mikolajczyk & Schmid’01] multi-scale Harris points selection of points at the characteristic scale with Laplacian

  5. Viewpoint changes • Locally approximated by an affine transformation detected scale invariant region projected region

  6. State of the art • Affine invariant regions (Tuytelaars et al.’00) • ellipses fitted to intensity maxima • parallelogram formed by interest points and edges

  7. Isotropicneighborhoodsrelated by rotation State of the art • Theory for affine invariant neighborhood (Lindeberg’94)

  8. State of the art • Localization & scale influence affine neighhorbood => affine invariant Harris points (Mikolajczyk & Schmid’02) • Iterative estimation of these parameters • localization– local maximum of the Harris measure • scale – automatic scale selection with the Laplacian • affine neighborhood – normalization with second moment matrix Repeat estimation until convergence • Initialization with multi-scale interest points

  9. Affine invariant Harris points • Iterative estimation of localization, scale, neighborhood Initial points

  10. Affine invariant Harris points • Iterative estimation of localization, scale, neighborhood Iteration #1

  11. Affine invariant Harris points • Iterative estimation of localization, scale, neighborhood Iteration #2

  12. Affine invariant Harris points • Iterative estimation of localization, scale, neighborhood Iteration #3, #4, ...

  13. Affine invariant Harris points • Initialization with multi-scale interest points • Iterative modification of location, scale and neighborhood

  14. affine Harris Harris-Laplace Harris-Laplace + affine regions Affine invariant Harris points

  15. Affine invariant neighborhhood affine Harris detector affine Laplace detector

  16. Image retrieval … > 5000 images change in viewing angle

  17. Matches 22 correct matches

  18. Image retrieval … > 5000 images change in viewing angle + scale change

  19. Matches 33 correct matches

  20. 3D Recognition

  21. 3D Recognition 3D object modeling and recognition using affine-invariant patches and multi-view spatial constraints, F. Rothganger, S. Lazebnik, C. Schmid, J. Ponce, CVPR 2003

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