Journal of Mathematical Imaging and Vision

, Volume 61, Issue 3, pp 292–309 | Cite as

Shearlet Features for Pedestrian Detection

  • Lienhard PfeiferEmail author


A long-time, hand-crafted features governed by a directional image analysis have been the base for the best performing pedestrian detection algorithms. In the past few years, approaches using convolutional neural networks have taken over the leadership concerning detection quality. We investigate in which way shearlets can be used for an improved hand-crafted feature computation in order to reduce the gap to CNNs. Shearlets are a relatively new mathematical framework for multiscale signal analysis, which can be seen as an extension of the wavelet framework. Shearlets are designed to capture directional information and can therefore be used for detecting the orientation of edges in images. We use this characteristic to compute image features with high informative content for pedestrian detection. Furthermore, we provide experimental results using these features and show that they outperform the results obtained by the currently best performing hand-crafted features for pedestrian detection.


Shearlets Multiscale image analysis Image features Pedestrian detection 



  1. 1.
    Appel, R., Fuchs, T., Dollár, P., Perona, P.: Quickly boosting decision trees—pruning underachieving features early. In: ICML (3), JMLR Proceedings, vol. 28, pp. 594–602. (2013)Google Scholar
  2. 2.
    Benenson, R., Mathias, M., Tuytelaars, T., Gool, L.V.: Seeking the strongest rigid detector. In: 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3666–3673 (2013).
  3. 3.
    Benenson, R., Omran, M., Hosang, J., Schiele, B.: Ten years of pedestrian detection, what have we learned? In: ECCV, CVRSUAD Workshop (2014)Google Scholar
  4. 4.
    Brazil, G., Yin, X., Liu, X.: Illuminating pedestrians via simultaneous detection & segmentation. In: Proceedings of the IEEE International Conference on Computer Vision, Venice, Italy (2017)Google Scholar
  5. 5.
    Cai, Z., Fan, Q., Feris, R.S., Vasconcelos, N.: A unified multi-scale deep convolutional neural network for fast object detection. In: Computer Vision—ECCV 2016—14th European Conference, Amsterdam, The Netherlands, October 11–14, 2016, Proceedings, Part IV, pp. 354–370 (2016).
  6. 6.
    Cai, Z., Saberian, M.J., Vasconcelos, N.: Learning complexity-aware cascades for deep pedestrian detection. In: 2015 IEEE International Conference on Computer Vision, ICCV 2015, Santiago, Chile, December 7–13, 2015, pp. 3361–3369 (2015).
  7. 7.
    Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8(6), 679–698 (1986).
  8. 8.
    Chui, C.K.: An Introduction to Wavelets. Wavelet analysis and its applications. Academic Press, Cambridge (1992)Google Scholar
  9. 9.
    Dalal, N., Triggs, B.: Histograms of oriented gradients for human detection. In: CVPR, pp. 886–893 (2005)Google Scholar
  10. 10.
    Dollár, P.: Piotr’s Computer Vision Matlab Toolbox (PMT). Accessed 7 July 2017
  11. 11.
    Dollár, P., Appel, R., Belongie, S., Perona, P.: Fast feature pyramids for object detection. IEEE Trans. Pattern Anal. Mach. Intell. 36(8), 1532–1545 (2014). CrossRefGoogle Scholar
  12. 12.
    Dollár, P., Belongie, S., Perona, P.: The fastest pedestrian detector in the west. In: Proceedings of BMVC, pp. 68.1–11 (2010).
  13. 13.
    Dollár, P., Tu, Z., Perona, P., Belongie, S.: Integral channel features. In: Proceedings of BMVC, pp. 91.1–91.11 (2009).
  14. 14.
    Dollár, P., Wojek, C., Schiele, B., Perona, P.: Pedestrian detection: A benchmark. In: CVPR (2009)Google Scholar
  15. 15.
    Dollár, P., Wojek, C., Schiele, B., Perona, P.: Pedestrian detection: an evaluation of the state of the art. IEEE Trans. Pattern Anal. Mach. Intell. 34(4), 743–761 (2012). CrossRefGoogle Scholar
  16. 16.
    Du, X., El-Khamy, M., Lee, J., Davis, L.S.: Fused DNN: a deep neural network fusion approach to fast and robust pedestrian detection. CoRR. arXiv:1610.03466 (2016)
  17. 17.
    Duval-Poo, M.A., Odone, F., Vito, E.D.: Edges and corners with shearlets. IEEE Trans. Image Process. 24(11), 3768–3780 (2015). MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Easley, G.R., Labate, D.: Shearlets: Multiscale Analysis for Multivariate Data. In: Kutyniok, G., Labate, D. (eds.) Image processing using shearlets, pp. 283–325. Birkhäuser, Boston (2012). Google Scholar
  19. 19.
    Grohs, P., Keiper, S., Kutyniok, G., Schfer, M.: \(\alpha \)-molecules. Appl. Comput. Harmon. Anal. 41(1), 297–336 (2016). (Sparse representations with applications in imaging science, data analysis and beyond)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Guo, K., Kutyniok, G., Labate, D.: Sparse multidimensional representations using anisotropic dilation and shear operators. In: Wavelets and splines: Athens 2005, Mod. Methods Math., pp. 189–201. Nashboro Press, Brentwood, TN (2006)Google Scholar
  21. 21.
    Guo, K., Labate, D., Lim, W.Q.: Edge analysis and identification using the continuous shearlet transform. Appl. Comput. Harmon. Anal. 27(1), 24–46 (2009). MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Guo, K., Labate, D., Lim, W.Q., Weiss, G., Wilson, E.: Wavelets with composite dilations. Electron. Res. Announc. Am. Math. Soc. 10(9), 78–87 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Häuser, S.: Shearlet coorbit spaces, shearlet transforms and applications in imaging. Ph.D. thesis, Technische Universität Kaiserslautern (2014)Google Scholar
  24. 24.
    Häuser, S., Steidl, G.: Fast finite shearlet transform: a tutorial. arXiv:1202.1773 (2014)
  25. 25.
    Kittipoom, P., Kutyniok, G., Lim, W.Q.: Construction of compactly supported shearlet frames. Constr. Approx. 35(1), 21–72 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Kutyniok, G., Labate, D.: Construction of regular and irregular shearlet frames. J. Wavelet Theory Appl. 1(1), 1–10 (2007)Google Scholar
  27. 27.
    Kutyniok, G., Labate, D.: Introduction to shearlets. In: Kutyniok, G., Labate, D. (eds.) Shearlets: Multiscale Analysis for Multivariate Data, pp. 1–38. Birkhäuser, Boston (2012). CrossRefGoogle Scholar
  28. 28.
    Kutyniok, G., Lim, W.Q., Reisenhofer, R.: Shearlab 3d: Faithful digital shearlet transforms based on compactly supported shearlets. ACM Trans. Math. Softw. 42(1), 5:1–5:42 (2016). MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Kutyniok, G., Shahram, M., Zhuang, X.: Shearlab: a rational design of a digital parabolic scaling algorithm. SIAM J. Imaging Sci. 5(4), 1291–1332 (2012). MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Labate, D., Lim, W.Q., Kutyniok, G., Weiss, G.: Sparse multidimensional representation using shearlets. In: Papadakis, M., Laine, A.F., Unser, M.A. (eds.) Wavelets XI, SPIE proceedings, vol. 5914, pp. 254–262 (2005).
  31. 31.
    Lee, J.M.: Smooth Maps. In: Introduction to Smooth Manifolds, 1st edn., pp. 30–59. Springer, New York (2003).
  32. 32.
    Li, J., Liang, X., Shen, S., Xu, T., Yan, S.: Scale-aware fast r-cnn for pedestrian detection. CoRR. arXiv:1510.08160 (2015)
  33. 33.
    Li, S., Shen, Y.: Shearlet frames with short support. CoRR. arXiv:1101.4725 (2011)
  34. 34.
    Lim, W.Q.: The discrete shearlet transform: a new directional transform and compactly supported shearlet frames. IEEE Trans. Image Process. 19(5), 1166–1180 (2010). MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, San Diego (1999)zbMATHGoogle Scholar
  36. 36.
    Mallat, S., Zhong, S.: Characterization of signals from multiscale edges. IEEE Trans. Pattern Anal. Mach. Intell. 14(7), 710–732 (1992). CrossRefGoogle Scholar
  37. 37.
    Meyer, Y.: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. American Mathematical Society, Providence (2001)CrossRefzbMATHGoogle Scholar
  38. 38.
    Nam, W., Dollár, P., Han, J.H.: Local decorrelation for improved pedestrian detection. In: Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, December 8–13 2014, Montreal, Quebec, Canada, pp. 424–432 (2014)Google Scholar
  39. 39.
    Ohn-Bar, E., Trivedi, M.M.: To boost or not to boost? on the limits of boosted trees for object detection. In: IEEE International Conference on Pattern Recognition (2016)Google Scholar
  40. 40.
    Ouyang, W., Zhou, H., Li, H., Li, Q., Yan, J., Wang, X.: Jointly learning deep features, deformable parts, occlusion and classification for pedestrian detection. IEEE Trans. Pattern Anal. Mach. Intell. PP(99), 1–1 (2017).
  41. 41.
    Paisitkriangkrai, S., Shen, C., van den Hengel, A.: Strengthening the effectiveness of pedestrian detection with spatially pooled features. In: European Conference on Computer Vision (ECCV’14), Zurich (2014)Google Scholar
  42. 42.
    Papageorgiou, C., Poggio, T.: A trainable system for object detection. Int. J. Comput. Vision 38(1), 15–33 (2000). CrossRefzbMATHGoogle Scholar
  43. 43.
    Schwartz, W.R., da Silva, R.D., Davis, L.S., Pedrini, H.: A novel feature descriptor based on the shearlet transform. In: ICIP, pp. 1033–1036. IEEE (2011)Google Scholar
  44. 44.
    Tian, Y., Luo, P., Wang, X., Tang, X.: Deep learning strong parts for pedestrian detection. In: 2015 IEEE International Conference on Computer Vision (ICCV), pp. 1904–1912 (2015).
  45. 45.
    Viola, P.A., Jones, M.J.: Rapid object detection using a boosted cascade of simple features. In: 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2001), 8–14 December 2001, Kauai, HI, USA, pp. 511–518 (2001).
  46. 46.
    Yi, S., Labate, D., Easley, G.R., Krim, H.: A shearlet approach to edge analysis and detection. IEEE Trans. Image Process. 18(5), 929–941 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Zhang, L., Lin, L., Liang, X., He, K.: Is faster R-CNN doing well for pedestrian detection? In: Computer Vision—ECCV 2016—14th European Conference, Amsterdam, The Netherlands, October 11–14, 2016, Proceedings, Part II, pp. 443–457 (2016).
  48. 48.
    Zhang, S., Bauckhage, C., Cremers, A.B.: Informed haar-like features improve pedestrian detection. In: 2014 IEEE Conference on Computer Vision and Pattern Recognition, pp. 947–954 (2014).
  49. 49.
    Zhang, S., Benenson, R., Omran, M., Hosang, J., Schiele, B.: How far are we from solving pedestrian detection? In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1259–1267 (2016).
  50. 50.
    Zhang, S., Benenson, R., Schiele, B.: Filtered channel features for pedestrian detection. In: CVPR (2015)Google Scholar

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Authors and Affiliations

  1. 1.Department of Mathematics/Computer SciencePhilipps-University of MarburgMarburgGermany
  2. 2.ITK Engineering GmbH, Computer Vision TeamLollarGermany

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