SURF : Speeded-Up Robust Features

1. CPSC 643, Presentation 2 SURF: Speeded-Up Robust Features Herbert Baya, Andreas Essa, Tinne Tuytellaresb, Luc Van Goola,b aETH Zurich bK. U. Leuven, ESAT-PSI Sternwartstrasse 7 Kasteel Arenberg 10 CH-8092 Zurich B-3001 Leuven Switzerland Belgium Computer Vision and Image Understanding (CVIU) Vol.110, No.3, pp. 346-359, 2008.

2. Mostly Related Works • Harris Corner Detector - Harris 1988 • Laplacian of Gaussian - Lindeberg 1998 • Harris - Laplace Detector- Mikolajczyk 2001 • Difference of Gaussian - Lowe 2004

3. Mostly Related Works • Harris Corner Detector - Harris 1988 • Laplacian of Gaussian - Lindeberg 1998 • Harris - Laplace Detector- Mikolajczyk 2001 • Difference of Gaussian - Lowe 2004

4. Mostly Related Works • Harris Corner Detector - Harris 1988 • Laplacian of Gaussian - Lindeberg 1998 • Harris - Laplace Detector- Mikolajczyk 2001 • Difference of Gaussian - Lowe 2004

5. Mostly Related Works • Harris Corner Detector - Harris 1988 • Laplacian of Gaussian - Lindeberg 1998 • Harris - Laplace Detector - Mikolajczyk 2001 • Difference of Gaussian - Lowe 2004

6. Mostly Related Works • Harris Corner Detector - Harris 1988 • Laplacian of Gaussian - Lindeberg 1998 • Harris - Laplace Detector - Mikolajczyk 2001 • Difference of Gaussian- Lowe 2004

7. Other Related Works • Salient Region Detector - Kadir 2001 • Edge-based Region Detector - Jurie 2004

8. Motivation • Using Laplacian of Gaussian, one could obtain scale invariant features. • Lowe uses difference of Gaussian to approximate Laplacian of Gaussian. • This paper uses Hessian - Laplacian to approximate Laplacian of Gaussian, to improve calculation speed.

9. Methodology • Using integral images for major speed up • Integral Image (summed area tables) is an intermediate representation for the image and contains thesum of gray scale pixel values of image.

10. Detection • Hessian-based interest point localization • Lxx(x,y,σ) is the Laplacian of Gaussian of the image. • It is the convolution of the Gaussian second order derivative with the image. • Lindeberg showed Gaussian function is optimal for scale-space analysis. • This paper use Dxx to approximateLxx.

11. Detection Approximated second order derivatives with box filters. Scale analysis with constant image size

12. Description Orientation Assignment x response y response Side length = 4s Cost 6 operation to compute the response Circular neighborhood of radius 6s around the interest point (s = the scale at which the point was detected)

13. Description • Dominant orientation • The Haar wavelet responses are represented as vectors • Sum all responses withina sliding orientationwindow covering an angle of 60 degree • The two summed response yield a new vector • The longest vector is the dominant orientation

14. Description • Split the interest region(20s x 20s) up into 4 x 4 square sub-regions. • CalculateHaar waveletresponse dx and dyand weight the response with a Gaussian kernel. • Sum the response over each sub-region for dxand dy, then sum the absolute value of resp-onse. • Normalize the vector into unit length

15. Matching Fast indexing through the sign of the Laplacian for the underlying interest point The sign of trace of the Hessian matrix Trace = Lxx + Lyy

16. Experiments

17. Experiments

18. Experiments

19. Analysis and Conclusion • SURF isfaster than SIFT by 3 times, and has recall precision not worse than SIFT. • SURF is good at handling image with blurring or rotation. • SURF is poor athandling image with viewpoint or illumination change.