F. L. Bookstein. Morphometric tools for landmark data: Geometry and Biology. Cambridge Univ. Press, New York, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....CAM REPORT From Landmark Matching to Shape and Open Curve Matching: A Level Set Approach W. H. Liao , A. Khuu , M. Bergsneider 2, L. Vese 3, S. C. Huang , and S. Osher 3 Department of Biomathematics and Department of Molecular and Medical Pharmacology, UCLA, L.A. CA 90095 2Brain Injury Research Center, UCLA, L.A. CA 90095 3Department of Mathematics, UCLA, L.A. CA 90095 All correspondences should be addressed to the first author at feuillet ucla. edu Abstract In this paper, we present a new framework for warping shapes and open curves between two images. ....

....to Shape and Open Curve Matching: A Level Set Approach W. H. Liao , A. Khuu , M. Bergsneider 2, L. Vese 3, S. C. Huang , and S. Osher 3 Department of Biomathematics and Department of Molecular and Medical Pharmacology, UCLA, L.A. CA 90095 2Brain Injury Research Center, UCLA, L.A. CA 90095 3Department of Mathematics, UCLA, L.A. CA 90095 All correspondences should be addressed to the first author at feuillet ucla. edu Abstract In this paper, we present a new framework for warping shapes and open curves between two images. This method could also handle multiple pairs of shapes ....

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F. L. Bookstein, Morphometric tools for landmark data : geometry and biology, 1 st pbk. ed. Cambridge England; New York: Cambridge University Press, 1997.

.... within an image from sparse information on the displacements of a finite number of points (landmarks) This is an important issue for image processing and computer graphics, and the problem has generated a large number of publications, starting with the seminal papers of Bookstein (see [3] and references therein) There are numerous applications: generating deformations from the position of control points is used, for example, to synthesize facial expressions, or to compute morphings; analyzing variations of shape has application in medical imaging or face recognition, matching is ....

.... of finding a diffeomorphism g , with minimal size (in a sense to be defined) such that, for all i, g(x i ) y i (inexact matching) The method which is developed in the sequel takes its roots from three main ideas: Interpolating splines, as pioneered by Bookstein in computer vision ([3]) and widely used to generate dense warpings from sparse information. Generation of diffeomorphisms as flows (solutions of an ODE) in a framework which guarantees smoothness and consistency, as in [10, 4] Computation of geodesic distances (minimal path length) on deformable data, as used ....

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L. Bookstein, F, Morphometric tools for landmark data; geometry and biology, Cambridge University press, 1991.

....the established correspondence [10, 21] Unfortunately there is no generally accepted definition for anatomically meaningful correspondence. It is thus di#cult to judge the correctness of an established correspondence. In 2D, correspondence is often established using manually determined landmarks [1], but this is a time consuming, error prone and subjective process. In principle, the method extends to 3D, but in practice, due to very small sets of reliably identifiable landmarks, manual landmarking becomes impractical. Most automated approaches posed the correspondence problem as that of ....

Bookstein, F.L.: Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press (1991)

....to deform one biological structure to another closely related structure is D arcy Thompson in his classical book On Growth and Form [109] where he deformed the skulls of human and primates, and other biological structures using deformable grids. Unlike classical morphometry in shape analysis [12, 13, 40, 62, 101] , the deformation based mor phometry tries to avoid anatomical landmarks in characterizing morphological changes. An anatomical landmark is a point assigned by an expert that corresponds between organism in some biologically meaningful way [40] However, it is very hard to identify such ....

F.L. Bookstein. Morphometric Tools for Landmark Data:Geometry and Biology. Cam- bridge University Press, Cambridge, 1991.

....P. Several desirable properties of C (P) are proved, as well. Keywords: Shape, polygons, convexity, measurement. 1 Introduction Shape is a cmcial component in many areas of scientific analysis [4, 5] with examples including geomorphology [10] powder particle characterisation [6] and biology [2]. This paper is concerned with the measurement of the convexity of polygons, which can be considered as one of the basic descriptors of shape [14] and has received some attention over the years [3, 15] A convexity measure can be used for a variety of applications, for instance shape decomposition ....

F. Bookstein. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge University Press, 1991.

....a transformation that maps the model into the target. For this purpose there are several options; perhaps most common is the affine model. In this work, we use the thin plate spline (TPS) model, which is commonly used for representing flexible coordinate transformations [30, 25] Bookstein [5], for example, found it to be highly effective for modeling changes in biological forms. The thin plate spline is the 2D generalization of the cubic spline. In its regularized form, which is discussed below, the TPS model includes the affine model as a special case. We will now provide some ....

F. L. Bookstein. Morphometric tools for landmark data: geometry and biology. Cambridge Univ. Press, 1991.

....class under a group of transformations. This definition is incomplete in the context of visual analysis. This only tells us when two shapes are exactly the same. We need more than that for a theory of shape similarity or shape distance. The statistician s definition of shape, e.g. Bookstein [6] or Kendall [29] addresses the problem of shape distance, but assumes that correspondences are known. Other statistical approaches to shape comparison do not require correspondences e.g. one could compare feature vectors containing descriptors such as area or moments but such techniques often ....

....contain the homogeneous coordinates of 7 9 and Q, respectively, i.e. 1 pn pm) 1 Pn Pn2 (6) Here, Q denotes the pseudoinverse of Q. In this work, we mostly use the thin plate spline (TPS) model [14] 37] which is commonly used for representing flexible coordinate transformations. Bookstein [6] found it to be highly effective for modeling changes in biological forms. Powell applied the TPS model to recover transformations between curves [44] The thin plate spline is the 2D generalization of the cubic spline. In its regularized form, which is discussed below, the TPS model includes the ....

F.L. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge Univ. Press, 1991.

....class under a group of trans formations. This definition is incomplete in the context of visual analysis. This only tells us when two shapes are exactly the same; we need more than that for a theory of shape simi larity or shape distance. The statistician s definition of shape, e.g. Bookstein [6] or Kendall [28] addresses the problem of shape distance, but assumes that correspondences are known. Other statistical approaches to shape comparison do not require correspondences e.g. one could compare feature vectors containing descriptors such as area or moments but such techniques often ....

....the homogeneous coordinates of and Q, respectively, i.e. I p pm P = 6) 1 pn pn2 Here, Q denotes the pseudo inverse of Q. In this work, we mostly use the thin plate spline (TPS) model [13, 36] which is commonly used for representing flexible coordinate transformations. Bookstein [6] found it to be highly effective for modeling changes in biological forms. Powell applied the TPS model to recover transformations between curves [43] The thin plate spline is the 2D generalization of the cubic spline. In its regularized form, which is discussed below, the TPS model includes the ....

F. L. Bookstein. Morphometric tools for landmark data: geometry and biology. Cam- bridge Univ. Press, 1991. 33

....prediction methods. Thirdly, our error estimation for comparison between traditional and our approach is based on experiments from tracking both real and synthetic motion sequences. In the future, we will later start exploring the possibility of incorporating information from morphometric analysis [3] into the integrated tracking model to analyze motion and improve tracking. 2 Background 2.1 Image Segmentation 2.1.1 Boundary Based Approach To achieve image segmentation, traditional boundary basedapproaches find object boundaries by locating intensity discontinuities and linking meaningful ....

....model occasionally outperforms others in efficiency because of good initial estimations for convergence. Future work can be further investigated on several aspects. New attraction functions and prediction methods can be developed because they contribute most of the errors. Morphometric analysis [3] can be experimented to refine the model in prediction and adaptive schemes. 5 Acknowledgement The author would like to thank Dr. John Gauch from the University of Kansas for invaluable discussions and assistance on this topic and Dr. Chandra Kambhamettu from the University of Delaware for his ....

Fred L. Bookstein. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge University Press, 1991.

....In this article, we consider mainly intensity based registration methods, which directly take into account the voxel values, c.f. 21] Other methods are based on matching surfaces [21 23] curves [24] or interpolating landmarks using radial basis functions, especially thin plate splines [21, 25 3 27]. A. Semi local model The model proposed in this article is situated between the above mentioned local and global methods, combining the advantages of both. We parametrize the warp space by a scale parameter h and denote it V h . The scale parameter corresponds loosely to the density of knots ....

....we want a solution that is invariant to the choice of a particular coordinate system, or to the choice of units. The simplest criterion satisfying these requirements is J = R g ## (x) 2 dx, which is compatible with the elasticity theory, as it corresponds to strain or bending energy [25]. Besides interpolation, other approximation schemes can be applied, the most popular being least squares fitting. It consists of minimizing an extended criterion J # = J # P l (g(x r l ) x o l ) 2 . This has the advantage of accommodating uncertainty (noise) in landmark positions. ....

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F. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge University Press, 1997.

....algorithms work on a set of characteristic features extracted from the images. The dimensionality of the features is usually drastically smaller than the dimensionality of the original image data. The extraction process is highly non linear, mostly using thresholding. Landmark based methods [14 17] use a relatively small and sparse set of landmarks; these are important points which can be (manually or automatically) identified in both images. Extrinsic markers refer to specifically designed artificial features attached to 22 the object (or subject, in medical imaging) before acquisition to ....

....is refined only where it is needed. In feature based methods, the basis functions of the warping model can be placed where the features are. The deformation field is interpolated in regions where no information is available. Typical example are radial basis functions such as thin plate splines [14, 15, 38]. See also Chapter 3 for more details. 2.3 Similarity metrics 2.3.1 Data term The quality of registration is described by a cost function. This function has a predominant term measuring the quality of the matching which we shall call the data term. For feature based methods it is a mean ....

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F. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, 1997.

....by the choice of feature space (data space) warp space (search space) cost function (similarity metrics) and optimization algorithm (search strategy) they use. 2.1. Feature space According to the feature space employed, we can identify three classes of algorithms. Landmark based methods [4], 5] 6] use a relatively small and sparse set of landmarks important points which can be (manually or automatically) identified in both images. Specifically designed artificial features attached to the object before acquisition can serve as landmarks. Otherwise, manual landmark identification ....

....knowledge, or eventually to stabilize the algorithm. We shall call it the regularization term. In the variational setting, the regularization term can define the warping function space. For instance, in the landmark case, minimization of the norm of the Laplacian r 2 g is often used in practice [4], 5] This leads to a thin plate spline solution [19] 2.3. Optimization algorithm Many non linear registration methods lead to a non linear optimization problem. Various optimization methods are used, depending on the size and structure of the problem. The most popular choices include gradient ....

F. Bookstein, Morphometric Tools for Landmark Data : Geometry and Biology, Cambridge-University-Press, New York, 1997.

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F. L. Bookstein. Morphometric tools for landmark data: Geometry and Biology. Cambridge Univ. Press, New York, 1991.

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F.L. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, Cambridge, 1991.

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F. L. Bookstein. Morphometric tools for landmark data: geometry and biology. Cambridge Univ. Press, 1991.

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F.L. Bookstein. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge Press, 1997.

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F.L. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, 1991.

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F. L. Bookstein. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge University Press, 1991.

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F. L. Bookstein. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge University Press, 1991.

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F. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, 1991.

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F. L. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, Cambridge, 1991.

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F. L. Bookstein. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge University Press, 1991.

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F.L. Bookstein. Morphometric Tools for Landmark Data: Geometry and Biology. Cambridhe University Press, 1991.

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F.L. Bookstein, Morphometric tools for landmark data: Geometry and biology, Cambridge University Press, 1991.

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F.L. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, Cambridge, 1991.

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