Shape Modeling by Optimising Description Length Using Gradients and Parameterisation Invariance
Författare
Redaktör
- Karl Åström
- Lars-Erik Persson
- Sergei Silvestrov
Summary, in English
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.
Avdelning/ar
- Matematik LTH
- Matematikcentrum
- Mathematical Imaging Group
- ELLIIT: the Linköping-Lund initiative on IT and mobile communication
Publiceringsår
2012
Språk
Engelska
Sidor
51-91
Publikation/Tidskrift/Serie
Analysis for Science, Engineering and Beyond, The Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 8-9, 2008
Volym
6
Dokumenttyp
Del av eller Kapitel i bok
Förlag
Springer
Ämne
- Mathematics
Status
Published
Forskningsgrupp
- Mathematical Imaging Group
ISBN/ISSN/Övrigt
- ISBN: 978-3-642-20235-3 (print)
- ISBN: 978-3-642-20236-0 (online)