Abstract

This work presents a novel local image descriptor based on the concept of pointwise signal regularity. Local image regions are extracted using either an interest point or an interest region detector, and discriminative feature vectors are constructed by uniformly sampling the pointwise Hölderian regularity around each region center. Regularity estimation is performed using local image oscillations, the most straightforward method directly derived from the definition of the Hölder exponent. Furthermore, estimating the Hölder exponent in this manner has proven to be superior, in most cases, when compared to wavelet based estimation as was shown in previous work. Our detector shows invariance to illumination change, JPEG compression, image rotation and scale change. Results show that the proposed descriptor is stable with respect to variations in imaging conditions, and reliable performance metrics prove it to be comparable and in some instances better than SIFT, the state-of-the-art in local descriptors.

© 2007 Optical Society of America

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References

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  1. H. P. Moravec, "Towards automatic visual obstacle avoidance," in IJCAI, pp. 584 (1977).
  2. L. Trujillo and G. Olague, "Synthesis of interest point detectors through genetic programming, " in Proceedings from GECCO 2006, M. Cattolico, ed., (ACM Press 2006), Vol. 1, pp. 887-894.
  3. L. Trujillo and G. Olague, "Using Evolution to learn how to perform interest point detection," in Proceedings from ICPR 2006, X.Y. Tang et al., eds., (IEEE 2006), Vol. 1, pp. 211-214.
  4. D. G. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int. J. Comput. Vision 2, 91-110 (2004).
    [CrossRef]
  5. C. Schmid and K. Mikolajczyk, "A performance evaluation of local descriptors," IEEE Transactions on PatternAnalysis and Machine Intelligence. 27, 1615-1630 (2005).
    [CrossRef]
  6. K. Falconer, Fractal geometry, Mathematical Foundations and Applications (Wiley, 1990).
  7. J. Lévy Véhel, "Fractal approaches in Signal Processing," Fractals 3, 755-775 (1995).
    [CrossRef]
  8. P. Legrand and J. Lévy Véhel, "Local regularity-based interpolation," in WAVELET X, Part of SPIE’s Symposium on Optical Science and Technology, SPIE 5207 (2003).
  9. P. Legrand, "Debruitage et interpolation par analyse de la regularite Hölderienne. Application a la modelisation du frottement pneumatique-chaussee," Ph. D. thesis, Université de Nantes (2004).
  10. C. Tricot, Curves and Fractal Dimension (Springer-Verlag 1995).
    [CrossRef]
  11. K. Mikolajczyk and C. Schmid, "Scale and affine invariant interest point detectors," Int. J. Comput. Vision 1, 63-86 (2004).
    [CrossRef]
  12. Visual Geometry Group: http://www.robots.ox.ac.uk/ vgg/research/

2005 (1)

C. Schmid and K. Mikolajczyk, "A performance evaluation of local descriptors," IEEE Transactions on PatternAnalysis and Machine Intelligence. 27, 1615-1630 (2005).
[CrossRef]

2004 (2)

D. G. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int. J. Comput. Vision 2, 91-110 (2004).
[CrossRef]

K. Mikolajczyk and C. Schmid, "Scale and affine invariant interest point detectors," Int. J. Comput. Vision 1, 63-86 (2004).
[CrossRef]

1995 (1)

J. Lévy Véhel, "Fractal approaches in Signal Processing," Fractals 3, 755-775 (1995).
[CrossRef]

Lowe, D. G.

D. G. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int. J. Comput. Vision 2, 91-110 (2004).
[CrossRef]

Mikolajczyk, K.

C. Schmid and K. Mikolajczyk, "A performance evaluation of local descriptors," IEEE Transactions on PatternAnalysis and Machine Intelligence. 27, 1615-1630 (2005).
[CrossRef]

K. Mikolajczyk and C. Schmid, "Scale and affine invariant interest point detectors," Int. J. Comput. Vision 1, 63-86 (2004).
[CrossRef]

Schmid, C.

C. Schmid and K. Mikolajczyk, "A performance evaluation of local descriptors," IEEE Transactions on PatternAnalysis and Machine Intelligence. 27, 1615-1630 (2005).
[CrossRef]

K. Mikolajczyk and C. Schmid, "Scale and affine invariant interest point detectors," Int. J. Comput. Vision 1, 63-86 (2004).
[CrossRef]

Analysis and Machine Intelligence. (1)

C. Schmid and K. Mikolajczyk, "A performance evaluation of local descriptors," IEEE Transactions on PatternAnalysis and Machine Intelligence. 27, 1615-1630 (2005).
[CrossRef]

Fractals (1)

J. Lévy Véhel, "Fractal approaches in Signal Processing," Fractals 3, 755-775 (1995).
[CrossRef]

Int. J. Comput. Vision (2)

K. Mikolajczyk and C. Schmid, "Scale and affine invariant interest point detectors," Int. J. Comput. Vision 1, 63-86 (2004).
[CrossRef]

D. G. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int. J. Comput. Vision 2, 91-110 (2004).
[CrossRef]

Other (8)

Visual Geometry Group: http://www.robots.ox.ac.uk/ vgg/research/

P. Legrand and J. Lévy Véhel, "Local regularity-based interpolation," in WAVELET X, Part of SPIE’s Symposium on Optical Science and Technology, SPIE 5207 (2003).

P. Legrand, "Debruitage et interpolation par analyse de la regularite Hölderienne. Application a la modelisation du frottement pneumatique-chaussee," Ph. D. thesis, Université de Nantes (2004).

C. Tricot, Curves and Fractal Dimension (Springer-Verlag 1995).
[CrossRef]

K. Falconer, Fractal geometry, Mathematical Foundations and Applications (Wiley, 1990).

H. P. Moravec, "Towards automatic visual obstacle avoidance," in IJCAI, pp. 584 (1977).

L. Trujillo and G. Olague, "Synthesis of interest point detectors through genetic programming, " in Proceedings from GECCO 2006, M. Cattolico, ed., (ACM Press 2006), Vol. 1, pp. 887-894.

L. Trujillo and G. Olague, "Using Evolution to learn how to perform interest point detection," in Proceedings from ICPR 2006, X.Y. Tang et al., eds., (IEEE 2006), Vol. 1, pp. 211-214.

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Figures (4)

Fig. 1.
Fig. 1.

Hölderian envelope of signal f at point x0.

Fig. 2.
Fig. 2.

Estimating the Hölder exponent with oscillations. Left: the region of interest λ, and three of the seven neighborhoods around point t, when r = 1,2, ⋯,7. Center: the neighborhood of radius τ5 = 32 pixels, with base = 2. Right: computing the supremum of the differences within radius τ5, where d denotes the Euclidian distance.

Fig. 3.
Fig. 3.

Descriptor building process. First, a region detector extrats a set Λ of interesting regions. Then, ∀λ ∈ Λ we compute a decriptor δλ . A descriptor contains the Hölder exponent at the region center (x λ, y λ), and of 32 points on the perimeter of four concentric rings, each ring with radii of 1 4 s λ , 1 2 s λ , 3 4 s λ and s λ respectively.

Fig. 4.
Fig. 4.

Columns, left to right: 1) Rotation (36 images in sequence), 2) Illumination change (10 images), 3) JPEG compression (6 images), and 4) Scale change (first 6 images of sequence). Rows, top to bottom: 1) Reference image, 2) Test Image, 3) Performance between test and reference with Hölder in green and SIFT in red, plotting Recall vs. 1-Precision, 4) & 5) Average performance on the complete image sequence for SIFT and Hölder respectively (y-axis with Recallin blue and 1-Precision in green and threshold on x-axis).

Equations (3)

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x B x 0 η , f ( x ) P ( x x 0 ) c x x 0 s .
f ( t ) f ( t ) c t t α p .
os c τ ( t ) = sup t t τ f ( t ) inf t t τ f ( t ) = sup t , t [ t τ , t + τ ] f ( t ) f ( t ) .

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