We describe an algorithm for obtaining correspondences across a group of images of deformable objects. The approach is to construct a statistical model of appearance which can encode the training images as compactly as possible (a Minimum Description Length framework). Correspondences are defined by piece-wise linear interpolation between a set of control points defined on each image. Given such points a model can be constructed, which can approximate every image in the set. The description length encodes the cost of the model, the parameters and most importantly, the residuals not explained by the model. By modifying the positions of the control points we can optimise the description length, leading to good correspondence. We describe the algorithm in detail and give examples of its application to MR brain images and to faces. We also describe experiments which use a recently-introduced specificity measure to evaluate the performance of different components of the algorithm. 1

Nonlinear registration is mostly performed after initialization by a global, linear transformation (in this work, we focus on similarity transformations), computed by a linear registration method. For the further processing of the results, it is mostly assumed that this preregistration step completely removes the respective linear transformation. However, we show that in deformable settings, this is not the case. As a consequence, a significant linear component is still existent in the deformation computed by the nonlinear registration algorithm. For construction of statistical shape models (SSM) from deformations, this is an unwanted property: SSMs should not contain similarity transformations, since these do not capture information about shape. We propose a method which performs an a posteriori extraction of a similarity transformation from a given nonlinear deformation field, and we use the processed fields as input for SSM construction. For computation of minimal displacements, a closed-form solution minimizing the squared Euclidean norm of the displacement field subject to similarity parameters is used. Experiments on real inter-subject data and on a synthetic example show that the theoretically justified removal of the similarity component by the proposed method has a large influence on the shape model and significantly improves the results. 1.

We describe a multiscale representation for diffeomorphisms. Our representation allows synthesis – e.g. generate random diffeomorphisms – and analysis – e.g. identify the scales and locations where the diffeomorphism has behavior that would be unpredictable based on its coarse-scale behavior. Our representation has a forward transform with coefficients that are organized dyadically, in a way that is familiar from wavelet analysis, and an inverse transform that is nonlinear, and generates true diffeomorphisms when the underlying object satisfies a certain sampling condition. Although both the forward and inverse transforms are nonlinear, it is possible to operate on the coefficients in the same way that one operates on wavelet coefficients; they can be shrunk towards zero, quantized, and can be randomized; such procedures are useful for denoising, compressing, and stochastic simulation. Observations include: (a) if a template image with edges is morphed by a complex but known transform, compressing the morphism is far more effective than compressing the morphed image. (b) One can create random morphisms with and desired self-similarity exponents by inverse transforming scaled Gaussian noise. (c) Denoising morpishms in a sense smooths the underlying level sets of the object. 1

This paper addresses the problem of face recognition in the presence of deformation due to expressions. Facial motion is considered as an isometric mapping between surfaces, which allows preservation of geodesic distance between facial points. Subject to this assumption, we propose a novel technique which integrates 2D and 3D information to establish a new deformation invariant representation of the face. The 3D surface is used to define a polar geodesic coordinate space which is independent of the intrinsic geometry of the face. The corresponding color image is embedded in this space and serves as the recognition data. A preceding stage of hierarchical diffeomorphic grid-based image warping before the recognition process combined with a lip segmentation technique are also employed to increase the overall performance of the algorithm.

We develop a statistical shape model for the analysis of local shape variation. In particular, we consider models of shapes that exhibit self-similarity along their contours such as fractal and space filling curves.

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Abstract. We present a study of the relationship between the changes in the shape of the human ear due to jaw movement and acoustical feedback (AF) in hearing aids. In particular, we analyze the deformation field of the outer ear associated with the movement of the mandible (jaw bone) to understand its effect on AF and identify local regions that play a significant role. Our data contains ear impressions of 42 hearing aid users, in two different positions: open and closed mouth, and survey data including information about experienced discomfort due to AF. We use weighted support vector machines (WSVM) to investigate the separation between the presence and lack of AF and achieve classification accuracy of 80 % based on the deformation field. To robustly localize the regions of the deformation field that significantly contribute to AF we employ logistic regression penalized with elastic net (EN). By visualizing the selected variables on the mean surface, we provide clinical interpretations of the results. 1

This appendix introduces the proofs of Property 1 and 2 related to the discretization scheme; and a new compact kernel that we use throughout our method. Notation. Matrix are in upper case bold (e.g. A) and vector in lower case bold (e.g. a). We consider two cameras: a source S and a target T. □ (a, b) ⊂ R 2 is the quad formed by the two points a ∈ R 2 and b ∈ R 2. o □(a,b) ∈ R 2 is the center of the quad □ (a, b) and c □(a,b) ∈ R 2×4 its four corners. E is the set of Essential Matrices [2]; it is a variety of dimension N (N ≤ 5) in R 9 (the set of 3 × 3 matrices). A. Overlapping properties As a reminder we redefine the relative rotation R (u) and translation t (u) cos (π − θ − α) 0 sin (π − θ − α) R (u) = ⎣ 0 1 0 ⎦, ⎡ − sin (π⎤ − θ − α) 0 cos (π − θ − α) sin (θ) t (u) = ⎣ 0 ⎦. cos (θ) (1) Property 1 Overlapping Property – See supplementary material for Proof ψ (u) = 0 ⇔ π + γS + γT < θ + α < 3π − γS − γT with γS (resp. γT) half the field of view of the source camera (resp. target). ψ (u) = 0 means no overlap.

Abstract. Statistical shape models (SSM) capture the variation of shape across a population, in order to allow further analysis. Previous work demonstrates that deformation fields contain global transformation components, even if global preregistration is performed. It is crucial to construction of SSMs to remove these global transformation components from the local deformations- thus obtaining minimal deformations- prior to using these as input for SSM construction. In medical image processing, parameterized SSMs based on control points of free-form deformations (FFD) are a popular choice, since they offer several advantages compared to SSMs based on dense deformation fields. In this work, we extend the previous approach by presenting a framework for construction of both, unparameterized and FFD-based SSMs from minimal deformations. The core of the method is computation of minimal deformations by extraction of the linear part from the original dense deformations. For FFD-based SSMs, the FFDparameterization of the minimal deformations is performed by projection onto the space of FFDs. Both steps are computed by close-form solutions optimally in the least-square sense. The proposed method is evaluated on a data set of 62 MR images of the corpus callosum. The results show a significant improvement achieved by the proposed method for SSMs built on dense fields, as well as on FFD-based SSMs. 1