We validate the usage of augmented 2D shape-size pattern spectra, calculated on arbitrary connected
regions. The evaluation is performed on MSER regions and competitive performance with SIFT descriptors
achieved in a simple retrieval system, by combining the local pattern spectra with normalized central
moments. An additional advantage of the proposed descriptors is their size: being half the size of SIFT,
they can handle larger databases in a time-efficient manner. We focus in this paper on presenting the challenges
faced when transitioning from global pattern spectra to the local ones. An exhaustive study on the
parameters and the properties of the newly constructed descriptor is offered, as well as performance results
from preliminary experiments, validating the usage of the descriptor. We also consider possible improvements
to the quality and computation efficiency of the proposed local descriptors.
If the inline PDF is not rendering correctly, you can download the PDF file here.
 R. Arandjelovic and A. Zisserman. Three things everyone should know to improve object retrieval. In Computer Vision and
Pattern Recognition (CVPR), 2012 IEEE Conference on, pages 2911–2918. IEEE, 2012.
 H. Bay, A. Ess, T. Tuytelaars, and L. Van Gool. Speeded-up robust features (SURF). Computer vision and image understanding,
 J. A. Benediktsson, M. Pesaresi, and K. Arnason. Classification and Feature Extraction for Remote Sensing Images from Urban
Areas based on Morphological Transformations. IEEE Transactions on Geoscience and Remote Sensing, 41(9):1940–1949,
 P. Bosilj, E. Kijak, M. H. F. Wilkinson, and S. Lefèvre. Short local descriptors from 2D connected pattern spectra. To appear
in ICIP 2015.
 Petra Bosilj, Michael HFWilkinson, Ewa Kijak, and Sébastien Lefèvre. Local 2d pattern spectra as connected region descriptors.
In Mathematical Morphology and Its Applications to Signal and Image Processing, pages 182–193. Springer, 2015.
 E. J. Breen and R. Jones. Attribute openings, thinnings, and granulometries. Computer Vision and Image Understanding,
 K. Dalla Mura, J. A. Benediktsson, B. Waske, and L. Bruzzone. Morphological Attribute Profiles for the Analysis of Very High
Resolution Images. IEEE Transactions on Geoscience and Remote Sensing, 48(10):3747–3762, 2010.
 Mayur Datar, Nicole Immorlica, Piotr Indyk, and Vahab S. Mirrokni. Locality-sensitive Hashing Scheme Based on P-stable
Distributions. In Proceedings of the Twentieth Annual Symposium on Computational Geometry, SCG ’04, pages 253–262,
 J. H. Friedman, J. L. Bentley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM
Transactions on Mathematical Software (TOMS), 3(3):209–226, 1977.
 M.-K. Hu. Visual pattern recognition by moment invariants. Information Theory, IRE Transactions on, 8(2):179–187, 1962.
 R. Jones. Component trees for image filtering and segmentation. In IEEE Workshop on Nonlinear Signal and Image Processing,
E. Coyle, Ed., Mackinac Island, 1997.
 Y. Ke and R. Sukthankar. PCA-SIFT: A more distinctive representation for local image descriptors. In Computer Vision and
Pattern Recognition, 2004. CVPR 2004. Proceedings of the 2004 IEEE Computer Society Conference on, volume 2, pages II–
506. IEEE, 2004.
 H. Lejsek, B. Þ. Jónsson, and L. Amsaleg. NV-Tree: Nearest Neighbors at the Billion Scale. In Proceedings of the 1st ACM
International Conference on Multimedia Retrieval, ICMR ’11, pages 54:1–54:8, 2011.
 D. G. Lowe. Distinctive image features from scale-invariant keypoints. International journal of computer vision, 60(2):91–
 P. Maragos. Pattern spectrum and multiscale shape representation. Pattern Analysis and Machine Intelligence, IEEE Transactions
on, 11(7):701–716, 1989.
 J. Matas, O. Chum, M. Urban, and T. Pajdla. Robust wide-baseline stereo from maximally stable extremal regions. Image
and vision computing, 22(10):761–767, 2004.
 K. Mikolajczyk and C. Schmid. A performance evaluation of local descriptors. Pattern Analysis and Machine Intelligence,
IEEE Transactions on, 27(10):1615–1630, 2005.
 K. Mikolajczyk, T. Tuytelaars, C. Schmid, A. Zisserman, J. Matas, F. Schaffalitzky, T. Kadir, and L. Van Gool. A comparison of
affine region detectors. International journal of computer vision, 65(1-2):43–72, 2005.
 M. Muja and D. G. Lowe. Fast Approximate Nearest Neighbors with Automatic Algorithm Configuration. In International
Conference on Computer Vision Theory and Application VISSAPP’09), pages 331–340. INSTICC Press, 2009.
 E. Mwebaze, P. Schneider, F.-M. Schleif, J. R. Aduwo, J. A. Quinn, S. Haase, T. Villmann, and M. Biehl. Divergence-based
classification in learning vector quantization. Neurocomputing, 74(9):1429–1435, 2011.
 D. Nistér and H. Stewénius. Linear timemaximally stable extremal regions. In Computer Vision–ECCV 2008, pages 183–196.
 G. K. Ouzounis, M. Pesaresi, and P. Soille. Differential Area Profiles: Decomposition Properties and Efficient Computation.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(8):1533–1548, 2012.
 P. Salembier, A. Oliveras, and L. Garrido. Antiextensive connected operators for image and sequence processing. Image
Processing, IEEE Transactions on, 7(4):555–570, 1998.
 G. Schaefer and M. Stich. UCID: An Uncompressed Colour Image Database. In Electronic Imaging 2004, pages 472–480.
International Society for Optics and Photonics, 2003.
 C. Schmid and R. Mohr. Object recognition using local characterization and semi-local constraints. IEEE Transactions on
Pattern Analysis and Machine Intelligence, 19(5):530–534, 1997.
 J. Sivic and A. Zisserman. Video Google: Efficient visual search of videos. In J. Ponce, M. Hebert, C. Schmid, and A. Zisserman,
editors, Toward Category-Level Object Recognition, volume 4170 of LNCS, pages 127–144. Springer, 2006.
 F. Tushabe and M. H. F. Wilkinson. Content-based image retrieval using combined 2D attribute pattern spectra. In Advances
in Multilingual and Multimodal Information Retrieval, pages 554–561. Springer, 2008.
 E. R. Urbach, J. B. T. M. Roerdink, and M. H. F. Wilkinson. Connected shape-size pattern spectra for rotation and scaleinvariant
classification of gray-scale images. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 29(2):272–
 E. R. Urbach and M. H. F. Wilkinson. Shape-only granulometries and grey-scale shape filters. In Proc. Int. Symp. Math.
Morphology (ISMM), volume 2002, pages 305–314, 2002.
 A. Vedaldi and B Fulkerson. VLFeat: An Open and Portable Library of Computer Vision Algorithms. http://www.vlfeat.org/,
 M. A. Westenberg, J. B. T. M. Roerdink, and M. H. F. Wilkinson. Volumetric Attribute Filtering and Interactive Visualization
using the Max-Tree Representation. IEEE Trans. Image Proc., 16:2943–2952, 2007.
 M. H. F. Wilkinson. Generalized pattern spectra sensitive to spatial information. In Pattern Recognition, International Conference
on, volume 1, pages 10021–10021. IEEE Computer Society, 2002.
 Y. Xu, T. Géraud, and L. Najman. Morphological filtering in shape spaces: Applications using tree-based image representations.
In Pattern Recognition (ICPR), 2012 21st International Conference on, pages 485–488. IEEE, 2012.
Mathematical Morphology – Theory and Applications (MMTA) is an open access, peer-reviewed, electronic journal publishing either purely theoretical advances, or new ways of applying mathematical morphology to real-world problems. MMTA serves also as a forum open to other related mathematical image processing approaches as discrete geometry, topological imaging and scale-space models.