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198
Robust Anisotropic Diffusion
, 1998
"... Relations between anisotropic diffusion and robust statistics are described in this paper. Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The "edge-stopping" function in the ani ..."
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Cited by 361 (17 self)
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Relations between anisotropic diffusion and robust statistics are described in this paper. Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The "edge-stopping" function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework. This connection leads to a new "edge-stopping" function based on Tukey's biweight robust estimator, that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in an image that has been smoothed with anisotropic diffusion. Additionally, we derive a relationship between anisotropic diffusion and regularization with line processes. Adding constraints on the spatial organization of the ...
A Riemannian Framework for Tensor Computing
- INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2006
"... Positive definite symmetric matrices (so-called tensors in this article) are nowadays a common source of geometric information. In this paper, we propose to provide the tensor space with an affine-invariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of ..."
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Cited by 286 (27 self)
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Positive definite symmetric matrices (so-called tensors in this article) are nowadays a common source of geometric information. In this paper, we propose to provide the tensor space with an affine-invariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular manifold of constant curvature without boundaries (null eigenvalues are at the infinity), the geodesic between two tensors and the mean of a set of tensors are uniquely defined, etc. We have
Adaptive Segmentation of MRI data
, 1995
"... Intensity-based classification of MR images has proven problematic, even when advanced techniques are used. Intra-scan and inter-scan intensity inhomogeneities are a common source of difficulty. While reported methods have had some success in correcting intra-scan inhomogeneities, such methods requi ..."
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Cited by 224 (15 self)
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Intensity-based classification of MR images has proven problematic, even when advanced techniques are used. Intra-scan and inter-scan intensity inhomogeneities are a common source of difficulty. While reported methods have had some success in correcting intra-scan inhomogeneities, such methods require supervision for the individual scan. This paper describes a new method called adaptive segmentation that uses knowledge of tissue intensity properties and intensity inhomogeneities to correct and segment MR images. Use of the EM algorithm leads to a method that allows for more accurate segmentation of tissue types as well as better visualization of MRI data, that has proven to be effective in a study that includes more than 1000 brain scans. Implementation and results are described for segmenting the brain in the following types of images: axial (dual-echo spin-echo), coronal (3DFT gradient-echo T1-weighted) all using a conventional head coil; and a sagittal section acquired using a surf...
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
- IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... We address the problem of vector-valued image regularization with variational methods and PDE's. From the study of existing formalisms, we propose a unifying framework based on a very local interpretation of the regularization processes. The resulting equations are then specialized into new reg ..."
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Cited by 181 (8 self)
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We address the problem of vector-valued image regularization with variational methods and PDE's. From the study of existing formalisms, we propose a unifying framework based on a very local interpretation of the regularization processes. The resulting equations are then specialized into new regularization PDE's and corresponding numerical schemes that respect the local geometry of vector-valued images. They are finally applied on a wide variety of image processing problems, including color image restoration, inpainting, magnification and flow visualization.
Coherence-Enhancing Diffusion Filtering
, 1999
"... The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operato ..."
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Cited by 137 (3 self)
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The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with respect to its well-posedness and scale-space properties. An efficient scheme is presented which uses a stabilization by a semi-implicit additive operator splitting (AOS), and the scale-space behaviour of this method is illustrated by applying it to both 2-D and 3-D images.
Magnetic resonance image tissue classification using a partial volume model
- NEUROIMAGE
, 2001
"... We describe a sequence of low-level operations to isolate and classify brain tissue within T1-weighted magnetic resonance images (MRI). Our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering, edge detection, and mathematical morphology. We compensate for imag ..."
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Cited by 137 (6 self)
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We describe a sequence of low-level operations to isolate and classify brain tissue within T1-weighted magnetic resonance images (MRI). Our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering, edge detection, and mathematical morphology. We compensate for image nonuniformities due to magnetic field inhomogeneities by fitting a tricubic B-spline gain field to local estimates of the image nonuniformity spaced throughout the MRI volume. The local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point. The measurement model uses mean tissue intensity and noise variance values computed from the global image and a multiplicative bias parameter that is estimated for each region during the histogram fit. Voxels in the intensity-normalized image are then classified into six tissue types using a maximum a posteriori classifier. This classifier combines the partial volume tissue measurement model with a Gibbs prior that models the spatial properties of the brain. We validate each stage of our algorithm on real and phantom data. Using data from the 20 normal MRI brain data sets of the Internet Brain Segmentation Repository, our method achieved average � indices of ��0.746 � 0.114 for gray matter (GM) and ��0.798 � 0.089 for white matter (WM) compared to expert labeled data. Our method achieved average � indices �� 0.893 � 0.041 for GM and ��0.928 � 0.039 for WM compared to the ground truth labeling on 12 volumes from the Montreal Neurological Institute’s BrainWeb phantom.
Creating connected representations of cortical gray matter for functional MRI visualization
- IEEE Transactions on Medical Imaging
, 1997
"... Abstract—We describe a system that is being used to segment gray matter from magnetic resonance imaging (MRI) and to create connected cortical representations for functional MRI visualization (fMRI). The method exploits knowledge of the anatomy of the cortex and incorporates structural constraints i ..."
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Cited by 127 (7 self)
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Abstract—We describe a system that is being used to segment gray matter from magnetic resonance imaging (MRI) and to create connected cortical representations for functional MRI visualization (fMRI). The method exploits knowledge of the anatomy of the cortex and incorporates structural constraints into the segmentation. First, the white matter and cerebral spinal fluid (CSF) regions in the MR volume are segmented using a novel techniques of posterior anisotropic diffusion. Then, the user selects the cortical white matter component of interest, and its structure is verified by checking for cavities and handles. After this, a connected representation of the gray matter is created by a constrained growing-out from the white matter boundary. Because the connectivity is computed, the segmentation can be used as input to several methods of visualizing the spatial pattern of cortical activity within gray matter. In our case, the connected representation of gray matter is used to create a flattened representation of the cortex. Then, fMRI measurements are overlaid on the flattened representation, yielding a representation of the volumetric data within a single image. The software is freely available to the research community. Index Terms — Functional MRI, human cortex, segmentation, structural MRI, visualization.
Adaptive, Template Moderated, Spatially Varying Statistical Classification
- Medical Image Analysis
, 1998
"... A novel image segmentation algorithm was developed to allow the automatic segmentation of both normal and abnormal anatomy. The new algorithm is a form of spatially varying classification (SVC), in which an explicit anatomical template is used to moderate the segmentation obtained by k Nearest Neigh ..."
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Cited by 113 (23 self)
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A novel image segmentation algorithm was developed to allow the automatic segmentation of both normal and abnormal anatomy. The new algorithm is a form of spatially varying classification (SVC), in which an explicit anatomical template is used to moderate the segmentation obtained by k Nearest Neighbour (\knnrule) statistical classification. The new algorithm consists of an iterated sequence of spatially varying classification and nonlinear registration, which creates an adaptive, template moderated (ATM), spatially varying classification (SVC). The ATM SVC algorithm was applied to several segmentation problems, involving different types of imaging and different locations in the body. Segmentation and validation experiments were carried out for problems involving the quantification of normal anatomy (MRI of brains of babies, MRI of knee cartilage of normal volunteers) and pathology of various types (MRI of patients with multiple sclerosis, MRI of patients with brain tumours, MRI of patients with damaged knee cartilage). In each case, the ATM SVC algorithm provided a better segmentation than statistical classification or elastic matching alone. \emph{Keywords:} template moderated segmentation, elastic matching, nearest neighbour classification, knee cartilage, neonate, brain, tumour
A Review of Nonlinear Diffusion Filtering
, 1997
"... . This paper gives an overview of scale-space and image enhancement techniques which are based on parabolic partial differential equations in divergence form. In the nonlinear setting this filter class allows to integrate a-priori knowledge into the evolution. We sketch basic ideas behind the differ ..."
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Cited by 100 (10 self)
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. This paper gives an overview of scale-space and image enhancement techniques which are based on parabolic partial differential equations in divergence form. In the nonlinear setting this filter class allows to integrate a-priori knowledge into the evolution. We sketch basic ideas behind the different filter models, discuss their theoretical foundations and scale-space properties, discrete aspects, suitable algorithms, generalizations, and applications. 1 Introduction During the last decade nonlinear diffusion filters have become a powerful and well-founded tool in multiscale image analysis. These models allow to include a-priori knowledge into the scale-space evolution, and they lead to an image simplification which simultaneously preserves or even enhances semantically important information such as edges, lines, or flow-like structures. Many papers have appeared proposing different models, investigating their theoretical foundations, and describing interesting applications. For a n...
