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71
Surface matching via currents
 IPMI 2005. LNCS
, 2005
"... Abstract. We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriat ..."
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Cited by 106 (2 self)
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Abstract. We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriate choice for representations because they inherit natural transformation properties from differential forms. We impose a Hilbert space structure on currents, whose norm gives a convenient and practical way to define a matching functional. Using this Hilbert space norm, we also derive and implement a surface matching algorithm under the large deformation framework, guaranteeing that the optimal solution is a onetoone regular map of the entire ambient space. We detail an implementation of this algorithm for triangular meshes and present results on 3D face and medical image data. 1
Evaluation of 3D Correspondence Methods for Model Building
 Information Processing in Medical Imaging (IPMI
, 2003
"... The correspondence problem is of high relevance in the construction and use of statistical models. Statistical models are used for a variety of medical application, e.g. segmentation, registration and shape analysis. In this paper, we present comparative studies in three anatomical structures of ..."
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Cited by 59 (11 self)
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The correspondence problem is of high relevance in the construction and use of statistical models. Statistical models are used for a variety of medical application, e.g. segmentation, registration and shape analysis. In this paper, we present comparative studies in three anatomical structures of four di#erent correspondence establishing methods.
Shape Registration in Implicit Spaces Using Information Theory and Free Form Deformations
 IEEE Trans. Pattern Analysis and Machine Intelligence (TPAMI
, 2006
"... We present a novel variational and statistical approach for shape registration. Shapes of interest are implicitly embedded in a higher dimensional space of distance transforms. In this implicit embedding space, registration is formulated in a hierarchical manner: the Mutual Information criterion s ..."
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Cited by 59 (13 self)
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We present a novel variational and statistical approach for shape registration. Shapes of interest are implicitly embedded in a higher dimensional space of distance transforms. In this implicit embedding space, registration is formulated in a hierarchical manner: the Mutual Information criterion supports various transformation models and is optimized to perform global registration; then a Bspline based Incremental Free Form Deformations (IFFD) model is used to minimize a SumofSquaredDifferences (SSD) measure and further recover a dense local nonrigid registration field. The key advantage of such framework is twofold: (1) it naturally deals with shapes of arbitrary dimension (2D, 3D or higher) and arbitrary topology (multiple parts, closed/open), and (2) it preserves shape topology during local deformation, and produces local registration fields that are smooth, continuous and establish onetoone correspondences. Its invariance to initial conditions is evaluated through empirical validation, and various hard 2D/3D geometric shape registration examples are used to show its robustness to noise, severe occlusion and missing parts. We demonstrate the power of the proposed framework using two applications: one for statistical modeling of anatomical structures, another for 3D face scan registration and expression tracking. We also compare the performance of our algorithm with that of several other wellknown shape registration algorithms.
ModelBased Segmentation of Medical Imagery by Matching Distributions
 IEEE Trans. Med. Imaging
, 2005
"... The segmentation of deformable objects from threedimensional (3D) images is an important and challenging problem, especially in the context of medical imagery. We present a new segmentation algorithm based on matching probability distributions of photometric variables that incorporates learned sha ..."
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Cited by 44 (4 self)
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The segmentation of deformable objects from threedimensional (3D) images is an important and challenging problem, especially in the context of medical imagery. We present a new segmentation algorithm based on matching probability distributions of photometric variables that incorporates learned shape and appearance models for the objects of interest. The main innovation over similar approaches is that there is no need to compute a pixelwise correspondence between the model and the image. This allows for a fast, principled algorithm. We present promising results on difficult imagery for 3D computed tomography images of the male pelvis for the purpose of imageguided radiotherapy of the prostate.
A unified informationtheoretic approach to the correspondence problem in image registration
 In Proceedings of the International Conference on Pattern Recognition (ICPR
, 2004
"... Abstract. The nonrigid registration of a group of images shares a common feature with building a model of a group of images: a dense, consistent correspondence across the group. Image registration aims to find the correspondence, while modelling requires it. This paper presents the theoretical fram ..."
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Cited by 44 (10 self)
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Abstract. The nonrigid registration of a group of images shares a common feature with building a model of a group of images: a dense, consistent correspondence across the group. Image registration aims to find the correspondence, while modelling requires it. This paper presents the theoretical framework required to unify these two areas, providing a groupwise registration algorithm, where the inherently groupwise model of the image data becomes an integral part of the registration process. The performance of this algorithm is evaluated by extending the concepts of generalisability and specificity from shape models to image models. This provides an independent metric for comparing registration algorithms of groups of images. Experimental results on MR data of brains for various pairwise and groupwise registration algorithms is presented, and demonstrates the feasibility of the combined registration/modelling framework, as well as providing quantitative evidence for the superiority of groupwise approaches to registration. 1
3d active shape models using gradient descent optimization of description length
 in Proc. IPMI
, 2005
"... Abstract. Active Shape Models are a popular method for segmenting threedimensional medical images. To obtain the required landmark correspondences, various automatic approaches have been proposed. In this work, we present an improved version of minimizing the description length (MDL) of the model. ..."
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Cited by 32 (4 self)
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Abstract. Active Shape Models are a popular method for segmenting threedimensional medical images. To obtain the required landmark correspondences, various automatic approaches have been proposed. In this work, we present an improved version of minimizing the description length (MDL) of the model. To initialize the algorithm, we describe a method to distribute landmarks on the training shapes using a conformal parameterization function. Next, we introduce a novel procedure to modify landmark positions locally without disturbing established correspondences. We employ a gradient descent optimization to minimize the MDL cost function, speeding up automatic model building by several orders of magnitude when compared to the original MDL approach. The necessary gradient information is estimated from a singular value decomposition, a more accurate technique to calculate the PCA than the commonly used eigendecomposition of the covariance matrix. Finally, we present results for several synthetic and realworld datasets demonstrating that our procedure generates models of significantly better quality in a fraction of the time needed by previous approaches. 1
Adding curvature to minimum description length shape models
 In Proc. British Machine Vision Conference
, 2003
"... The Minimum Description Length (MDL) approach to shape modelling seeks a compact description of a set of shapes in terms of the coordinates of marks on the shapes. It has been shown that the mark positions resulting from this optimisation to a large extent solve the socalled point correspondence pr ..."
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Cited by 28 (1 self)
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The Minimum Description Length (MDL) approach to shape modelling seeks a compact description of a set of shapes in terms of the coordinates of marks on the shapes. It has been shown that the mark positions resulting from this optimisation to a large extent solve the socalled point correspondence problem: How to select points on shapes defined as curves so that the points correspond across a data set. However, this MDL approach does not capture important shape characteristics related to the curvature of the curves, and occasionally it places marks in obvious conflict with the human notion of point correspondence. This paper shows how the MDL approach can be finetuned by adding a term to the cost function expressing the mismatch of curvature features across the data set. The method is illustrated on silhouettes of adult heads. The MDL method is able to solve the point correspondence problem and a classification of the heads into male and female improves dramatically when using the MDLgenerated marks.
I.: A shapeguided deformable model with evolutionary algorithm initialization for 3D soft tissue segmentation
 In: Proc IPMI. Volume 4584 of LNCS
, 2007
"... Abstract. We present a novel method for the segmentation of volumetric images, which is especially suitable for highly variable soft tissue structures. Core of the algorithm is a statistical shape model (SSM) of the structure of interest. A global search with an evolutionary algorithm is employed to ..."
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Cited by 26 (2 self)
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Abstract. We present a novel method for the segmentation of volumetric images, which is especially suitable for highly variable soft tissue structures. Core of the algorithm is a statistical shape model (SSM) of the structure of interest. A global search with an evolutionary algorithm is employed to detect suitable initial parameters for the model, which are subsequently optimized by a local search similar to the Active Shape mechanism. After that, a deformable mesh with the same topology as the SSM is used for the final segmentation: While external forces strive to maximize the posterior probability of the mesh given the local appearance around the boundary, internal forces governed by tension and rigidity terms keep the shape similar to the underlying SSM. To prevent outliers and increase robustness, we determine the applied external forces by an algorithm for optimal surface detection with smoothness constraints. The approach is evaluated on 54 CT images of the liver and reaches an average surface distance of 1.6 ± 0.5 mmincomparisonto manual reference segmentations. 1
Shape modeling and analysis with entropybased particle systems
 In Proceedings of the 20th International Conference on Information Processing in Medical Imaging
, 2007
"... Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. I ..."
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Cited by 26 (13 self)
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Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. Increasingly, however, researchers are exploring the use of more detailed models that are derived computationally from threedimensional images and surface descriptions. While computationallyderived models of shape are promising new tools for biomedical research, they also present some significant engineering challenges, which existing modeling methods have only begun to address. In this dissertation, I propose a new computational framework for statistical shape modeling that significantly advances the stateoftheart by overcoming many of the limitations of existing methods. The framework uses a particlesystem representation of shape, with a fast correspondencepoint optimization based on information content. The optimization balances the simplicity of the model (compactness) with the accuracy of the shape representations by using two commensurate entropy
Images as Bags of Pixels
 In International Conference on Computer Vision
, 2003
"... We propose modeling images and related visual objects as bags of pixels or sets of vectors. For instance, gray scale images are modeled as a collection or bag of (X; Y; I) pixel vectors. This representation implies a permutational invariance over the bag of pixels which is naturally handled by endow ..."
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Cited by 25 (2 self)
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We propose modeling images and related visual objects as bags of pixels or sets of vectors. For instance, gray scale images are modeled as a collection or bag of (X; Y; I) pixel vectors. This representation implies a permutational invariance over the bag of pixels which is naturally handled by endowing each image with a permutation matrix. Each matrix permits the image to span a manifold of multiple con gurations, capturing the vector set's invariance to orderings or permutation transformations. Permutation congurations are optimized while jointly modeling many images via maximum likelihood. The solution is a uniquely solvable convex program which computes correspondence simultaneously for all images (as opposed to traditional pairwise correspondence solutions). Maximum likelihood performs a nonlinear dimensionality reduction, choosing permutations that compact the permuted image vectors into a volumetrically minimal subspace. This is highly suitable for principal components analysis which, when applied to the permutationally invariant bag of pixels representation, outperforms PCA on appearancebased vectorization by orders of magnitude. Furthermore, the bag of pixels subspace bene ts from automatic correspondence estimation, giving rise to meaningful linear variations such as morphings, translations, and jointly spatiotextural image transformations. Results are shown for several datasets.