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A Comprehensive Survey on Two and Three-Dimensional Fourier Shape Descriptors: Biomedical Applications

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Abstract

Medical image analysis plays an essential role in the diagnosis, management, and treatment of various diseases. Today, due to the capacity for fast and accurate access to high-quality images of the anatomical structures using modern medical imaging scanners, the opportunity to study and assess the shape with a wide range of medical applications is provided. One of the efficient and conscientious representation techniques to model and analyze the shape data is Fourier-based descriptors. Different studies addressed these descriptors with various clinical applications and contributed a lot in this area. This review gives a comprehensive overview of the theories and methodologies of the Fourier descriptors approaches involving 2D contours and 3D surfaces for shape modeling and analysis. This article collected studies that have employed Fourier-based descriptors in different organs with a wide range of clinical applications and placed them in five different groups, including “Segmentation,” “Classification,” “Modeling,” “Shape analysis,” and “others” from 1994 to 2021. To clarify several aspects of the research, we have summarized both the opportunities and challenges of the considered studies. In addition, we have introduced three novel subject evaluation metrics to analyze the influence and concentration of the collected studies on these five various topics. These metrics suggest a new insight into different researches usage and impact, which can be extended simply to the other works. This review is recommended for researchers working in various fields of medical image analysis using shapes containing two-dimensional contours and three-dimensional surfaces.

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References

  1. Kendall DG (1989) A survey of the statistical theory of shape. Stat Sci 4(2):87–99

    MathSciNet  MATH  Google Scholar 

  2. Guo Y, Bennamoun M, Sohel F, Lu M, Wan J, Kwok NM (2016) A comprehensive performance evaluation of 3D local feature descriptors. Int J Comput Vis 116(1):66–89

    Article  MathSciNet  Google Scholar 

  3. Zhang D, Lu G (2004) Review of shape representation and description techniques. Pattern Recogn 37(1):1–19

    Article  Google Scholar 

  4. Valizadeh G, Mofrad FB, Shalbaf A (2021) Parametric-based feature selection via spherical harmonic coefficients for the left ventricle myocardial infarction screening. Med Biol Eng Comput 1–23

  5. Zhang D, Lu G A (2001) comparative study on shape retrieval using Fourier descriptors with different shape signatures. In: Proc. of international conference on intelligent multimedia and distance education (ICIMADE01), pp 1–9

  6. Bulow T (2004) Spherical diffusion for 3D surface smoothing. IEEE Trans Pattern Anal Mach Intell 26(12):1650–1654

    Article  Google Scholar 

  7. Zhou K, Bao H, Shi J (2004) 3D surface filtering using spherical harmonics. Comput Aided Des 36(4):363–375

    Article  Google Scholar 

  8. Shen L, Saykin AJ, Chung MK, Huang H (2007) Morphometric analysis of hippocampal shape in mild cognitive impairment: an imaging genetics study. In: 2007 IEEE 7th international symposium on bioinformatics and bioengineering, pp 211–217. IEEE

  9. Shen L, Farid H, McPeek MA (2009) Modeling three-dimensional morphological structures using spherical harmonics. Evolution 63(4):1003–1016

    Article  Google Scholar 

  10. Ballard DH, Brown CM (1982) Computer vision. Prenice-Hall, Englewood Cliffs

    Google Scholar 

  11. Chung MK, Dalton KM, Shen L, Evans AC, Davidson RJ (2007) Weighted Fourier series representation and its application to quantifying the amount of gray matter. IEEE Trans Med Imaging 26(4):566–581

    Article  Google Scholar 

  12. Pham DL, Xu C, Prince JL (2000) Current methods in medical image segmentation. Annu Rev Biomed Eng 2(1):315–337

    Article  Google Scholar 

  13. Heimann T, Meinzer H-P (2009) Statistical shape models for 3D medical image segmentation: a review. Med Image Anal 13(4):543–563

    Article  Google Scholar 

  14. Tavakoli V, Amini AA (2013) A survey of shaped-based registration and segmentation techniques for cardiac images. Comput Vis Image Underst 117(9):966–989

    Article  Google Scholar 

  15. Frangi AF, Niessen WJ, Viergever MA (2001) Three-dimensional modeling for functional analysis of cardiac images, a review. IEEE Trans Med Imaging 20(1):2–5

    Article  Google Scholar 

  16. Peng P, Lekadir K, Gooya A, Shao L, Petersen SE, Frangi AF (2016) A review of heart chamber segmentation for structural and functional analysis using cardiac magnetic resonance imaging. Magn Reson Mater Phys Biol Med 29(2):155–195

    Article  Google Scholar 

  17. Petitjean C, Dacher J-N (2011) A review of segmentation methods in short axis cardiac MR images. Med Image Anal 15(2):169–184

    Article  Google Scholar 

  18. McInerney T, Terzopoulos D (1996) Deformable models in medical image analysis: a survey. Med Image Anal 1(2):91–108

    Article  Google Scholar 

  19. Tiwari A, Srivastava S, Pant M (2020) Brain tumor segmentation and classification from magnetic resonance images: review of selected methods from 2014 to 2019. Pattern Recogn Lett 131:244–260

    Article  Google Scholar 

  20. Afzali A, Mofrad FB, Pouladian M (2018) Inter-patient modelling of 2D lung variations from chest X-ray imaging via Fourier descriptors. J Med Syst 42(11):1–12

    Article  Google Scholar 

  21. Kuhl FP, Giardina CR (1982) Elliptic Fourier features of a closed contour. Comput Graph Image Process 18(3):236–258

    Article  Google Scholar 

  22. Staib LH, Duncan JS (1996) Model-based deformable surface finding for medical images. IEEE Trans Med Imaging 15(5):720–731

    Article  Google Scholar 

  23. Afzali A, Mofrad FB, Pouladian M (2020) Contour-based lung shape analysis in order to tuberculosis detection: modeling and feature description. Med Biol Eng Comput 58(9):1965–1986

    Article  Google Scholar 

  24. Afzali A, Mofrad FB, Pouladian M (2021) 2D statistical lung shape analysis using chest radiographs: modelling and segmentation. J Digital Imaging 1–18

  25. Afzali A, Mofrad FB, Pouladian M (2019) 2D statistical shape model for lung using apex anatomical landmark-based registration criteria. In: 2019 26th National and 4th international iranian conference on biomedical engineering (ICBME), pp 21–25. IEEE

  26. Kelemen CB, Gerig G (1996) Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models. Med Image Anal 1(1):19–34

    Article  Google Scholar 

  27. Davatzikos C, Tao X, Shen D (2003) Hierarchical active shape models, using the wavelet transform. IEEE Trans Med Imaging 22(3):414–423

    Article  Google Scholar 

  28. Gotardo PF, Boyer KL, Saltz J, Raman SV (2006) A new deformable model for boundary tracking in cardiac MRI and its application to the detection of intra-ventricular dyssynchrony. In: 2006 IEEE computer society conference on computer vision and pattern recognition (CVPR'06), pp 736–743. IEEE

  29. Burger W, Burge MJ (2016) Digital image processing: an algorithmic introduction using Java. Springer, New York

    Book  Google Scholar 

  30. Tomakova R, Komkov V, Emelianov E, Tomakov M (2017) The use of Fourier descriptors for the classification and analysis of peripheral blood smears image. Appl Math 8(11):1563

    Article  Google Scholar 

  31. Medyukhina A, Blickensdorf M, Cseresnyés Z, Ruef N, Stein JV, Figge MT (2020) Dynamic spherical harmonics approach for shape classification of migrating cells. Sci Rep 10(1):1–12

    Article  Google Scholar 

  32. Schudy R (1979) Towards an anatomical model of heart motion as seen in 4-d cardiac ultrasound data. In: Proc. 6th conference on computer applications in radiology and computer aided analysis of radiological images

  33. Brechbühler C, Gerig G, Kübler O (1995) Parametrization of closed surfaces for 3-D shape description. Comput Vis Image Underst 61(2):154–170

    Article  Google Scholar 

  34. Shen L, Kim S, Saykin AJ (2009) Fourier method for large-scale surface modeling and registration. Comput Graph 33(3):299–311

    Article  Google Scholar 

  35. Praun E, Hoppe H (2003) Spherical parametrization and remeshing. ACM Trans Graph 22(3):340–349

    Article  Google Scholar 

  36. Shen L, Makedon F (2006) Spherical mapping for processing of 3D closed surfaces. Image Vis Comput 24(7):743–761

    Article  Google Scholar 

  37. Gu X, Wang Y, Chan TF, Thompson PM, Yau S-T (2004) Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans Med Imaging 23(8):949–958

    Article  Google Scholar 

  38. Healy DM, Rockmore DN, Kostelec PJ, Moore S (2003) FFTs for the 2-sphere-improvements and variations. J Fourier Anal Appl 9(4):341–385

    Article  MathSciNet  MATH  Google Scholar 

  39. Shen L, Huang H, Makedon F, Saykin AJ (2007) Efficient registration of 3D SPHARM surfaces. In: Fourth Canadian conference on computer and robot vision (CRV'07), pp 81–88. IEEE

  40. Shen L, Ford J, Makedon F, Saykin A (2003) Hippocampal shape analysis: surface-based representation and classification. In: Medical imaging: image processing. international society for optics and photonics, pp 253–264

  41. Epifanio I, Ventura-Campos N (2014) Hippocampal shape analysis in Alzheimer’s disease using functional data analysis. Stat Med 33(5):867–880

    Article  MathSciNet  Google Scholar 

  42. Shen L, Ford J, Makedon F, Saykin A (2004) A surface-based approach for classification of 3D neuroanatomic structures. Intell Data Anal 8(6):519–542

    Article  Google Scholar 

  43. Mofrad FB, Zoroofi RA, Tehrani-Fard AA, Akhlaghpoor S, Sato Y (2014) Classification of normal and diseased liver shapes based on spherical harmonics coefficients. J Med Syst 38(5):1–9

    Article  Google Scholar 

  44. Babapour Mofrad F, Abbaspour Tehrani-Fard A, Aghaeizadeh Zoroofi R, Akhlaghpoor S, Chen Y-W (2010) A novel wavelet based multi-scale statistical shape model-analysis for the liver application: segmentation and classification. Curr Med Imaging 6(3):145–155

    Article  Google Scholar 

  45. Tanaka T, Tateyama T, Mofrad FB, Chen Y-W, Chihara K (2010) Spherical harmonics based 3-D shape modeling for spleen. In: The 2nd international conference on software engineering and data mining, pp 635–639. IEEE

  46. Tateyama T, Okegawa M, Uetani M, Tanaka H, Kohara S, Han X, Kanasaki S, Sato S, Wakamiya M, Furukawa A (2012) Efficient shape representation and statistical shape modeling of the liver using spherical harmonic functions (spharm). In: The 6th international conference on soft computing and intelligent systems, and the 13th international symposium on advanced intelligence systems, pp 428–431. IEEE

  47. Kelemen A, Székely G, Gerig G (1999) Elastic model-based segmentation of 3-D neuroradiological data sets. IEEE Trans Med Imaging 18(10):828–839

    Article  Google Scholar 

  48. Nain D, Haker S, Bobick A, Tannenbaum A (2007) Multiscale 3-d shape representation and segmentation using spherical wavelets. IEEE Trans Med Imaging 26(4):598–618

    Article  Google Scholar 

  49. Eck S, Wörz S, Müller-Ott K, Hahn M, Biesdorf A, Schotta G, Rippe K, Rohr K (2016) A spherical harmonics intensity model for 3D segmentation and 3D shape analysis of heterochromatin foci. Med Image Anal 32:18–31

    Article  Google Scholar 

  50. Gerig G, Styner M, Shenton ME, Lieberman JA (2001) Shape versus size: Improved understanding of the morphology of brain structures. In: International conference on medical image computing and computer-assisted intervention. Springer, New York, pp 24-32

  51. Styner M, Gerig G, Lieberman J, Jones D, Weinberger D (2003) Statistical shape analysis of neuroanatomical structures based on medial models. Med Image Anal 7(3):207–220

    Article  Google Scholar 

  52. Huang H, Shen L, Ford J, Makedon F, Zhang R, Gao L, Pearlman J (2005) Functional analysis of cardiac MR images using SPHARM modeling. In: Medical imaging: image processing. International society for optics and photonics, pp 1384–1391

  53. Jallouli M, Khalifa WB, Mabrouk AB, Mahjoub MA (2019) Assessment of global left ventricle deformation using recursive spherical harmonics. In: The international conference on natural computation, fuzzy systems and knowledge discovery. Springer, pp 498–505

  54. Bosco P, Giuliano A, Delafield-Butt J, Muratori F, Calderoni S, Retico A (2019) Brainstem enlargement in preschool children with autism: results from an intermethod agreement study of segmentation algorithms. Hum Brain Mapp 40(1):7–19

    Article  Google Scholar 

  55. Mofrad FB, Zoroofi RA, Chen Y-W, Tehrani-Fard AA, Sato Y, Furukawa A (2009) Evaluation of liver shape approximation and characterization. In: 2009 fifth international conference on intelligent information hiding and multimedia signal processing, pp 1297–1300. IEEE

  56. Sampathkumar U, Nowroozilarki Z, Reece GP, Hanson SE, Merchant FA (2020) Spherical harmonics for modeling shape transformations of breasts following breast surgery. In: Medical imaging 2020: image-guided procedures, robotic interventions, and modeling. International Society for Optics and Photonics, p 113152H

  57. Babapour Mofrad F, Aghaeizadeh Zoroofi R, Abbaspour Tehrani-Fard A, Akhlaghpoor S, Hori M, Chen Y-W, Sato Y (2010) Statistical construction of a Japanese male liver phantom for internal radionuclide dosimetry. Radiat Prot Dosimetry 141(2):140–148

    Article  Google Scholar 

  58. Cosgriff R (1960) Identification of shape, Ohio State Univ. Res Foundation, Columbus, Rep, pp 820–811

  59. Rohlf FJ, Archie JW (1984) A comparison of Fourier methods for the description of wing shape in mosquitoes (Diptera: Culicidae). Syst Zool 33(3):302–317

    Article  Google Scholar 

  60. Quicken M, Brechbuhler C, Hug J, Blattmann H, Székely G (2000) Parameterization of closed surfaces for parametric surface description. In: Proceedings IEEE conference on computer vision and pattern recognition. CVPR 2000 (Cat. No. PR00662) , pp 354–360. IEEE

  61. Shen L, Chung MK (2006) Large-scale modeling of parametric surfaces using spherical harmonics. In: Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06), pp 294–301. IEEE

  62. Ritchie DW, Kemp GJ (1999) Fast computation, rotation, and comparison of low resolution spherical harmonic molecular surfaces. J Comput Chem 20(4):383–395

    Article  Google Scholar 

  63. Zhang G, Ma Z, Tong Q, He Y, Zhao T (2008) Shape feature extraction using Fourier descriptors with brightness in content-based medical image retrieval. In: 2008 international conference on intelligent information hiding and multimedia signal processing, pp 71–74. IEEE

  64. Persoon E, Fu K-S (1977) Shape discrimination using Fourier descriptors. IEEE Trans Syst Man Cybern 7(3):170–179

    Article  MathSciNet  Google Scholar 

  65. Huang H, Shen L, Zhang R, Makedon F, Hettleman B, Pearlman J (2005) Surface alignment of 3D spherical harmonic models: application to cardiac MRI analysis. In: International conference on medical image computing and computer-assisted intervention. Springer, New York, pp 67–74

  66. Shen L, Firpi HA, Saykin AJ, West JD (2009) Parametric surface modeling and registration for comparison of manual and automated segmentation of the hippocampus. Hippocampus 19(6):588–595

    Article  Google Scholar 

  67. Styner M, Gorczowski K, Fletcher T, Jeong J, Pizer S, Gerig G (2006) Multi-object statistics using principal geodesic analysis in a longitudinal pediatric study. LNCS 4091:1–8

    Google Scholar 

  68. Shen L, Makedon F, Saykin A (2004) Shape-based discriminative analysis of combined bilateral hippocampi using multiple object alignment. In: Medical imaging: image processing. International society for optics and photonics, pp 283–293

  69. Besl PJ, McKay ND (1992) Method for registration of 3-D shapes. In: Sensor fusion IV: control paradigms and data structures. International society for optics and photonics, pp 586–606

  70. Ross A (2004) Procrustes analysis. Course report, Department of Computer Science and Engineering, University of South Carolina, p 26

  71. Styner M, Oguz I, Xu S, Brechbühler C, Pantazis D, Levitt JJ, Shenton ME, Gerig G (2006) Framework for the statistical shape analysis of brain structures using SPHARM-PDM. Insight J 1071:242

    Google Scholar 

  72. https://www.nitrc.org/projects/spharm-pdm/

  73. http://lishenlab.com/spharm/

  74. http://www.slicer.org

  75. http://salt.slicer.org/

  76. Paniagua B, Styner M, Macenko M, Pantazis D, Niethammer M (2009) Local shape analysis using MANCOVA. Insight J 21

  77. Worsley KJ, Taylor J, Carbonell F, Chung M, Duerden E, Bernhardt B, Lyttelton O, Boucher M, Evans A (2009) A Matlab toolbox for the statistical analysis of univariate and multivariate surface and volumetric data using linear mixed effects models and random field theory. In: NeuroImage organisation for human brain mapping 2009 annual meeting, p S102

  78. Gerig G, Styner M, Székely G (2002) Statistical shape models for segmentation and structural analysis. In: Proceedings IEEE international symposium on biomedical imaging, pp 18–21. IEEE

  79. Yu P, Grant PE, Qi Y, Han X, Ségonne F, Pienaar R, Busa E, Pacheco J, Makris N, Buckner RL (2007) Cortical surface shape analysis based on spherical wavelets. IEEE Trans Med Imaging 26(4):582–597

    Article  Google Scholar 

  80. Ruan X, Murphy RF (2019) Evaluation of methods for generative modeling of cell and nuclear shape. Bioinformatics 35(14):2475–2485

    Article  Google Scholar 

  81. Gerardin E, Chételat G, Chupin M, Cuingnet R, Desgranges B, Kim H-S, Niethammer M, Dubois B, Lehéricy S, Garnero L (2009) Multidimensional classification of hippocampal shape features discriminates Alzheimer’s disease and mild cognitive impairment from normal aging. Neuroimage 47(4):1476–1486

    Article  Google Scholar 

  82. Gutman B, Wang Y, Morra J, Toga AW, Thompson PM (2009) Disease classification with hippocampal shape invariants. Hippocampus 19(6):572–578

    Article  Google Scholar 

  83. Van Kaick O, Hamarneh G, Ward AD, Schweitzer M, Zhang H (2010) Learning Fourier descriptors for computer-aided diagnosis of the supraspinatus. Acad Radiol 17(8):1040–1049

    Article  Google Scholar 

  84. El-Baz A, Nitzken M, Khalifa F, Elnakib A, Gimel’farb G, Falk R, El-Ghar MA (2011) 3D shape analysis for early diagnosis of malignant lung nodules. In: Biennial international conference on information processing in medical imaging. Springer, pp 772–783

  85. Li Y, Mu Z, Zeng H (2013) A rotation invariant feature extraction for 3D ear recognition. In: 2013 25th Chinese control and decision conference (CCDC), pp 3671–3675. IEEE

  86. Hosseinbor AP, Chung MK, Koay CG, Schaefer SM, Van Reekum CM, Schmitz LP, Sutterer M, Alexander AL, Davidson RJ (2015) 4D hyperspherical harmonic (HyperSPHARM) representation of surface anatomy: a holistic treatment of multiple disconnected anatomical structures. Med Image Anal 22(1):89–101

    Article  Google Scholar 

  87. Uhl A, Liedlgruber M, Butz K, Höller Y, Kuchukhidze G, Taylor A, Thomschewski A, Tomasi O, Trinka E (2018) Hippocampus segmentation and SPHARM coefficient selection are decisive for MCI detection. In: Bildverarbeitung für die Medizin, pp 239–244

  88. Ferrando L, Ventura-Campos N, Epifanio I (2020) Detecting and visualizing differences in brain structures with SPHARM and functional data analysis. Neuroimage 222:117209

    Article  Google Scholar 

  89. Chan AH-L, Luo Y, Shi L, Lui RL-M (2020) QC-SPHRAM: quasi-conformal spherical harmonics based geometric distortions on hippocampal surfaces for early detection of the Alzheimer’s disease. arXiv preprint arXiv:200310229

  90. Tutar IB, Pathak SD, Gong L, Cho PS, Wallner K, Kim Y (2006) Semiautomatic 3-D prostate segmentation from TRUS images using spherical harmonics. IEEE Trans Med Imaging 25(12):1645–1654

    Article  Google Scholar 

  91. Gerig G, Styner M, Jones D, Weinberger D, Lieberman J (2001) Shape analysis of brain ventricles using spharm. In: Proceedings IEEE workshop on mathematical methods in biomedical image analysis (MMBIA 2001), pp 171–178. IEEE

  92. Goldberg-Zimring D, Azhari H, Miron S, Achiron A (2001) 3-D surface reconstruction of multiple sclerosis lesions using spherical harmonics. Magn Reson Med 46(4):756–766

    Article  Google Scholar 

  93. Styner M, Lieberman JA, Pantazis D, Gerig G (2004) Boundary and medial shape analysis of the hippocampus in schizophrenia. Med Image Anal 8(3):197–203

    Article  Google Scholar 

  94. Styner M, Lieberman JA, McClure RK, Weinberger DR, Jones DW, Gerig G (2005) Morphometric analysis of lateral ventricles in schizophrenia and healthy controls regarding genetic and disease-specific factors. Proc Natl Acad Sci USA 102(13):4872–4877

    Article  Google Scholar 

  95. Shen L, Saykin A, McHugh T, West J, Rabin L, Wishart H, Chung MK, Makedon F (2005) Morphometric MRI study of hippocampal shape in MCI using spherical harmonics. Alzheimers Dement 1(1):S47

    Google Scholar 

  96. Huang H, Shen L, Zhang R, Makedon F, Hettleman B, Pearlman J (2006) Cardiac motion analysis to improve pacing site selection in CRT. Acad Radiol 13(9):1124–1134

    Article  Google Scholar 

  97. Gutman B, Wang Y, Lui LM, Chan TE, Thompson PM (2006) Hippocampal surface analysis using spherical harmonic function applied to surface conformal mapping. In: 18th international conference on pattern recognition (ICPR'06), pp 964–967. IEEE

  98. Tootoonian S, Abugharbieh R, Huang X, McKeown MJ (2006) Shape vs. volume: Invariant shape descriptors for 3D region of interest characterization in MRI. In: 3rd IEEE international symposium on biomedical imaging: nano to macro, pp 754–757. IEEE

  99. Chung MK, Dalton KM, Davidson RJ (2007) Encoding neuroanatomical information using weighted spherical harmonic representation. In: 2007 IEEE/SP 14th workshop on statistical signal processing, pp 146–150. IEEE

  100. Shi Y, Thompson PM, de Zubicaray GI, Rose SE, Tu Z, Dinov I, Toga AW (2007) Direct mapping of hippocampal surfaces with intrinsic shape context. Neuroimage 37(3):792–807

    Article  Google Scholar 

  101. Styner M, Xu S, El-Sayed M, Gerig G (2007) Correspondence evaluation in local shape analysis and structural subdivision. In: 2007 4th IEEE international symposium on biomedical imaging: from nano to macro, pp 1192–1195. IEEE

  102. Uthama A, Abugharbieh R, Traboulsee A, McKeown MJ Invariant (2007) SPHARM shape descriptors for complex geometry in MR region of interest analysis. In: 2007 29th annual international conference of the IEEE engineering in medicine and biology society, pp 1322–1325. IEEE

  103. Khelifa WBH, Abdallah AB, Ghorbel F (2008) Three dimensional modeling of the left ventricle of the heart using spherical harmonic analysis. In: 2008 5th IEEE international symposium on biomedical imaging: from nano to macro, pp 1275–1278. IEEE

  104. Uthama A, Abugharbieh R, Palmer SJ, Traboulsee A, McKeown MJ (2008) SPHARM-based spatial fMRI characterization with intersubject anatomical variability reduction. IEEE J Sel Topics Signal Process 2(6):907–918

    Article  Google Scholar 

  105. McKeown MJ, Uthama A, Abugharbieh R, Palmer S, Lewis M, Huang X (2008) Shape (but not volume) changes in the thalami in Parkinson disease. BMC Neurol 8(1):1–8

    Article  Google Scholar 

  106. Abdallah AB, Ghorbel F, Chatti K, Essabbah H, Bedoui MH (2010) A new uniform parameterization and invariant 3D spherical harmonic shape descriptors for shape analysis of the heart’s left ventricle—a pilot study. Pattern Recogn Lett 31(13):1981–1990

    Article  Google Scholar 

  107. Esmaeil-Zadeh M, Soltanian-Zadeh H, Jafari-Khouzani K (2010) SPHARM-based shape analysis of hippocampus for lateralization in mesial temporal lobe epilepsy. In: 2010 18th Iranian conference on electrical engineering, pp 39–44. IEEE

  108. Paniagua B, Cevidanes L, Walker D, Zhu H, Guo R, Styner M (2011) Clinical application of SPHARM-PDM to quantify temporomandibular joint osteoarthritis. Comput Med Imaging Graph 35(5):345–352

    Article  Google Scholar 

  109. Nitzken M, Casanova M, Gimel'farb G, Khalifa F, Elnakib A, Switala AE, El-Baz A (2011) 3D shape analysis of the brain cortex with application to autism. In: 2011 IEEE international symposium on biomedical imaging: from nano to macro, pp 1847–1850. IEEE

  110. Nitzken M, Casanova M, Gimel'farb G, Elnakib A, Khalifa F, Switala A, El-Baz A 3D shape analysis of the brain cortex with application to dyslexia. In: 2011 18th IEEE international conference on image processing, 2011. IEEE, pp 2657–2660

  111. Paniagua B, Lyall A, Berger J-B, Vachet C, Hamer RM, Woolson S, Lin W, Gilmore J, Styner M (2013) Lateral ventricle morphology analysis via mean latitude axis. In: Medical imaging 2013: biomedical applications in molecular, structural, and functional imaging. International Society for Optics and Photonics, p 86720M

  112. Hibar DP, Medland SE, Stein JL, Kim S, Shen L, Saykin AJ, De Zubicaray GI, McMahon KL, Montgomery GW, Martin NG (2013) Genetic clustering on the hippocampal surface for genome-wide association studies. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 690–697

  113. Ayari R, Abdallah AB, Sfar R, Ghorbel F, Bedoui MH (2014) Analysis of regional deformation of the heart’s left ventricle using invariant SPHARM descriptors. IRBM 35(5):226–232

    Article  Google Scholar 

  114. Wu J, Simon MA, Brigham JC (2016) A comparative analysis of global shape analysis methods for the assessment of the human right ventricle. Comput Methods Biomech Biomed Eng 4(6):327–343

    Google Scholar 

  115. Kumar SS, Nandhini M (2019) Analysis of surface-based morphometric of hippocampal subfield volumetry in Alzheimer’s disease and MCI. Inst Integr Omics Appl Biotechnol 10(1):21–26

    Google Scholar 

  116. Bosco P, Harrison L, Retico A, Butera C, Calderoni S, Muratori F, Aziz-Zadeh L, Delafield-Butt J (2021) Brainstem morphometric differences in children with autism spectrum disorder, developmental coordination disorder, and those typically developing. In: International society for autism research virtual annual meeting

  117. Chen CW, Huang TS, Arrott M (1994) Modeling, analysis, and visualization of left ventricle shape and motion by hierarchical decomposition. IEEE Trans Pattern Anal Mach Intell 16(4):342–356

    Article  Google Scholar 

  118. Shenton ME, Gerig G, McCarley RW, Szekely G, Kikinis R (2002) Amygdala–hippocampal shape differences in schizophrenia: the application of 3D shape models to volumetric MR data. Psychiatry Res 115(1–2):15–35

    Article  Google Scholar 

  119. Goldberg-Zimring D, Achiron A, Guttmann CR, Azhari H (2003) Three-dimensional analysis of the geometry of individual multiple sclerosis lesions: detection of shape changes over time using spherical harmonics. J Magn Reson Imaging 18(3):291–301

    Article  Google Scholar 

  120. Goldberg-Zimring D, Shalmon B, Zou KH, Azhari H, Nass D, Achiron A (2005) Assessment of multiple sclerosis lesions with spherical harmonics: comparison of MR imaging and pathologic findings. Radiology 235(3):1036–1044

    Article  Google Scholar 

  121. Goldberg-Zimring D, Talos I-F, Bhagwat JG, Haker SJ, Black PM, Zou KH (2005) Statistical validation of brain tumor shape approximation via spherical harmonics for image-guided neurosurgery. Acad Radiol 12(4):459–466

    Article  Google Scholar 

  122. El-Shenawee M, Miller EL (2006) Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumor. IEEE Trans Med Imaging 25(10):1258–1271

    Article  Google Scholar 

  123. Dillenseger J-L, Guillaume H, Patard J-J (2006) Spherical harmonics based intrasubject 3-D kidney modeling/registration technique applied on partial information. IEEE Trans Biomed Eng 53(11):2185–2193

    Article  Google Scholar 

  124. Price GJ, Moore CJ (2007) A method to calculate coverage probability from uncertainties in radiotherapy via a statistical shape model. Phys Med Biol 52(7):1947

    Article  Google Scholar 

  125. AlHadidi A, Cevidanes LH, Paniagua B, Cook R, Festy F, Tyndall D (2012) 3D quantification of mandibular asymmetry using the SPHARM-PDM tool box. Int J Comput Assist Radiol Surg 7(2):265–271

    Article  Google Scholar 

  126. Paniagua B, Cevidanes L, Zhu H, Styner M (2011) Outcome quantification using SPHARM-PDM toolbox in orthognathic surgery. Int J Comput Assist Radiol Surg 6(5):617–626

    Article  Google Scholar 

  127. Fang YH, Wu B, Yang ZY (2014) Study on virtual liver surgery simulation system with real-time haptic feedback. In: Applied mechanics and materials. Trans Tech Publ, pp 900–906

  128. Bompard L, Xu S, Styner M, Paniagua B, Ahn M, Yuan Y, Jewells V, Gao W, Shen D, Zhu H (2014) Multivariate longitudinal shape analysis of human lateral ventricles during the first twenty-four months of life. PLoS ONE 9(9):e108306

    Article  Google Scholar 

  129. Bergamasco LCC, Rochitte CE, Nunes FL (2018) 3D medical objects processing and retrieval using spherical harmonics: a case study with congestive heart failure MRI exams. In: Proceedings of the 33rd annual ACM symposium on applied computing. pp 22–29

  130. Valizadeh G, Mofrad FB, Shalbaf A (2019) Impacts of spherical harmonics shape descriptors on the inter-slice interpolation of MR images. In: 2019 26th national and 4th international Iranian conference on biomedical engineering (ICBME), pp 26–30. IEEE

  131. Styner M, Gerig G (2001) Medial models incorporating object variability for 3D shape analysis. In: Biennial international conference on information processing in medical imaging. Springer, pp 502–516

  132. Bookstein FL (1997) Shape and the information in medical images: a decade of the morphometric synthesis. Comput Vis Image Underst 66(2):97–118

    Article  Google Scholar 

  133. Cootes TF, Taylor CJ, Cooper DH, Graham J (1995) Active shape models-their training and application. Comput Vis Image Underst 61(1):38–59

    Article  Google Scholar 

  134. Borgefors G (1984) Distance transformations in arbitrary dimensions. Comput Vis Graph Image Process 27(3):321–345

    Article  Google Scholar 

  135. Shen L, Saykin A, Mchugh T, West J, Rabin L, Wishart H, Chung MK, Makedon F (2005) Morphometric analysis of 3D surfaces: application to hippocampal shape in mild cognitive impairment. In: CVPRIP 2005: 6th Int. conf. on computer vision, pattern recognition and image processing in conjunction with 8th joint conference on information sciences, JCIS, Citeseer

  136. Csernansky JG, Joshi S, Wang L, Haller JW, Gado M, Miller JP, Grenander U, Miller MI (1998) Hippocampal morphometry in schizophrenia by high dimensional brain mapping. Proc Natl Acad Sci USA 95(19):11406–11411

    Article  Google Scholar 

  137. Nitzken MJ, Casanova MF, Gimel’farb G, Inanc T, Zurada El-Baz JMA (2014) Shape analysis of the human brain: a brief survey. IEEE J Biomed Health Inform 18(4):1337–1354

    Article  Google Scholar 

  138. Golland P, Fischl B, Spiridon M, Kanwisher N, Buckner RL, Shenton ME, Kikinis R, Dale A, Grimson WEL (2002) Discriminative analysis for image-based studies. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 508–515

  139. Golland P, Grimson WEL, Shenton ME, Kikinis R (2000) Small sample size learning for shape analysis of anatomical structures. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 72–82

  140. Timoner SJ, Golland P, Kikinis R, Shenton ME, Grimson WEL, Wells WM (2002) Performance issues in shape classification. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 355–362

  141. Vetsa YSK, Styner M, Pizer SM, Lieberman JA, Gerig G (2003) Caudate shape discrimination in schizophrenia using template-free non-parametric tests. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 661–669

  142. Chupin M, Mukuna-Bantumbakulu AR, Hasboun D, Bardinet E, Baillet S, Kinkingnéhun S, Lemieux L, Dubois B, Garnero L (2007) Anatomically constrained region deformation for the automated segmentation of the hippocampus and the amygdala: method and validation on controls and patients with Alzheimer’s disease. Neuroimage 34(3):996–1019

    Article  Google Scholar 

  143. Chupin M, Hammers A, Liu RS, Colliot O, Burdett J, Bardinet E, Duncan JS, Garnero L, Lemieux L (2009) Automatic segmentation of the hippocampus and the amygdala driven by hybrid constraints: method and validation. Neuroimage 46(3):749–761

    Article  Google Scholar 

  144. Hosseinbor AP, Chung MK, Schaefer SM, Van Reekum CM, Peschke-Schmitz L, Sutterer M, Alexander AL, Davidson RJ (2013) 4D hyperspherical harmonic (HyperSPHARM) representation of multiple disconnected brain subcortical structures. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 598–605

  145. Chung MK, Worsley KJ, Nacewicz BM, Dalton KM, Davidson RJ (2010) General multivariate linear modeling of surface shapes using SurfStat. Neuroimage 53(2):491–505

    Article  Google Scholar 

  146. Khairy K, Foo J, Howard J (2008) Shapes of red blood cells: comparison of 3D confocal images with the bilayer-couple model. Cell Mol Bioeng 1(2):173–181

    Article  Google Scholar 

  147. Khairy K, Howard J (2011) Minimum-energy vesicle and cell shapes calculated using spherical harmonics parameterization. Soft Matter 7(5):2138–2143

    Article  Google Scholar 

  148. Morris RJ, Najmanovich RJ, Kahraman A, Thornton JM (2005) Real spherical harmonic expansion coefficients as 3D shape descriptors for protein binding pocket and ligand comparisons. Bioinformatics 21(10):2347–2355

    Article  Google Scholar 

  149. Venkatraman V, Sael L, Kihara D (2009) Potential for protein surface shape analysis using spherical harmonics and 3D Zernike descriptors. Cell Biochem Biophys 54(1):23–32

    Article  Google Scholar 

  150. Ducroz C, Olivo-Marin J-C, Dufour A (2012) Characterization of cell shape and deformation in 3D using Spherical Harmonics. In: 2012 9th IEEE international symposium on biomedical imaging (ISBI), pp 848–851. IEEE

  151. Ducroz C, Olivo-Marin J-C, Dufour A (2011) Spherical Harmonics based extraction and annotation of cell shape in 3D time-lapse microscopy sequences. In: 2011 annual international conference of the IEEE engineering in medicine and biology society, pp 6619–6622. IEEE

  152. Limkin EJ, Reuzé S, Carré A, Sun R, Schernberg A, Alexis A, Deutsch E, Ferté C, Robert C (2019) The complexity of tumor shape, spiculatedness, correlates with tumor radiomic shape features. Sci Rep 9(1):1–12

    Article  Google Scholar 

  153. Alksas A, Shehata M, Saleh GA, Shaffie A, Soliman A, Ghazal M, Khelifi A, Khalifeh HA, Razek AA, Giridharan GA (2021) A novel computer-aided diagnostic system for accurate detection and grading of liver tumors. Sci Rep 11(1):1–18

    Article  Google Scholar 

  154. Shehata M, Alksas A, Abouelkheir RT, Elmahdy A, Shaffie A, Soliman A, Ghazal M, Abu Khalifeh H, Salim R, Abdel Razek AAK (2021) A comprehensive computer-assisted diagnosis system for early assessment of renal cancer tumors. Sensors 21(14):4928

    Article  Google Scholar 

  155. Davies RH (2002) Learning shape: optimal models for analysing natural variability. University of Manchester Manchester

  156. Powers DM (2020) Evaluation: from precision, recall and F-measure to ROC, informedness, markedness and correlation. arXiv preprint arXiv:201016061

  157. Sokolova M, Lapalme G (2009) A systematic analysis of performance measures for classification tasks. Inf Process Manag 45(4):427–437

    Article  Google Scholar 

  158. Dice LR (1945) Measures of the amount of ecologic association between species. Ecology 26(3):297–302

    Article  Google Scholar 

  159. Jaccard P (1912) The distribution of the flora in the alpine zone. 1. New Phytol 11(2):37–50

    Article  Google Scholar 

  160. Taha AA, Hanbury A (2015) An efficient algorithm for calculating the exact Hausdorff distance. IEEE Trans Pattern Anal Mach Intell 37(11):2153–2163

    Article  Google Scholar 

  161. Mingqiang Y, Kidiyo K, Joseph R (2008) A survey of shape feature extraction techniques. Pattern Recogn 15(7):43–90

    Google Scholar 

  162. Tangelder JW, Veltkamp RC (2008) A survey of content based 3D shape retrieval methods. Multimed Appl 39(3):441–471

    Article  Google Scholar 

  163. Iyer N, Jayanti S, Lou K, Kalyanaraman Y, Ramani K (2005) Three-dimensional shape searching: state-of-the-art review and future trends. Comput Aided Des 37(5):509–530

    Article  Google Scholar 

  164. Zhang D, Lu G (2002) Shape-based image retrieval using generic Fourier descriptor. Signal Process 17(10):825–848

    Google Scholar 

  165. El-ghazal A, Basir O, Belkasim S (2007) A new shape signature for Fourier descriptors. In: 2007 IEEE international conference on image processing, pp I-161–I-164. IEEE

  166. Kunttu I, Lepistö L, Visa AJ (2005) Efficient Fourier shape descriptor for industrial defect images using wavelets. Opt Eng 44(8):080503

    Article  Google Scholar 

  167. Shen L, Kim S, Wan J, West JD, Saykin AJ (2012) Fourier methods for 3D surface modeling and analysis. In: Emerging topics in computer vision and its applications. World Scientific, pp 175–196

  168. Yushkevich P, Pizer SM, Joshi S, Marron JS (2001) Intuitive, localized analysis of shape variability. In: Biennial international conference on information processing in medical imagings. Springer, pp 402–408

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  1. Department of Medical Radiation Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Gelareh Valizadeh & Farshid Babapour Mofrad

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Valizadeh, G., Babapour Mofrad, F. A Comprehensive Survey on Two and Three-Dimensional Fourier Shape Descriptors: Biomedical Applications. Arch Computat Methods Eng 29, 4643–4681 (2022). https://doi.org/10.1007/s11831-022-09750-7

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