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Statistical models of shape and appearance are powerful tools for interpreting medical images. We assume a training set of images in which corresponding `landmark' points have been marked on every image. From this data we can compute a statistical model of the shape variation, a model of the texture variation and a model of the correlations between shape and texture. With enough training examples such models should be able to synthesize any image of normal anatomy. By finding the parameters which optimize the match between a synthesized model image and a target image we can locate all the structures represented by the model. Two approaches to the matching will be described. The Active Shape Model essentially matches a model to boundaries in an image. The Active Appearance Model finds model parameters which synthesize a complete image which is as similar as possible to the target image. By using a `difference decomposition' approach the current difference between target image and synthesi...

Biomedical images usually contain complex objects, which will vary in appearance significantly from one image to another. Attempting to measure or detect

We consider the problem of robustly and accurately locating facial features. The relative positions of different feature points are represented using a statistical shape model. We construct an individual detector for each feature point, which is used to generate a feature response image. The quality of a given hypothesised shape can be evaluated quickly by combining values from each response image. We use global search to predict the approximate position of the face, then refine the hypothesis using non-linear optimisation. The result is an algorithm capable of robustly and accurately matching a face model to new images, which we refer to as Shape Optimised Search (SOS). We describe SOS in detail and compare the performance of the algorithm when three different classes of feature detectors are used. We demonstrate that the approach is capable of outperforming the well known Active Appearance Model method. 1.

We describe a method of constructing parametric statistical models of shape variation which can generate continuous diffeomorphic (non-folding) deformation fields. Traditional statistical shape models are constructed by analysis of the positions of a set of landmark points. Here we analyse the parameters of continuous warp fields, constructed by composing simple parametric diffeomorphic warps. The warps are composed in such a way that the deformations are always defined in a reference frame. This allows the parameters controlling the deformations to be meaningfully compared from one example to another. A linear model is learnt to represent the variations in the warp parameters across the training set. This model can then be used to generalise the deformations. Models can be built either from sets of annotated points, or from unlabelled images. In the latter case, we use techniques from non-rigid registration to construct the warp fields deforming a reference image into each example. We describe the technique in detail and give examples of the resulting models.

The paper reviews various topics in shape analysis. In particular, matching configurations using regression is emphasized. Connections with general shape spaces and shape distances are discussed. Kendall's shape space and the affine shape space are considered in particular detail. Matching two configurations and the extension to generalized matching are illustrated with applications in electrophoresis and biology. Shape distributions are briefly discussed and inference in tangent spaces is considered. Finally, some robustness and smoothing issues are highlighted. 1 Introduction The geometrical description of an object can be decomposed into registration and shape information. For example, an object's location, rotation and size could be the registration information and the geometrical information that remains is the object's shape. An object's shape is invariant under registration transformations and two objects have the same shape if they can be registered to match exactly. Depending...

Typical aims of shape analysis are to match or register configurations, to estimate mean shapes and to investigate shape variability. Procrustes analysis is a popular method for the shape analysis of labeled point configurations, based on a least squares criterion. We consider alternative procedures which are highly resistant to outlier points. In particular we consider procedures based on S-estimators, Least Median of Squares and Least Quartile Difference estimators. Practical implementation issues and relative performances are discussed in a simulation study. A procedure for mean shape estimation is also considered. We demonstrate the methodology by comparing resistant mean estimation and principal component analysis with the Procrustes procedure on a dataset of mouse vertebral landmarks and a simulated dataset. In our examples the estimated mean configurations from the resistant and Procrustes procedures were very similar, and the principal components did not differ substantially. I...

Abstract The major challenge in constructing a statistical shape model for a structure is shape correspondence, which identifies a set of corresponded landmarks across a population of shape instances to accurately estimate the underlying shape variation. Both global or pairwise shapecorrespondence methods have been developed to automatically identify the corresponded landmarks. For global methods, landmarks are found by optimizing a comprehensive objective function that considers the entire population of shape instances. While global methods can produce very accurate shape correspondence, they tend to be very inefficient when the population size is large. For pairwise methods, all shape instances are corresponded to a given template independently. Therefore, pairwise methods are usually very efficient. However, if the population exhibits a large amount of shape variation, pairwise methods may produce very poor shape correspondence. In this paper, we develop a new method that attempts to address the limitations of global and pairwise methods. In particular, we first construct a shape tree to globally organize the population of shape instances by identifying similar shape instance pairs. We then perform pairwise shape correspondence between

Point Distribution Models are useful tools for modelling the variability of particular classes of shapes. A common approach is to apply a Principle Component Analysis to the data, to reduce the dimensionality of the representation. However, a single multivariate Gaussian model of the probability density, estimated from the principle covariances, can be substantially inaccurate. In this paper, we examine how the specificity of a model can be improved by using a mixture of Gaussians, trained with the Expectation-Maximization algorithm, with reference to hand and vehicle profiles. 1.