Pattern Analysis and Applications

, Volume 19, Issue 3, pp 621–629 | Cite as

Hyperplane arrangements for the fast matching and classification of visual landmarks

Theoretical Advances


Many robotics and mechatronics systems rely on a fast analysis of visual landmarks. Recently, binary feature representations of the popular SIFT and SURF landmarks have been proposed that offer large speed improvements and low memory consumption at high accuracy. In this paper, we compare a binarisation based on median-centred hyperplanes to the dominating approach of random hyperplanes. We describe the algorithms in a joint taxonomy and show that the kernel for median-centred hyperplanes satiesfies Mercer’s condition. Speed and accuracy are benchmarked in a registration and classification task. Both methods achieve the same dramatic speedup in kernel evaluation. But we show that median-centred hyperplanes are faster in binarisation, find better matches and generalise better over pose and individual variation in the classification.


Feature extraction SIFT Random projections 


  1. 1.
    André B, Vercauteren T, Buchner AM, Wallace MB, Ayache N (2011) Retrieval evaluation and distance learning from perceived similarity between endomicroscopy videos. In: Medical Image Computing and Computer Assisted Intervention (MICCAI), LNCS. Springer, Heidelberg Google Scholar
  2. 2.
    Anvaripour M, Ebrahimnezhad H (2013) Accurate object detection using local shape descriptors. Pattern Anal Appl Google Scholar
  3. 3.
    Bay H, Ess A, Tuytelaars T, van Gool L (2006) SURF: speeded up robust features. Computer Vision Image Underst (CVIU) 110(3):346–359CrossRefGoogle Scholar
  4. 4.
    Chandrasekhar V, Takacs G, Chen DM, Tsai SS, Singh JP, Girod B (2009) Transform coding of image feature descriptors. In: visual Communication and Image Processing (VCIP)Google Scholar
  5. 5.
    Chen H, Sun D, Yang J (2009) Global localization of multirobot formations using ceiling vision SLAM strategy. Mechatronics 19(5):617–628CrossRefGoogle Scholar
  6. 6.
    Choras M, Kozik R (2013) Contactless palmprint and knuckle biometrics for mobile devices. Pattern Anal Appl 15:73–85MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297MATHGoogle Scholar
  8. 8.
    Dani A, Fischer N, Kan Z, Dixon W (2012) Globally exponentially stable observer for vision-based range estimation. Mechatronics 22(4):381–389CrossRefGoogle Scholar
  9. 9.
    Diephuis M, Voloshynovskiy S, Koval O, Beekhof F (2011) Statistical Analysis of Binarized SIFT Descriptors. In: International Symposium on Image and Signal Processing and Analysis (ISPA) Google Scholar
  10. 10.
    Dong Y, Gao S, Tao K, Liu J, Wang H (2013) Performance evaluation of early and late fusion methods for generic semantics indexing. Pattern Anal ApplGoogle Scholar
  11. 11.
    Donoho DL, Tanner J (2010) Counting the faces of randomly-projected hypercubes and orthants, with applications. Discrete Comput Geom 43:522–541MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Edelkamp S, Stommel M (2012) The bitvector machine: a fast and robust machine learning algorithm for non-linear problems. In: Flach PA, Bie TD, Cristianini N (eds) European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), pp 175–190. Springer .Google Scholar
  13. 13.
    Gong Y, Lazebnik S (2011) Iterative quantization: a procrustean approach to learning binary codes. In: Computer Vision and Pattern Recognition (CVPR) Google Scholar
  14. 14.
    Hsu CW, Lin CJ (2002) A comparison of methods for multi-class support vector machines. IEEE Trans Neural Networks 13:415–425CrossRefGoogle Scholar
  15. 15.
    Jain V, Learned-Miller E (2010) Fddb: A benchmark for face detection in unconstrained settings. Tech Rep UM-CS-2010-009, University of Massachusetts, AmherstGoogle Scholar
  16. 16.
    Jarrett K, Kavukcuoglu K, Ranzato M, LeCun Y (2009) What is the best multi-stage architecture for object recognition? In: International Conference on Computer Vision (ICCV) Google Scholar
  17. 17.
    Ke Y, Sukthankar R (2004) PCA-SIFT: A More Distinctive Representation for Local Image Descriptors. Computer Vision and Pattern Recognition (CVPR) 2:506–513Google Scholar
  18. 18.
    Kuo YH, Lin HT, Cheng WH, Yang YH, Hsu WH (2011) Unsupervised auxiliary visual words discovery for large-scale image object retrieval. In: IEEE Comp Vision Pattern Recognit (CVPR) Google Scholar
  19. 19.
    Lee IH, Chai TS (2013) Accurate registration using adaptive block processing for multi-spectral images. Circuits Syst Video Technol, IEEE Trans on PP(99), 1–1 Google Scholar
  20. 20.
    Lowe DG (1999) Object recognition from local scale-invariant features. In: International Converence on Computer Vision (ICCV), pp 1150–1157 Google Scholar
  21. 21.
    Lyu S (2005) Mercer kernels for object recognition with local features. Comp Vision Pattern Recognit (CVPR) 2:223–229Google Scholar
  22. 22.
    Makar M, Chang CL, Chen D, Tsai SS, Girod B (2009) Compression of image patches for local feature extraction. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) pp. 821–824. DOI
  23. 23.
    Mikolajczyk K, Leibe B, Schiele B (2005) Local features for object class recognition. In: International Conference on Computer Vision (ICCV’05) Google Scholar
  24. 24.
    Mikolajczyk K, Leibe B, Schiele B (2006) Multiple object class detection with a generative model. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR’06) Google Scholar
  25. 25.
    Mikolajczyk K, Schmid C (2005) A performance evaluation of local descriptors. IEEE Trans. Pattern Anal Mach Intell 27(10):1615–1630CrossRefGoogle Scholar
  26. 26.
    Minh HQ, Niyogi P, Yao Y (2006) Mercer’s theorem, feature maps, and smoothing. In: The 19th Annual Conference on Learning Theory (COLT), pp 154–168 Google Scholar
  27. 27.
    Mühling M, Ewerth R, Freisleben B (2011) On the spatial extents of SIFT descriptors for visual concept detection. In: International Conference on Computer Vision Systems (ICVS), pp 71–80. Springer, Berlin, HeidelbergGoogle Scholar
  28. 28.
    Opelt A, Fussenegger M, Pinz A, Auer P (2004) Weak hypotheses and boosting for generic object detection and recognition. In: European Conference on Computer Vision (ECCV), pp 71–84 Google Scholar
  29. 29.
    Pavani SK, Delgado-Gomez D, Frangi AF (2012) Gaussian weak classifiers based on co-occurring haar-like features for face detection. Pattern Analy Appl Google Scholar
  30. 30.
    Phillips PJ, Rauss PJ, Der SZ (1996) FERET (Face Recognition Technology) recognition algorithm development and test results. Tech Rep 995, Army Research Lab Google Scholar
  31. 31.
    Rifkin R, Klautau A (2004) In defence of one-vs-all classification. J Mach Learn Res 5:101–141MathSciNetMATHGoogle Scholar
  32. 32.
    Roy S, Sun Q (2007) Robust hash for detecting and localizing image tampering. In: Proc. IEEE Int. Conf. on Image Processing, pp 117–120. San Antonio, TX Google Scholar
  33. 33.
    Savicky P, Robnik-Sikonja M (2008) Learning random numbers: a MATLAB anomaly. Appl Artif Intell 22(3):254–265CrossRefGoogle Scholar
  34. 34.
    Sleumer NH (2000) Hyperplane arrangements. construction, visualization and application. Ph.D. thesis, Technische Wissenschaften ETH Zürich, Nr. 13502 Google Scholar
  35. 35.
    Stanley RP (2007) An introduction to hyperplane arrangements, IAS/Park City Math. Ser., vol. 13, pp 389–496. Amer Math SocGoogle Scholar
  36. 36.
    Stommel M, Herzog O (2009) Binarising SIFT-descriptors to reduce the curse of dimensionality in histogram-based object recognition. In: Slezak D, Pal SK, Kang BH, Gu J, Kurada H, Kim TH (eds) Signal Processing, Image Processing and Pattern Recognition, pp 320–327. Springer Google Scholar
  37. 37.
    Stommel M, Langer M, Herzog O, Kuhnert KD (2011) A fast, robust and low bit-rate representation for SIFT and SURF features. In: Proc. IEEE International Symposium on Safety, Security, and Rescue Robotics, pp 278n++-283 Google Scholar
  38. 38.
    Strecha C, Bronstein AM, Bronstein MM, Fua P (2010) LDAHash: Improved matching with smaller descriptors. In: EPFL-REPORT-152487 Google Scholar
  39. 39.
    Su Y, Jurie F (2011) Visual word disambiguation by semantic contexts. In: International Conference on Computer Vision (ICCV) Google Scholar
  40. 40.
    Vapnik VN, Chervonenkis AY (1974) Theory of pattern recognition [in Russian]. Nauka, USSRMATHGoogle Scholar
  41. 41.
    Viola P, Jones MJ (2004) Robust real-time face detection. Intern J Comp Vision 57(2):137–154CrossRefGoogle Scholar
  42. 42.
    Wiedemeyer T, Stommel M, Herzog O (2011) Wide range face pose estimation by modelling the 3D arrangement of robustly detectable sub-parts. In: Intl. Conf. on Computer Analysis of Images and Patterns (CAIP), pp 237–244. Springer Google Scholar
  43. 43.
    Winder SAJ, Brown M (2007) Learning Local Image Descriptors. In: IEEE Computer Vision and Pattern Recognition (CVPR)Google Scholar
  44. 44.
    Yang L, Jin R, Sukthankar R, Jurie F (2008) Unifying discriminative visual codebook generation with classifier training for object category recognition. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Google Scholar
  45. 45.
    Yeo C, Ahammad P, Ramchandran K (2008) Rate-efficient visual correspondences using random projections. In: IEEE International Conference on Image Processing, pp 217–220. San Diego, CAGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.School of EngineeringAuckland University of TechnologyAucklandNew Zealand
  2. 2.Visual Information TechnologiesJacobs University BremenBremenGermany
  3. 3.Mechatronics GroupUniversity of AucklandAucklandNew Zealand

Personalised recommendations