Skip to main content
Article thumbnail
Location of Repository

Statistical shape analysis for bio-structures : local shape modelling, techniques and applications

By Daniel Alejandro Valdés Amaro


A Statistical Shape Model (SSM) is a statistical representation of a shape obtained\ud from data to study variation in shapes. Work on shape modelling is constrained by\ud many unsolved problems, for instance, difficulties in modelling local versus global\ud variation. SSM have been successfully applied in medical image applications such\ud as the analysis of brain anatomy. Since brain structure is so complex and varies\ud across subjects, methods to identify morphological variability can be useful for\ud diagnosis and treatment.\ud The main objective of this research is to generate and develop a statistical shape\ud model to analyse local variation in shapes. Within this particular context, this\ud work addresses the question of what are the local elements that need to be identified for effective shape analysis. Here, the proposed method is based on a Point\ud Distribution Model and uses a combination of other well known techniques: Fractal\ud analysis; Markov Chain Monte Carlo methods; and the Curvature Scale Space\ud representation for the problem of contour localisation. Similarly, Diffusion Maps\ud are employed as a spectral shape clustering tool to identify sets of local partitions\ud useful in the shape analysis. Additionally, a novel Hierarchical Shape Analysis\ud method based on the Gaussian and Laplacian pyramids is explained and used to\ud compare the featured Local Shape Model.\ud Experimental results on a number of real contours such as animal, leaf and brain\ud white matter outlines have been shown to demonstrate the effectiveness of the\ud proposed model. These results show that local shape models are efficient in modelling\ud the statistical variation of shape of biological structures. Particularly, the\ud development of this model provides an approach to the analysis of brain images\ud and brain morphometrics. Likewise, the model can be adapted to the problem of\ud content based image retrieval, where global and local shape similarity needs to be\ud measured

Topics: QA
OAI identifier:

Suggested articles


  1. (2007). 2D Ane-Invariant Contour Matching Using B-Spline Model.
  2. (2002). 3D Statistical Shape Models Using Direct Optimisation of Description Length.
  3. (2005). A bayesian method for automatic landmark detection in segmented images.
  4. (2001). A Comparative Study on Shape Retrieval Using Fourier Descriptors with Dierent Shape Signatures.
  5. (2001). A comparison of Shape Retrieval Using Fourier Descriptors and Short-Time Fourier Descriptors.
  6. (1991). A Contour-Oriented Approach to Shape Analysis.
  7. (2000). A Framework for Automatic Landmark Identi Using a New Method of Nonrigid Correspondence.
  8. (2002). A framework for computational anatomy,
  9. (2000). A Global Geometric Framework for Nonlinear Dimensionality Reduction.
  10. (1998). A Glossary for Geometric Morphometrics,
  11. (2003). A morphometric study on morphological plasticity of shell form in crevice-dwelling pterioida (bivalvia).
  12. (2003). A nondestructive impulse hammer for evaluating the bond between asphalt layers in a road pavement.
  13. (1995). A procedure for determining rigid body transformation parameters.
  14. (1978). A review of algorithms for shape analysis.
  15. (2007). A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape.
  16. (1993). A revolution in morphometrics.
  17. (2004). A statistical shape model of individual tracts extracted from diusion tensor MRI.
  18. (1998). A Survey of Shape Analysis Techniques. Pattern Recognition,
  19. (2008). A Survey of Shape Feature Extraction Techniques.
  20. (1995). A theory of multiscale, curvaturebased shape representation for planar curves.
  21. (2006). A three-dimensional fractal analysis method for quantifying white matter structure in human brain.
  22. (2002). A tutorial on Principal Components Analysis, url:,
  23. (1998). Active Appearance Models.
  24. (1999). Active Shape Focusing.
  25. (1995). Active Shape Models-Their Training and Application.
  26. (1992). Active Shape Models: Smart Snakes.
  27. (2000). Advances in morphometric identi of stocks.
  28. (2001). An adaptive-focus statistical shape model for segmentation and shape modeling of 3-D brain structures.
  29. (2006). An Approach for the Automatic Cephalometric Landmark Detection Using Mathematical Morphology and Active Appearance Models.
  30. (2001). An Invariant Approach to Statistical Analysis of Shapes. Chapman and Hall/CRC,
  31. (2005). and Eam Khwang Teoh. A novel 3D Partitioned Active Shape Model for Segmentation of Brain MR Images.
  32. (2005). and Eam Khwang Teoh. A novel framework for automated 3D PDM construction using deformable models.
  33. (2001). Ane curvature scale space with ane length parametrisation.
  34. (1970). Applications of the Karhunen-Loeve expansion to feature selection and ordering.
  35. (2005). Arti enlargement of a training set for statistical shape models: Application to cardiac images.
  36. (2001). Automated manifold surgery: Constructing geometrically accurate and topologically correct models of the human cerebral cortex.
  37. Automatic of digitised contours at multiple scales through the curvature scale space technique.
  38. (2007). Automatic identi of morphometric landmarks in digital images.
  39. (2009). Automatic Landmark Detection on Epicondyles of Distal Femur in X-Ray Images.
  40. Automatic segmentation and reconstruction of the cortex from neonatal MRI.
  41. (1995). Bayesian Data Analysis. Chapman and Hall,
  42. (2004). Bayesian Statistics.
  43. (1973). Biological shape and visual science.
  44. (2000). Boundary Finding with Prior Shape and Smoothness Models.
  45. (2004). Classi Parameter Estimation and State Estimation: An Engineering Approach Using MATLAB.
  46. (1984). Cluster Analysis. Sage Publicatons,
  47. (1985). Codon constraints on closed 2-d shapes.
  48. (1995). Combining Point Distribution Models with Shape Models Based on Finite Element Analysis. Image and Vision Computing,
  49. (1994). Comparative fractal analysis of cultured glia derived from optic nerve and brain demonstrate dierent rates of morphological dierentiation.
  50. (1999). Comparing Active Shape Models with Active Appearance Models.
  51. (1998). Computational anatomy: An emerging discipline.
  52. (2004). Computer-aided multivariate analysis.
  53. (2003). Computer-assisted imaging to assess brain structure in healthy and diseased brains.
  54. (2007). Cortical Surface Shape Analysis Based on Spherical Wavelets.
  55. (2004). Craniofacial sexual dimorphism patterns and allometry among extant hominids.
  56. (1986). Curvature Primal Sketch.
  57. (2003). Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization.
  58. (2008). Curve by fractal interpolation.
  59. (2005). Databasing the Brain: From Data to Knowledge (Neuroinformatics).
  60. (1996). Deformable models in medical image analysis: A survey.
  61. (2003). Deformable Mreps for 3D medical image segmentation.
  62. (2003). Detecting discriminative functional mri activation patterns using space curves.
  63. (2006). Diusion Maps and Coarse-Graining: A Uni Framework for Dimensionality Reduction, Graph Partitioning, and Data Set Parameterization.
  64. (2006). Diusion maps.
  65. (1976). Early processing of visual information.
  66. (1997). Eciency of simple shape descriptors.
  67. (1984). Eigenshape analysis of microfossils: A general morphometric procedure for describing changes in shape.
  68. (2008). Elke Th onnes. Monte Carlo methods.
  69. (2000). Enhancing CSS-based shape retrieval for objects with shallow concavities.
  70. (2002). Estimation of error in curvature computation on multi-scale free-form surfaces.
  71. (2003). Evaluation of 3d correspondence methods for model building.
  72. (2004). Exploratory Data Analysis with MATLAB. Chapman & Hall/CRC,
  73. (2009). Factor analysis, url:,
  74. (2000). Finite Mixture Models.
  75. Fourier descriptors and handwritten digit recognition.
  76. (2009). Fractal - from mathworld{a wolfram web resource, url:,
  77. (2007). Fractal Active Shape Models.
  78. (2003). Fractal dimension in human cerebellum measured by magnetic resonance imaging.
  79. (1990). Fractal Geometry: Mathematical Foundations and Applications.
  80. (1996). Fractal patterns for dendrites and axon terminals. Physica A: Statistical Mechanics and its Applications,
  81. (1990). Fractal Physiology and Chaos in Medicine. World Scienti
  82. (1993). Fractals in Biology and Medicine.
  83. (2009). Fractals, chaos, url:,
  84. (2006). Framework for the statistical shape analysis of brain structures using SPHARM-PDM.
  85. (2004). Gender dierences in cortical complexity.
  86. (1999). General Shape and Registration Analysis. In Stochastic geometry: likelihood and computation,
  87. (1975). Generalized Procrustes Analysis.
  88. (1999). Generalizing and extending the eigenshape method of shape space visualization and analysis.
  89. (2002). Geometric morphometrics and geological shape-classi systems.
  90. (2004). Geometric morphometrics: Ten years of progress following the `revolution'.
  91. (2004). Global and Local Shape Analysis of the Hippocampus Based on Level-of-Detail Representations.
  92. (1960). Harold Hotelling's Research in Statistics.
  93. (2007). Heinz Handels, and Nicholas Ayache. Point-Based Statistical Shape Models with Probabilistic Correspondences and Ane EM-ICP.
  94. (2003). Hessian Eigenmaps: New Locally Linear Embedding Techniques For High-Dimensional Data.
  95. (2003). Hierarchical active shape models, using the wavelet transform.
  96. (2008). Hierarchical statistical shape analysis and prediction of sub-cortical brain structures. Medical Image Analysis,
  97. (1998). Identifying global anatomical dierences: Deformation-based morphometry. Human Brain Mapping,
  98. (1993). Inferring locomotor behavior in paleogene mammals via eigenshape analysis.
  99. (2002). Integration of Local and Global Shape Analysis for Logo Classi
  100. (1971). Introduction to Statistical Theory.
  101. (2001). Intuitive, Localized Analysis of Shape Variability.
  102. (1998). Is nature fractal?
  103. (2003). Is the brain cortex a fractal?
  104. (1998). Is the geometry of nature fractal?
  105. (2002). Isolated leaves dataset, oregon state university web resource, url: tgd/leaves/,
  106. (2003). Laplacian Eigenmaps for Dimensionality Reduction and Data Representation.
  107. (2004). Learning an image manifold for retrieval.
  108. (1988). Linear Algebra and Its Applications.
  109. (2001). Linear Algebra. Schaum's Outline Series.
  110. (2005). Local Shape Modelling Using Warplets.
  111. MANI fold Learning Matlab Demo,
  112. (2009). Manifold - from mathworld{a wolfram web resource, url:,
  113. (2006). Manifold Clustering of Shapes. In
  114. (2005). Manifold Clustering.
  115. (2008). Manifold Learning and Dimensionality Reduction with Diffusion Maps. Seminar report,
  116. Mapping cortical asymmetry and complexity patterns in normal children.
  117. (2000). Mathematical/computational challenges in creating deformable and probabilistic atlases of the human brain.
  118. (2008). Methods of arti enlargement of the training set for statistical shape models.
  119. (1999). Monte Carlo Statistical Methods.
  120. (2001). Morphology of reactive microglia in the cerebral cortex: Fractal analysis and complementary quantitative methods.
  121. (1991). Morphometric Tools for Landmark Data: Geometry and Biology.
  122. (1994). Multiresolution stochastic hybrid shape models with fractal priors.
  123. (2006). Multiscale Active Contours.
  124. (1979). Multivariate Analysis. Probability and Mathematical Statistics.
  125. (1985). Multivariate morphometrics and analysis of shape.
  126. (1976). Multivariate statistical methods.
  127. (2004). Mutual information in coupled multi-shape model for medical image segmentation.
  128. (1999). Neuroimaging primer, url:,
  129. (2000). Nonlinear Dimensionality Reduction by Locally Linear Embedding.
  130. (1917). On Growth and Form.
  131. (2001). On spectral clustering: Analysis and an algorithm.
  132. (1989). On the Detection of Dominant Points on Digital Curves.
  133. (1981). On the relationships between SVD,
  134. (2009). PDPhoto: Free Public Domain Photo Database, url:,
  135. (1989). Principal Component Analysis,
  136. (1986). Principal Component Analysis.
  137. (1992). Probability and Random Processes.
  138. (2004). Procrustes Analysis.
  139. (1991). Procrustes Methods in the Statistical Analysis of Shape.
  140. (2004). Procrustes Problems.
  141. (1996). Robust and ecient shape indexing through curvature scale space.
  142. (1991). Robust contour decomposition using a constant curvature criterion.
  143. (1986). Scale base description and recognition of planar curves and two-dimensional shapes.
  144. (1983). Scale-Space Filtering.
  145. (1988). Segmentation of two-dimensional boundaries using the chain code.
  146. (1999). Segmentation, registration, and measurement of shape variation via image object shape.
  147. (2004). Self-Tuning Spectral Clustering. In
  148. (2008). Shape analysis of brain ventricles for improved classi of Alzheimer's patients.
  149. (1999). Shape and Shape Theory.
  150. (2002). Shape Matching and Object Recognition Using Shape Contexts.
  151. (2001). Shape versus size: Improved understanding of the morphology of brain structures.
  152. (1997). Silhouette-based occluded object recognition through curvature scale space.
  153. Snakes: Active Contour Models.
  154. (1994). Space-Filling Curves.
  155. (2006). Spline-Based Probabilistic Model for Anatomical Landmark Detection.
  156. (2003). Statistical Shape Analysis of Neuroanatomical Structures Based on Medial Models. Medical Image Analysis,
  157. (1998). Statistical Shape Analysis.
  158. (2009). Statistical shape models for 3D medical image segmentation: A review.
  159. (1953). Stochastic Processes.
  160. (1992). Surface Parametrization and Shape Description.
  161. (2004). Survey on 3D Shape Descriptors.
  162. (1998). Symmetry-based indexing of image databases.
  163. (1995). Tapio Sepp anen, and Matti Pietik ainen. An Experimental Comparison of Autoregressive and Fourier-Based Descriptors in 2D Shape Classi
  164. (2005). Terra Virtual, url:,
  165. (1964). The Feynman Lectures on
  166. (1982). The fractal geometry of nature. Freeman,
  167. (1983). The laplacian pyramid as a compact image code.
  168. (1996). The Statistical Theory of Shape.
  169. (2003). Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds.
  170. (1996). Three-dimensional fractal analysis of the white matter surface from magnetic resonance images of the human brain.
  171. (1996). Three-dimensional statistical analysis of sulcal variability in the human brain.
  172. (2005). Tissue deformation and shape models in image-guided interventions: a discussion paper.
  173. (2007). Towards Segmentation Based on a Shape Prior Manifold.
  174. (1992). Training models of shape from sets of examples.
  175. (2006). Twenty new digital brain phantoms for creation of validation image data bases.
  176. (1995). Understanding the MetropolisHastings Algorithm.
  177. (2007). Unsupervised learning of shape manifolds.
  178. (1994). Use of active shape models for locating structures in medical images.
  179. Visualizing concave and convex partitioning of 2d contours.
  180. (2005). Warplets: An image-dependent wavelet representation.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.