Multimedia Tools and Applications

, Volume 76, Issue 5, pp 6993–7040 | Cite as

Comparative analysis of shape descriptors for 3D objects

  • Graciela Lara López
  • Adriana Peña Pérez Negrón
  • Angélica De Antonio Jiménez
  • Jaime Ramírez Rodríguez
  • Ricardo Imbert Paredes
Article

Abstract

One of the basic characteristics of an object is its shape. Several research areas in mathematics and computer science have taken an interest in object representation in both 2D images and 3D models, where shape descriptors are a powerful mechanism enabling the processes of classification, retrieval and comparison for object matching. In this paper, we present a literature survey of this broad field, including a comparative analysis based on the above shape descriptor processes. In view of their significance, we identified the shape descriptors implemented using the concept of visual salience. This paper gives an overview of this topic.

Keywords

Shape descriptors Matching and similarity Voxelization Pose normalization and visual salience 

References

  1. 1.
    Akgül CB (2007) Density-based shape descriptors and similarity learning for 3D object retrieval. Bo§aziçi University, Istanbul. PhD. ThesisGoogle Scholar
  2. 2.
    Akgül CB, Sankur B, Yemez Y, Schmitt F (2006) A framework for histogram-induced 3D descriptors. 14th European signal processing conference (EUSIPCO 2006). EURASIP Florence, ItalyGoogle Scholar
  3. 3.
    Akgül CB, Sankur B, Yemez Y, Schmitt F (2009) 3D model retrieval using probability density-based shape descriptors. IEEE Trans Pattern Anal Mach Intell 31(6):1117–1133CrossRefMATHGoogle Scholar
  4. 4.
    Ankerst M, Kastenmüller G, Kriegel H-P, Seidl T (1999) 3D shape histograms for similarity search and classification in spatial databases In: Hartmut GR, Papadias D, Lochovscky F (eds) Proceedings of the 6th international symposium on spatial database, vol 1651. Springer Berlin Heidelberg, Hong Kong ChinaGoogle Scholar
  5. 5.
    Atmosukarto I, Leow WK, Huang Z (2005) Feature combination and relevance feedback for 3D model retrieval. IEEE proceedings of the 11th international multimedia modelling conference. IEEE, pp 334–339Google Scholar
  6. 6.
    Bakhadyrov I, Jafari MA (1999) Inertia tensor as a way of feature vector definition for one-dimensional signatures IEEE SMC '99. Proceedings international conference on systems, man, and cybernetics, vol 2. IEEE Tokyo, pp 904–909Google Scholar
  7. 7.
    Barrios JM, Bustos B (2011) Automatic weight selection for multi-metric distances. ACM. In proceeding of the 4th international conference on similarity search and applications (SISAP’ll). ACM New York, NY, USA, pp 61–68Google Scholar
  8. 8.
    Basri R, Costa L, Geiger D, Jacobs D (1998) Determining the similarity of deformable shapes. Sci Vis Res 38:2365–2385, ElsevierCrossRefGoogle Scholar
  9. 9.
    Behley J, Steinhage V, Cremers AB (2012) Performance of histogram descriptors for the classification of 3D laser range data in urban environments IEEE. International conference on robotics and automation (ICRA). IEEE Saint Paul, MN, pp 4391–4398Google Scholar
  10. 10.
    Belongie S, Malik J, Puzicha J (2002) Shape matching and object recognition using shape contexts. IEEE Trans Pattern Anal Mach Intell 24(4):509–522CrossRefGoogle Scholar
  11. 11.
    Bespalov D, Regli WC, Shokoufandeh A (2006) Local feature extraction and matching partial objects. Comput Aided Des 38(9):1020–1037, ElsevierCrossRefMATHGoogle Scholar
  12. 12.
    Biasotti S, Giorgi D, Spanuolo M, Falcidieno B (2006) Size functions for 3D shape retrieval. In: Polthier K, Sheffer A (eds) Eurographics symposium on geometry proceessing. The Eurographics Association Cigliari, Sardinia, Italy, pp 239–242Google Scholar
  13. 13.
    Bober M (2001) MPEG-7 visual shape descriptors. IEEE Trans Circ Syst Video Technol 11(6):716–719CrossRefGoogle Scholar
  14. 14.
    Bu S, Han P, Lui Z, Han J, Lin H (2015) Local deep feature learning framework for 3D shape. Comput Graph 46:117–129CrossRefGoogle Scholar
  15. 15.
    Bustos B, Keim DA, Saupe D, Schreck T, Vranić DV (2005) Feature-based similarity search in 3D object databases. ACM Comput Surv 37(4):345–387CrossRefGoogle Scholar
  16. 16.
    Cerri A, Biasotti S, Giorgi D (2007) K-dimensional size functions for shape description and comparison. IEEE. 14th International Conference on Image Analysis and Processing, vol IEEE Modena, pp 795–800Google Scholar
  17. 17.
    Chen L, McAuley JJ, Feris RS, Caetano TS, Turk M (2009) Shape classification through structured learning of matching measures. Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on. IEEE Miami, FL., pp 365–372Google Scholar
  18. 18.
    Chen D-Y, Tian X-P, Shen Y-T, Ouhyoung M (2003) On visual similarity based 3D model retrieval. The Eurographics Association and Blackwell Publishers 22(3):223–232Google Scholar
  19. 19.
    Chung FRK (1997) Spectral graph theory. Regional conference series in mathematics American mathematical society. Published for the conference board of the mathematical sciences Washington DCGoogle Scholar
  20. 20.
    Dorai C, Jain AK (1997) Shape spectrum based view grouping and matching of 3D free-form objects. IEEE Trans Pattern Anal Mach Intell 19(10):1139–1146CrossRefGoogle Scholar
  21. 21.
    Dos Santos FJ (2007) Retrieval of 3D models using partial matching Universidade Tecnica de Lisboa. PhD. ThesisGoogle Scholar
  22. 22.
    Dutağaci H, Sankur B, Yemez Y (2005) Transform-based methods for Indexing and retrieval of 3D objects. IEEE proceedings of the fifth international conference on 3D - digital imaging and modeling. computer society. (3DIM’05). IEEE Washington DC, USA., pp 188–195Google Scholar
  23. 23.
    EINaghy H, Hamad S, Khalifa E (2013) Taxonomy for 3D content-based object retrieval methods. IJARRAS 14(2):412–446Google Scholar
  24. 24.
    El Wardani D, El Mostafa D, Tadonki C (2012) Improving 3D shape retrieval methods based on Bag-of-feature approach by using local codebooks. Int J Futur Gener Commun Netw 5(4):29–38Google Scholar
  25. 25.
    El-Mehalawi M, Miller RA (2003) A database system of mechanical components based on geometric and topological similarity. Comput Aided Des 35:83–94, ElsevierCrossRefGoogle Scholar
  26. 26.
    Funkhouser T, Min P, Kazhdan M, Chen J, Halderman A, Dobkin D (2003) A search engine for 3D models. ACM Trans Graph 22(1):83–105CrossRefGoogle Scholar
  27. 27.
    Gal R, Cohen-Or D (2006) Salient geometric features for partial shape matching and similarity. ACM Trans Graph 25(1):130–150CrossRefGoogle Scholar
  28. 28.
    Godil A, Wagan AI (2011) Salient local 3D features for 3D shape retrieval. In IS&T/SPIE electronic imaging. Int. Soc. Opt. Photonics 78640S - 78640S-78648Google Scholar
  29. 29.
    Guo Y, Bennamoun M, Sohel F, Lu M, Wan J, Kwok NM (2015) A comprehensive performance evaluation of 3D local feature descriptors. Int. J Comput Vis 116:66–89Google Scholar
  30. 30.
    Healy DM, Rockmore DN, Kostelec PJ (2003) FFTs for the 2-sphere-improvements and variations. J Fourier Anal Appl 9(4):341–385, SpringerMathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Heczko M, Keim DA, Saupe D, Vranic DV (2002) Methods for similarity search os 3D databases (verfahren zur ähnlichkeitssuche auf 3D-objekten). Datenbank-Spektrum (DBSK) 2(2):54–63Google Scholar
  32. 32.
    Heider P, Pierre-Pierre A, Li R, Mueller R, Grimm C (2012) Comparing local shape descriptors. Vis Comput 28(9):919–929CrossRefGoogle Scholar
  33. 33.
    Hilaga M, Shinagawa Y, Kohmura T (2001) Topology matching for fully automatic similarity estimation of 3D shapes. ACM. SIGGRAPH '01. Proceedings of the 28th annual conference on computer graphics and interactive techniques. ACM New York, NY, USA, pp 203–212Google Scholar
  34. 34.
    Hoffmann CM (1989) Geometric and solid modeling. Morgan Kaufmann Pub https://www.cs.purdue.edu/homes/cmh/distribution/books/geo.html, p 338
  35. 35.
    Horn BKP (1984) Extended gaussian images. Proc IEEE 72(12):1671–1686CrossRefGoogle Scholar
  36. 36.
    Huang P, Starck J, Hilton A (2007) A study of shape similarity for temporal surface sequences of people. International conference on 3-D imaging and modeling - 3DIM pp 408–418Google Scholar
  37. 37.
    Icke I (2004) Content based 3D shape retrieval a survey of state of the art. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.303.353&rep=rep1&type=pdf. Accessed May 2014
  38. 38.
    Ikeuchi K (1981) Recognition of 3-D objects using the extended gaussian image. Proc. 7th International joint conference on artificial intelligence, pp 595–600Google Scholar
  39. 39.
    Johnson AE, Hebert M (1999) Using spin images for efficient object recognition in cluttered 3D scenes. IEEE Trans Pattern Anal Mach Intell 21(5):433–449CrossRefGoogle Scholar
  40. 40.
    Kang SB, Ikeuchi K (1993) The complex EGI: a new representation for 3-D pose determination. IEEE Trans Pattern Anal Mach Intell 5(7):707–721CrossRefGoogle Scholar
  41. 41.
    Kazhdan M, Chazelle B, Dobkin D, Furkhouser T, Rusinkiewicz S (2003) A reflective symmetry descriptor for 3D models. ACM J Algorithmica 38(1):201–225MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    Kazhdan M, Funkhouser T, Rusinkiewicz S (2003b) Rotation invariant spherical harmonic representation of 3D shape descriptors eurographics symposium on geometry processing. The eurographics association, pp 156–164Google Scholar
  43. 43.
    Keim DA (1999) Efficient geometry-based similarity search of 3D spatial databases ACM. In proceedings of the international conference on management of data (SIGMOD’99), vol 28(2). ACM New York, NY, pp 419–430Google Scholar
  44. 44.
    Koenderink JJ, Van Doorn AJ (1992) Surface shape and curvature scales. ACM Image Vis Comput 10(8):557–565CrossRefGoogle Scholar
  45. 45.
    Körtgen M, Park G-J, Novotni M, Klein R (2003) 3D shape matching with 3D shape contexts. In proceedings of the 7th central european seminar on computer graphics Budmerice, Slovakia, pp 34–43Google Scholar
  46. 46.
    Laga H, Takahashi H, Nakajima M (2006) Spherical wavelet descriptors for content based 3D model retrieval. IEEE proceedings of the international conference on shape modeling and applications. IEEE. Computer Society Washington DC, USA, pp 15–25Google Scholar
  47. 47.
    Lamdan Y, Wolfson HJ (1988) Geometric hashing: a general and efficiente model-based recognition scheme. IEEE proceeding of the second international conference on computer vision. IEEE Tampa, FL, pp 238–249Google Scholar
  48. 48.
    Latecki LJ, Lakämper R, Eckhardt U (2000) Shape descriptors for non-rigid shapes with a single closed contour. IEEE Conference on computer vision and pattern recognition (CVPR) vol 1 Hilton Head Island, SC, pp 424–429Google Scholar
  49. 49.
    Lazebnik S, Cordelia, Ponce J (2005) A sparse texture representation using affine invariant regions. IEEE proceeding computer society. Comp Vision Recog Pattern 27(8):1265–1278Google Scholar
  50. 50.
    Leifman G, Meir R, Tal A (2005) Semantic-oriented 3d shape retrieval using relevance feedback. Vis Comput 21(8–10):865–875, Springer-VerlangCrossRefGoogle Scholar
  51. 51.
    Li C, Hamza B (2013) A multiresolution descriptor for deformable 3D shape retrieval. Vis Comput 29(6–8):513–514CrossRefGoogle Scholar
  52. 52.
    Ling H, Jacobs DW (2007) Shape classification using the inner-distance. IEEE Trans Pattern Anal Mach Intell 29(2):286–299CrossRefGoogle Scholar
  53. 53.
    Liu W, He Y-j (2006) Multi-level spherical moments based 3D model retrieval. J Zhejiang Univ (Sci) 7(9):1500–1507MathSciNetCrossRefMATHGoogle Scholar
  54. 54.
    Liu Y, Zha H, Qin H (2006a) The generalized shape distributions for shape matching and analysis. IEEE proceedings of the international conference on shape modeling and applications (SMI’06). Computer Society Matsushima JapanGoogle Scholar
  55. 55.
    Liu Y, Zha H, Qin H (2006b) Shape topics: a compact representation and new algorithms for 3D partial shape retrieval. IEEE proceedings of the computer society conference on computer vision and pattern recognition 2025–2032Google Scholar
  56. 56.
    Lowe DG (1999) Object recognition from local scale-invariant features. IEEE proceedings of the seventh international conference on computer vision 2:1150–1157Google Scholar
  57. 57.
    Lowe DG (2004) Distinctive image feature from sacale-invariant keypoints. J Comput Vis 60(2):91–110, Kluwer Academic PublishersCrossRefGoogle Scholar
  58. 58.
    Mateus LDC (2010) Spectral tools for unsupervised modeling of articulated objects from multipe-view videos. Institut National Polytechnique de Grenoble. PhD. ThesisGoogle Scholar
  59. 59.
    Mikolajczyk K, Schmid C (2006) A performance evaluation of local descriptors. IEEE Trans Pattern Anal Mach Intell 27(10):1615–1630CrossRefGoogle Scholar
  60. 60.
    Mitsumoto H, Tamura S, Okazaki K, Kajimi N, Fukui Y (1992) Reconstruction using mirror images based on a plane symmetry recovering method. IEEE Trans Pattern Anal Mach Intell 14(9):941–946CrossRefGoogle Scholar
  61. 61.
    Mortara M, Patanè G (2002) Shape-covering for skeleton extraction. World scientific publishing company. Int J Shape Model 8(2):139–158CrossRefMATHGoogle Scholar
  62. 62.
    Mortensen EN, Deng H, Shapiro L (2005) A SIFT Descriptor with Global Context. Proc IEEE Conf Comput. Vis Pattern Recognit (CVPR) 1:184–190Google Scholar
  63. 63.
    Novotni M, Klein R (2001a) A geometric approach to 3D object comparison. IEEE international conference on shape modeling and applications. IEEE, pp 166–175Google Scholar
  64. 64.
    Novotni M, Klein R (2003) 3D Zernike descriptors for content based shape retrieval. ACM proceedings of the eighth ACM symposium on solid modeling and applications. ACM Seattle, Washington, USA, pp 216–225Google Scholar
  65. 65.
    O’Hara S, Draper B (2010) Introduction to the bag of features paradigm for image classification and retrievalGoogle Scholar
  66. 66.
    Ohbuchi R, Minamitani T, Takei T (2005) Shape-similarity search of 3D models by using enhanced shape functions. Int J Comput. Appl Technol (IJCAT)) 23(2/3/4):1–27Google Scholar
  67. 67.
    Ohbuchi R, Otagiri T, Ibato M, Takei T (2002) Shape-similarity search of three-dimensional models using parameterized statistics. IEEE proceedings of the 10th pacific conference on computer graphics and applications. Computer Society. IEEE Washington DC, pp 265–274Google Scholar
  68. 68.
    Osada R, Furkhouser T, Chazelle B, Dobkin D (2002) Shape distributions. ACM Trans Graph 21(4):807–832MathSciNetCrossRefMATHGoogle Scholar
  69. 69.
    Papadakis P, Pratikakis I, Theoharis T, Perantonis S (2010) PANORAMA: a 3D shape descriptor based on panoramic views for unsupervised 3D object retrieval. Int J Comput Vis 89(2–3):177–192Google Scholar
  70. 70.
    Paquet E, Rioux M (1997) Nefertiti: a query by content software for three-dimensional models databases management. IEEE proceedings international conference on recent advances in 3D digital imaging and modeling Ottawa, Ont, pp 345–352Google Scholar
  71. 71.
    Paquet E, Rioux M (1998) Content-based access of VRML libraries. In: Horace HSI, Smeulders AWM (eds) Springer, Berlin Heidelberg. IAPR. Proceeding international workshop MINAR’ 98 multimedia information analysis and retrieval, vol 1464, Lectures notes in computer science. Springer, Berlin Heidelberg Hong Kong, China, pp 20–32Google Scholar
  72. 72.
    Paquet E, Rioux M (1999) The MPEG-7 standard and the contet-based management of three-dimensional data: a case study. IEEE Proc Int Conf Multimed Comput Syst (ICMCS’99) 1:375–380. FlorenceGoogle Scholar
  73. 73.
    Paquet E, Rioux M, Murching A, Naveen T, Tabatabai A (2000) Description of shape information for 2-D and 3D objects. Signal Process Image Commun 16:103–122, ElsevierCrossRefGoogle Scholar
  74. 74.
    Passalis G, Kakadiaris IA, Theoharis T (2004) Efficient hardware voxelization. IEEE Proc Comput Graph Int 374–377Google Scholar
  75. 75.
    Peleg S, Werman M, Rom H (1989) A unified approach to the change of resolution: space and gray-level. IEEE Trans Pattern Anal Mach Intell 11(7):739–742CrossRefGoogle Scholar
  76. 76.
    Podolak J, Shilane P, Golovinsky A, Rusinkiewicz S, Funkhouser T (2006) A planar-reflective symmetry transform for 3D shapes. ACM proceedings of international conference on computer graphics and interactive techniques: ACM SIGGRAPH, vol 25. ACM. Press New York. USA, pp 549–559Google Scholar
  77. 77.
    Ricard J, Coeurjolly D, Baskurt A (2005) Generalizations of angular radial transform for 2D and 3D shape retieval. Pattern Recog Latters 26(14):2174–2186CrossRefGoogle Scholar
  78. 78.
    Saupe D, Vranić DV (2001) 3D model retrieval with spherical harmonics and moments. Springer proceedings of the 23rd DAGM-symposium on pattern recognition. Springer. Berlin, Germany, pp 392–397Google Scholar
  79. 79.
    Schmitt W, Sotomayor JL, Telea A, Silva CT, Comba JLD (2015) A 3D shape descriptor based on depth complexity and thickness histograms in graphics, patterns and images (SIBGRAPI), 2015 28th SIBGRAPI conference on, pp 226–233Google Scholar
  80. 80.
    Shamir A, Scharf A, Cohen-or D (2004) Enhanced hierarchical shape matching for shape transformation. World scientific publishing company. Int J Shape Model 9(2):203–222CrossRefMATHGoogle Scholar
  81. 81.
    Shih J-L, Lee C-H, Wang JT (2007) A New model retrieval approach based on the elevation descriptor. Pattern Recogn 40(1):283–295, ElsevierCrossRefMATHGoogle Scholar
  82. 82.
    Shilane P, Min P, Kazhdan M, Furkhouser T (2004) The princeton shape benchmark. IEEE proceedings of the shape modeling international. IEEE Washington, DC, USA, pp 167–168Google Scholar
  83. 83.
    Shinagawa Y, Kunii TL (1991) Constructing a reeb graph automatically from cross sections. IEEE Comput Graph Appl 11(6):44–51CrossRefGoogle Scholar
  84. 84.
    Sun J, Ovsjanikov M, Guibas L (2009) A concise and provably informative multi-scale signature based on heat diffusion. Eurographics association and Blackwell publishing. Proc Symp Geom Proc 28(5):1383–1392Google Scholar
  85. 85.
    Sundar H, Silver D, Gagvani N, Dickinson S (2003) Skeleton based shape matching and retrieval. IEEE proceedings of the shape modeling international. IEEE Computer Society Washington, DC, pp 130–142Google Scholar
  86. 86.
    Suzuki MT, Kato T, Otsu N (2000) A similarity retrieval of 3D polygonal model using rotation invariant shape descriptors. IEEE pp 2946–2952Google Scholar
  87. 87.
    Taimouri V, Hua J (2014) Deformation similarity measurement in quasi-conformal shape space. Graph Model 76:57–69, ElsevierGoogle Scholar
  88. 88.
    Tangelder JWH, Veltkamp RC (2003) Polyhedral model retrieval using weighted point sets. Proc Int Conf Shape Model Appl 3(1):119–129Google Scholar
  89. 89.
    Tangelder JWH, Veltkamp RC (2008) A survey of content based 3D shape retrieval methods. Sci Multimed Tools Appl 39:441–471, SpringerCrossRefGoogle Scholar
  90. 90.
    Tung T, Schmitt F (2004) Augmented reeb graphs for content-based retrieval of 3D mesh model. IEEE Proc Shape Model Appl pp 157–166Google Scholar
  91. 91.
    Undurraga C, Mery D (2011) Improving tracking algorithms using saliency. In: César SM, Kim S-W (eds) Springer-Verlag Berlin Heidelberg. Progress in pattern recognition, image analysis, computer vision, and applications. Proceedings 16th iberoamerican congress (CIARP). Springer-Verlag Berlin Heidelberg Chile, pp 141–148Google Scholar
  92. 92.
    Vandeborre J-P, Couillet V, Daoudi M (2002) A practical approach for 3D model indexing by combining local and global invariants. IEEE. 1st international symposium on 3D data processing visualization transmission. IEEE Padova, Italy, pp 19–21Google Scholar
  93. 93.
    Vaxman A, Ben-Chen M, Gotsman C (2010) A multi-resolution approach to heat kernels on discrete surfaces. ACM Trans Graph 29(4):121Google Scholar
  94. 94.
    Veltkamp RC (2001) Shape matching: similarity measures and algorithms. IEEE. In shape modeling and applications, SMI. International conference. IEEE computer society, pp 188–197Google Scholar
  95. 95.
    Venkatraman V, Lee S, Kihara D (2009) Potential for protein surface shape analysis using spherical harmonics and 3D zernike descriptors. Vol 54(1–3). Springer http://link.springer.com/article/10.1007/s12013-009-9051-x/fulltext.html, pp 23–32
  96. 96.
    Vranić DV (2004) 3D model retrieval. University of Leipzing. PhD. ThesisGoogle Scholar
  97. 97.
    Vranić DV, Saupe D (2001a) 3D shape descriptor based on 3D fourier transform. Proceedings of the EURASIP conference on digital signal processing for multimedia communications and services (ECMCS 2001) Budapest, Hungary, pp 271–274Google Scholar
  98. 98.
    Vranić DV, Saupe D (2002) Description of 3D-shape using a complex function on the sphere. In proceedings of: IEEE Int Conf Multimed Expo 1:177–180Google Scholar
  99. 99.
    Vranić DV, Saupe D, Richter J (2001b) Tool for 3D-object retrieval: karhumen-loeve transform and spherical hamonics. IEEE proceedings of the 4th workshop on multimedia signal processing. IEEE Cannes, pp 293–298Google Scholar
  100. 100.
    Yu M, Atmosukarto A, Leow WK, Huan Z, Xu R (2003) 3D model retrieval with morphing-based geometric and topological feature maps. Proc Comput Soc Conf Comput Vision Pattern Recog 2:656–661Google Scholar
  101. 101.
    Zaharia T, Prêteux F (2001b) Hough transform-based 3D mesh retrieval. Proceeding of the SPIE conference on vision geometry X, pp 175–185Google Scholar
  102. 102.
    Zaharia T, Prêteux F (2001a) 3D shape-based retrieval within the MPEG-7 framework. Proceedings of the SPIE conference nonlinear image processing and pattern analysis XII., vol 4304 San Jose, CA, pp 133–145Google Scholar
  103. 103.
    Zaharia T, Prêteux F (2002) Shape-based retrieval of 3D mesh models. IEEE proceedings international conference on multimedia and Expo. (ICME). IEEE, pp 437–440Google Scholar
  104. 104.
    Zhang C, Chen T (2001) Efficient feature extraction for 2D/3D object in mesh representation. IEEE proceedings international conference on image processing, vol 3. IEEE Thessaloniki, pp 935–938Google Scholar
  105. 105.
    Zhang L, Gao Y, Xia Y, Dai Q, Li X (2015) A fine-grained image categorization system by cellet-encoded spatial pyramid modeling. IEEE Trans Ind Electron 62(1):564–571CrossRefGoogle Scholar
  106. 106.
    Zhang L, Han Y, Yang Y, Song M, Yan S (2013) Discovering discriminative graphlets for aerial image categories recognition. IEEE Trans Image Process 22(12):5071–5084MathSciNetCrossRefGoogle Scholar
  107. 107.
    Zhang L, Joao DS, Manuel, Ferreira A (2004) Survey on 3D shape descriptors. In: POSC/EIA/59938 DR (ed) Republica Portuguesa, pp 1–28Google Scholar
  108. 108.
    Zhang D, Lu G (2004) Review of shape representation and description techniques. Pattern Recogn 37:1–19, ElsevierCrossRefGoogle Scholar
  109. 109.
    Zhang L, Yang Y, Gao Y, Yu Y, Wang C, Li X (2014) A probabilistic associative model for segmenting weakly supervised images. IEEE Trans Image Process 23(9):4150–4159Google Scholar
  110. 110.
    Zhao X, Lu M (2013) 3D object retrieval based on PSO-K-modes method academy publisher. J Softw 8(4):963–970MathSciNetCrossRefGoogle Scholar
  111. 111.
    Zhu Z, Wang X, Bai S, Yao C, Bai X (2014) Deep learning representation using autoencoder for 3D shape retrieval in security, pattern analysis, and cybernetics (SPAC), 2014 international conference on, pp 279–284Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Graciela Lara López
    • 1
  • Adriana Peña Pérez Negrón
    • 1
  • Angélica De Antonio Jiménez
    • 2
  • Jaime Ramírez Rodríguez
    • 2
  • Ricardo Imbert Paredes
    • 2
  1. 1.Módulo “O” División de Electrónica y ComputaciónCUCEI, Universidad de GuadalajaraGuadalajaraMexico
  2. 2.Escuela Técnica Superior de Ingenieros InformáticoUniversidad Politécnica de MadridMadridSpain

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