G. Christensen. Deformable Shape Models for Anatomy. PhD thesis, Washington University, August 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the expert registration and almost all structural differences in the images have been corrected, cf. Fig. 1d. For the non linear registration we used the so called elastic matching algorithm. This method is based on a linear elasticity model and is also used in other projects, e.g. 1] 2] 5] [6], 18] We present a parallel implementation of a FFT based algorithm for the elastic matching. Using an appropriate communication strategy and a high speed network on a PC Cluster, it is possible to end up with almost linear speed up. Thus, the designed algorithm provides a basis for the ....

G.E. Christensen, Deformable Shape Models for Anatomy, Ph.D. thesis, Sever Institute of Technology, Washington University (1994).

....from template space to study space are smooth, elastic mechanics have been employed to constrain the deformations. A full description of the use of the kinematics of elastic solids to deform the templates can be found in [18] and a full mathematical development of the technique can be found in [21]. In short, these transformations based on the theory of elasticity develop restoring forces proportional to the square of the deformed distance. This is a sound model for minor transformations, but to accommodate the high variability present in anatomical data this model has proved too ....

....by ) v T r r r in the PDE. The viscosity coefficients are the l , coefficients. More detailed descriptions of the application of the fluid dynamic PDE above to the transformation of textbooks can be found in [18] and [22] A complete mathematical development of the technique can be found in [21]. An Eulerian reference frame is used to track the deformation. It places reference points at each of the pixels of the study to observe the deformation of the coordinate system of the textbook. As the textbook deforms in space over time, the points (particles in the viscous fluid mechanical ....

Gary E. Christensen, "Deformable Shape Models for Anatomy". Dissertation for Doctor of Science degree, Washington University, Sever Institute of Technology, 1994.

....criterion (resp. that solves a given PDE) is sought for in a very large and unrestrictive function space, e.g. the Sobolev space W 2 2 . The essence of these methods is entirely in the criterion (resp. PDE) The PDE come from the optical flow approach (gradient methods) 9] viscous fluid model [10 12], elastic deformations with physical analogs [13, 14] or without [15] Some elastic deformations can also be modeled as potential fields [16] At the other end, we have parametric, global methods that describe the correspondence function using a global model with a relatively small number of ....

G. Christensen, Deformable Shape Models for Anatomy. PhD thesis, Washington University, Saint Louis, Mississippi, 1994.

....and unrestrictive functional space, e.g. Sobolev space W 2 2 . The essence of these methods is entirely in the criterion (resp. PDE) The PDE come from 2 Biomedical Image Registration by Elastic Warping, Jan Kybic the optical flow approach (gradient methods) 25] viscous fluid model [26], 27] 28] elastic deformations with physical analogs [13] 29] or without it [30] Despite some restrictions, deformation fields are also being modeled as potential fields [31] At the other end, we have parametric, global methods that describe the correspondence function using a global model ....

G. Christensen, Deformable Shape Models for Anatomy, PhD. thesis, Washington University, Saint Louis, 1994.

....framework for non rigid registration of brains, combining a global registration approach with sparse constraints. We explicitly use it with cortical sulci constraints in that case. 1. 1 Non linear registration with local constraints An increasing number of authors study this registration problem [1, 3, 7, 9, 14, 16, 18, 19, 33, 4, 35, 38, 40, 47, 51]. We refer the reader to [28] for an overall survey on that subject. These methods are generally divided into two groups: those which deal with image similarities to find a good match between brain images, and those which try to use landmarks to solve this problem. Very few methods propose a ....

G. Christensen. Deformable shape models for anatomy. PhD thesis, Washington University, August 1994.

....and deformation. Non linear registration was first introduced by Bajcsy et al. 1] who used an elastic deformable template model and a correlation based similarity measure. Non linear registration based on a viscous fluid model instead of elasticity was introduced by Christensen et al. [4]. This approach was significantly accelerated by Bro Nielsen [2] using convolution with filter kernels. Thirion [12] proposed a similar method based on determination of force fields, that deform the image. Although these approaches are theoretically applicable to volumetric data, the ....

G.E. Christensen. Deformable shape models for anatomy. PhD thesis, Washington Univ., August 1994.

.... structures by matching with an atlas of normal anatomy (Bajcsy and Kovacic, 1989; Gee et al. 1994; Collins et al. 1992) ffl develop a probabilistic atlas of gross morphometric variability of the human brain (Collins et al. 1994) ffl improve the estimation of metabolism from PET images (Christensen et al. 1994), ffl segment anatomical structures in the presence of white matter abnormalities (Warfield et al. 1995) ffl characterize sulcal variability (Thompson et al. 1996) and abnormal brain structure (Thompson et al. 1997) ffl characterize the hippocampus (Haller et al. 1997; Joshi et al. 1997) ....

....for abnormalities such as tumours, abscesses, strokes and hemorrhages. Several groups have proposed automatic elastic matching schemes for volumetric anatomical models (Dengler and Schmidt, 1988; Nagel, 1983; Collins et al. 1992; Bajcsy and Kovacic, 1989; Gee et al. 1992; Miller et al. 1993; Christensen et al. 1994). These matching techniques will be reviewed in detail below. Most of these techniques have been successfully applied to the matching of structures of normal brains. An important problem is the development of automatic methods capable of matching successfully in the presence of a range of ....

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Christensen, G. E. (1994). Deformable Shape Models For Anatomy. PhD thesis, Washington University.

....John Ashburner Karl Friston 5 warp two images together (i.e. the problem is very high dimensional) The forms of spatial normalization tend to differ in how they cope with the large number of parameters. Some have abandoned conventional optimization approaches, and use viscous fluid models (Christensen et al. 1994; Christensen et al. 1996) to describe the warps. In these models, finite element methods are used to solve the partial differential equations that model one image as it flows to the same shape as the other. The major advantage of these methods is that they are able to account for large ....

....the parameters describing a transformation are determined. Then there is the transformation, where one of the images is transformed according to the set of parameters. The registration step involves matching the object image to some form of standardized template image. Unlike in the work of Christensen et al. 1994; 1996) or the segmentation work by Collins et al. 1994a; 1995) spatial normalization requires that the images themselves are transformed to the space of the template, rather than a transformation being determined that transforms the template to the individual images. The nonlinear spatial ....

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Christensen, G. E. 1994. Deformable Shape Models for Anatomy. Doctoral Thesis.

....of the source image is interpolated to agree with pre computed surface warps. Another group of methods dealing with non rigid image registration is the physically based numerical methods where non rigid transformations are modeled as deformations of physical bodies (solids, fluids) 2] [10], see also Section 2. The traditional image registration scheme using physically based numerical methods is the following: Forces are first derived from image data using some similarity measure and then applied to deform the source image driving it to a correspondence with the target image. The ....

....structures in the human brain, possible deformations by the registration of brain images are not limited to locally small displacements. To cope with this problem, another group of physically based numerical methods based on the theory of fluid mechanics has been introduced by Christensen et al. [10], 11] In addition to fluid methods, one can also mention the hyperelastic approach of Rabbitt et al. 33] where the same sensor model for forces derivation is used. These models exploit the property that fluids do not carry memory about their initial state. The mathematical model involves a ....

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G.E. Christensen. Deformable Shape Models for Anatomy. Doctoral dissertation, Washington University, August 1994.

....used a globally elastic model, but derived the driving force from the derivative of a Gaussian sensor model. These previous approaches to non rigid registration have all suffered from the use of either global transformations or small deformation assumptions (as used in linear elasticity) In [5] Christensen et al. extended their work and described a registration approach in which they use a viscous fluid model to control the deformation. The template image is modelled as a thick fluid that flows out to match the study under the control of the same derivative of a Gaussian sensor model ....

....extended their work and described a registration approach in which they use a viscous fluid model to control the deformation. The template image is modelled as a thick fluid that flows out to match the study under the control of the same derivative of a Gaussian sensor model they used in [4] In [5] Christensen argue that this gaussian sensor model theoretically is better than the correlation based similarity measure used by Bajcsy et al. 1] Elastic models constrain the possible deformation because the deformation is a compromise between internal and external forces. Elastic displacements ....

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G.E. Christensen, Deformable shape models for anatomy, Washington University Ph.D. thesis, August 1994

.... (deformable template) has to be completely transformed onto another one (study) One group of methods dealing with non rigid image registration is the so called non parametric methods, where the degrees of freedom of admissible deformations are not defined by a fixed number of parameters [1] [3]. The non parametric methods model the non rigid transformations as deformations of physical bodies (solids, liquids) caused by applied forces. The traditional image registration scheme using non parametric methods is the following: Applied forces are first derived from image data using some ....

.... Gee et al. 11] proposed a probabilistic approach based on the finite element method which has been reported to have properties similar to those of [2] 1] Another group of non parametric methods which is based on the principles of fluid mechanics has been introduced by Christensen et al. [3], 4] These methods use properties of fluids that do not carry memory about their initial state, thus allowing large deformations. However, a local similarity measure is still used, which considerably limits the applicability of the fluid model as a general model for registration problems. The ....

G.E. Christensen. Deformable Shape Models for Anatomy. PhD thesis, Washington University, August 1994.

....instead of just the spatial dimension. Figure 1. Simple objects used to test the image registration algorithm. Registration methods that accommodate largedeformation, nonlinear transformations are often based on continuum mechanical models such as hyperelasticity[10] and viscous fluids [3, 5, 7, 8, 1, 9]. In the case of a hyperelasticity model, one image is deformed into the shape of the other assuming that it is a fully elastic material while accommodating the nonlinear behavior due to the path of the deformation. Registration algorithms based on the viscous fluid transformation model ....

G. Christensen. Deformable Shape Models for Anatomy. Sever Institute of Technology, Washington University, St. Louis, MO. 63130, Aug 1994.

....di#erential equations (PDE) The continuously defined deformation function minimizes a given criterion, or solves a given PDE. The essence of these methods is thus entirely in the criterion (resp. PDE) The PDE come from the optical flow approach (gradient methods) 22] viscous fluid model [23 25], elastic deformations with physical analogs [3, 26] or without it [27] Sometimes the deformation function is also modeled indirectly. For example, it can be modeled using a potential field [28] This reduces the dimensionality of the problem, at the expense of reduced generality of the ....

....(resp. that solves a given PDE) is sought for in a very large and unrestrictive function space, e.g. the Sobolev space W 2 2 . The essence of these methods is entirely in the criterion (resp. PDE) The PDE come from the optical flow approach (gradient methods) 22] viscous fluid model [23 25], elastic deformations with physical analogs [3, 26] or without [27] Some elastic deformations can also be modeled as potential fields [28] At the other end, we have parametric, global methods that describe the correspondence function using a global model with a relatively small number of ....

Gary Christensen, Deformable Shape Models for Anatomy, Ph.D. thesis, Washington University, Saint Louis, Mississippi, 1994. 162

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G. E. Christensen, "Deformable shape models for anatomy," D.Sc. Dissertation, Department of Electrical Engineering, Sever Institute of Technology, Washington University, St. Louis, MO, Aug. 1994.

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G. Christensen. Deformable Shape Models for Anatomy. PhD thesis, Washington University, August 1994.

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