J. C. Gower. Generalized procrustes analysis. Psychometrika, 40:33--51, 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to unseen images in a fraction of a second, given a reasonable initialisation. Variability is modelled by means of a Principal Component Analysis (PCA) i.e. an eigen analysis of the dispersions of shape and texture. Shapes are brought into alignment using a Generalised Procrustes Analysis (GPA) [16], and textures are warped into correspondence using a thinplate spline [17] or piece wise ane warp, thereby compensating for any variation in shape. Let x and t denote the shape and texture mean, respectively. The (ranked) model parameters, c, can then generate new instances in a simple linear ....

J. C. Gower, \Generalized Procrustes analysis," Psychometrika, vol. 40, pp. 33-50, 1975.

....dense correspondence The next step is to establish a dense correspondence between the surface meshes. This could be done using any set of landmarks as a frame of reference but it is desirable that the landmarks are typical of the distribution, so we have used the generalized Procrustes algorithm [9] to compute the mean landmarks. The key step in this process that is used repeatedly is a least squares alignment of two sets of 3D landmarks for which we use the quaternion method described for example in [11] Each surface is then warped onto the mean landmarks using the thin plate spline (TPS) ....

J. Gower. Generalized procrustes analysis. Psychometrika, 40:33--51, 1975.

....1 ; g n2 G I( gx o ) is taken over a compact set and the function I( gx o ) is continuous with respect to g = f g 1 ; g n g ae G. 2 10 Let us now consider four particular applications of our theory. First, Gower s and Ziezold s theory of mean landmark configurations ([11], 24] 26] has to be mentioned. It was the starting point for our general theory. There ae G is a special case of the procrustes metric (without scale transformations) Gower and Ziezold studied k tuples in the complex plane and showed that a configuration of such k tuples is in optimal ....

....special case of the procrustes metric (without scale transformations) Gower and Ziezold studied k tuples in the complex plane and showed that a configuration of such k tuples is in optimal position when all centres of gravity coincide. Thus it suffices to determine the optimum rotations. Goodall [11] adapted this method for shape analysis of landmark configurations. Our second example is the case of convex compact sets, which are described by support functions. Each n tuple K 1 ; K n of convex compact sets corresponds uniquely to the configuration x = fs K 1 ; s Kn g in the ....

J.C. Gower, "Generalized procrustes analysis," Psychometrika 40, pp. 33--51, 1975.

....together and a Principal Components Analysis (PCA) is performed on the supermatrix which includes the attributes of all assessors. On the basis of two data sets it was shown that the results of the proposed method match up to a large extent with those of Generalized Procrustes Analysis (GPA) (Gower, 1975; Arnold and Williams, 1986) Note that the method proposed by Kunert and Qannari is applicable to data obtained by means of a fixed vocabulary, i.e. all assessors use the same attributes, as well as to data derived from a free choice profiling procedure which allows each panelist to use his or ....

GOWER, J. C. (1975). Generalized Procrustes Analysis. Psychometrika, 40, 33-51.

....(b) These points are manually selected on each of the images in the training set 4 . Once selected, the set of points for each image is aligned to one another with respect to translation, rotation, and scaling. This is accomplished using an iterative algorithm based on the Procrustes method [80]. This linear alignment allows studying the object shape in a common coordinate frame, which we will refer to as the model space of the ASM. After the alignment, there is typically still a substantial amount of variability in the coordinates of each point. To compactly describe this variability as ....

J. C. Gower, "Generalized Procrustes analysis," Psychometrika, vol. 40, pp. 33--51, 1975.

....is based upon a simulation study involving the permutation procedure. Keywords : Sensory profiling, Principal Components Analysis, Generalized Procrustes Analysis, Isotropic scaling factors, Permutation test. 3 Introduction Generalized Procrustes Analysis (GPA) was introduced and popularized by Gower (1975). It is used for the analysis of sensory profiling data obtained by means of free choice profiling or fixed vocabulary profiling (Arnold and Williams, 1986 ; Dijkterhuis and Gower, 1991) However, a wider use of GPA is impeded by the fact that this statistical method involves sophisticated ....

GOWER J. C. 1975. Generalized Procrustes analysis. Psychometrika, 40, 33-51.

....is minimal. It is also the maximum likelihood estimate for the average shape in certain statistical models (Dryden and Mardia 1993; Kent 1994) It may be computed using an iterative procedure that has been called generalized least squares Procrustes superimposition method, GLS, as described by Gower (1975) and Rohlf and Slice (1990) This method is also called generalized Procrustes analysis, GPA, since it is not what is now commonly called a generalized least squares procedure in the statistical literature (e.g. McCullagh and Nelder 1989) Weighted means can also be used (Goodall 1991, is an ....

Gower, J. C. 1975. Generalized Procrustes analysis. Psychometrika 40:33-51.

....; y n Gamma1 ) T where (x i ; y i ) is the position of the i th landmark point on the training shape. 9 0 5 8 12 16 20 24 28 32 36 39 42 Figure 2. 1: A PDM representation of a hand shape The training shapes are aligned using a Generalised Procrustes Analysis technique (as derived by Gower [20]) A weighted least squares method is used to align each shape to the mean shape. The weights are chosen so that more signi#cance is given to the more #stable# landmark points. This process results in a mean shape vector x and a set of aligned training shape vectors x i . The next stage in the ....

J C Gower. Generalized procrustes analysis. Psychometrika, (40):33#51, 1975.

....Note the inverse projection from v to z = CT=kCTk is given by, z = e i [ 1 Gamma v v) 1 2 v] 9) For m 2 dimensions generalized matching for shape must proceed with an iterative algorithm, as linear regression cannot be used. The generalized Procrustes algorithm was given by Gower (1975) and is described in detail by Goodall (1991) Stoyan and Molchanov (1995) also provide a general matching algorithm for the shapes of random sets. Example A random sample of 23 second thoracic (T2) mouse vertebrae outlines was taken from the Large group of mice in the evolutionary study ....

Gower, J. C. (1975). Generalized Procrustes analysis. Psychometrika, 40:33--50.

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J. C. Gower. Generalized procrustes analysis. Psychometrika, 40:33--51, 1975.

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J. C. Gower, "Generalized Procrustes analysis," Psychometrika, vol. 40, pp. 33--51, 1975.

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J. C. Gower. Generalized procrustes analysis. Psychometrika, pages 33--51, 1975.

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J.C. Gower, Generalized Procrustes Analysis. Psychometrika. 40, 1975, 33-51.

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