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Shape Modeling by Optimising Description Length Using Gradients and Parameterisation Invariance

Karlsson, Johan LU ; Ericsson, Anders LU and Åström, Karl LU (2012) In Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008 6. p.51-91
Abstract
In Statistical Shape Modeling, a dense correspondence between the shapes in the training set must be established. Traditionally this has been done by hand, a process that commonly requires a lot of work and is difficult, especially in 3D. In recent years there has been a lot of work on automatic construction of Shape Models. In recent papers (Davies et al., Medical Image Computing and Computer-Assisted Intervention MICCAI’2001, pp. 57–65, 2001; Davies et al., IEEE Trans. Med. Imaging. 21(5):525–537 2002; Kotcheff and Taylor, Med. Image Anal. 2:303–314 1998) Minimum Description Length, (MDL), is used to locate a dense correspondence between shapes. In this paper the gradient of the description length is derived. Using the gradient, MDL is... (More)
In Statistical Shape Modeling, a dense correspondence between the shapes in the training set must be established. Traditionally this has been done by hand, a process that commonly requires a lot of work and is difficult, especially in 3D. In recent years there has been a lot of work on automatic construction of Shape Models. In recent papers (Davies et al., Medical Image Computing and Computer-Assisted Intervention MICCAI’2001, pp. 57–65, 2001; Davies et al., IEEE Trans. Med. Imaging. 21(5):525–537 2002; Kotcheff and Taylor, Med. Image Anal. 2:303–314 1998) Minimum Description Length, (MDL), is used to locate a dense correspondence between shapes. In this paper the gradient of the description length is derived. Using the gradient, MDL is optimised using steepest descent. The optimisation is therefore faster and experiments show that the resulting models are better. To characterise shape properties that are invariant to similarity transformations, it is first necessary to normalise with respect to the similarity transformations. This is normally done using Procrustes analysis. In this paper we propose to align shapes using the MDL criterion. The MDL based algorithm is compared to Procrustes on a number of data sets. It is concluded that there is improvement in generalisation when using MDL to align the shapes. In this paper novel theory to prevent the commonly occurring problem of clustering under correspondence optimisation is also presented. The problem is solved by calculating the covariance matrix of the shapes using a scalar product that is invariant to mutual reparameterisations. An algorithm for implementing the ideas is proposed and compared to Thodberg’s state of the art algorithm for automatic shape modeling. The suggested algorithm is more stable and the resulting models are of higher quality according to the generalisation measure and according to visual inspection of the specificity. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008
editor
Åström, Karl; Persson, Lars-Erik; Silvestrov, Sergei; ; and
volume
6
pages
51 - 91
publisher
Springer
external identifiers
  • scopus:84887375478
ISBN
978-3-642-20235-3 (print)
978-3-642-20236-0 (online)
DOI
10.1007/978-3-642-20236-0_4
language
English
LU publication?
yes
id
8182a4af-ac50-4bd6-9cdb-33cbc6cf4784 (old id 3437192)
date added to LUP
2013-09-06 17:25:23
date last changed
2017-01-01 07:57:11
@inbook{8182a4af-ac50-4bd6-9cdb-33cbc6cf4784,
  abstract     = {In Statistical Shape Modeling, a dense correspondence between the shapes in the training set must be established. Traditionally this has been done by hand, a process that commonly requires a lot of work and is difficult, especially in 3D. In recent years there has been a lot of work on automatic construction of Shape Models. In recent papers (Davies et al., Medical Image Computing and Computer-Assisted Intervention MICCAI’2001, pp. 57–65, 2001; Davies et al., IEEE Trans. Med. Imaging. 21(5):525–537 2002; Kotcheff and Taylor, Med. Image Anal. 2:303–314 1998) Minimum Description Length, (MDL), is used to locate a dense correspondence between shapes. In this paper the gradient of the description length is derived. Using the gradient, MDL is optimised using steepest descent. The optimisation is therefore faster and experiments show that the resulting models are better. To characterise shape properties that are invariant to similarity transformations, it is first necessary to normalise with respect to the similarity transformations. This is normally done using Procrustes analysis. In this paper we propose to align shapes using the MDL criterion. The MDL based algorithm is compared to Procrustes on a number of data sets. It is concluded that there is improvement in generalisation when using MDL to align the shapes. In this paper novel theory to prevent the commonly occurring problem of clustering under correspondence optimisation is also presented. The problem is solved by calculating the covariance matrix of the shapes using a scalar product that is invariant to mutual reparameterisations. An algorithm for implementing the ideas is proposed and compared to Thodberg’s state of the art algorithm for automatic shape modeling. The suggested algorithm is more stable and the resulting models are of higher quality according to the generalisation measure and according to visual inspection of the specificity.},
  author       = {Karlsson, Johan and Ericsson, Anders and Åström, Karl},
  editor       = {Åström, Karl and Persson, Lars-Erik and Silvestrov, Sergei},
  isbn         = {978-3-642-20235-3 (print)},
  language     = {eng},
  pages        = {51--91},
  publisher    = {Springer},
  series       = {Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008},
  title        = {Shape Modeling by Optimising Description Length Using Gradients and Parameterisation Invariance},
  url          = {http://dx.doi.org/10.1007/978-3-642-20236-0_4},
  volume       = {6},
  year         = {2012},
}