Based on recent work on Stochastic Partial Differential Equations (SPDEs), this paper presents a simple and well-founded method to implement the stochastic evolution of a curve. First. we explain why great care should...
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Based on recent work on Stochastic Partial Differential Equations (SPDEs), this paper presents a simple and well-founded method to implement the stochastic evolution of a curve. First. we explain why great care should be taken when considering such an evolution in a levelset framework. To guarantee the well-posedness of the evolution and to make it independent of the implicit representation of the initial curve, a Stratonovich differential has to be introduced. To implement this differential. a standard Ito plus drift approximation is proposed to turn an implicit scheme into an explicit one. Subsequently, we consider shape optimization techniques, which are a common framework to address various applications in computervision, like segmentation, tracking, stereo vision etc. The objective of our approach is to improve these methods through the introduction of stochastic motion principles. The extension we propose can deal with local minima and with complex cases where the gradient of the objective function with respect to the shape is impossible to derive exactly. Finally. as an application. we focus on image segmentation methods, leading to what we call Stochastic Active Contours.
We propose an algorithm to increase the resolution of multispectral satellite images knowing the panchromatic image at high resolution and the spectral channels at lower resolution. Our algorithm is based on the assum...
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We propose an algorithm to increase the resolution of multispectral satellite images knowing the panchromatic image at high resolution and the spectral channels at lower resolution. Our algorithm is based on the assumption that, to a large extent,. the geometry of the spectral channels is contained in the topographic map of its panchromatic image. This assumption, to-ether with the relation of the panchromatic image to the spectral channels. and the expression of the low-resolution pixel in terms of the high-resolution pixels given by some convolution kernel followed by subsampling, constitute the elements for constructing an energy functional (with several variants) whose minima will give the reconstructed spectral images at higher resolution. We discuss the validity of the above approach and describe our numerical procedure. Finally. some experiments on a set of multispectral satellite images are displayed.
In this paper we consider a new approach for single object segmentation in 3D images. Our method improves the classical geodesic active surface model. It greatly simplifies the model initialization and naturally avoid...
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In this paper we consider a new approach for single object segmentation in 3D images. Our method improves the classical geodesic active surface model. It greatly simplifies the model initialization and naturally avoids local minima by incorporating user extra information into the segmentation process. The initialization procedure is reduced to introducing 3D curves into the image. These curves are supposed to belong to the surface to extract and thus, also constitute user given information. Hence. our model finds a surface that has these curves as boundary conditions and that minimizes the integral of a potential function that corresponds to the image features. Our goal is achieved by using globally minimal paths. We approximate the surface to extract by a discrete network of paths. Furthermore, an interpolation method is used to build a mesh or an implicit representation based on the information retrieved from the network of paths. Our paper describes a fast construction obtained by exploiting the Fast Marching algorithm and a fast analytical interpolation method. Moreover, a levelset method can be used to refine the segmentation when higher accuracy is required. The algorithm has been successfully applied to 3D medical images and synthetic images.
Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently. there arises the need to filte...
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Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently. there arises the need to filter and segment such tensor fields. In order to detect edge-like structures in tensor fields, we first generalise Di Zenzo's concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the Corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments oil three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts.
The proceedings contain 24 papers. The topics discussed include: a variational approach to multi-modal image matching;optimal mass transport and image registration;on smoothness measures of active contours and surface...
ISBN:
(纸本)076951278X
The proceedings contain 24 papers. The topics discussed include: a variational approach to multi-modal image matching;optimal mass transport and image registration;on smoothness measures of active contours and surfaces;on affine invariance in the Beltrami framework for vision;combining total variation and wavelet packet approaches for image deburring;stability of image restoration by minimizing regularized objective functions;multiple contour finding and perceptual grouping using minimal paths;affine invariant edge completion with affine geodesics;3D automated segmentation and structural analysis of vascular trees using deformable models;cortex segmentation-a fast variational geometric approach;diffusion-snakes: combining statistical shape knowledge and image information in a variational framework;and a self-referencing level-set method for image reconstruction from sparse Fourier samples.
In this paper we propose a levelset method to segment MR cardiac images. Our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints. The visua...
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In this paper we propose a levelset method to segment MR cardiac images. Our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints. The visual information is expressed through a gradient vector flow-based boundary component and a region term that aims at best separating the cardiac contours/regions according to their global intensity properties. In order to deal with misleading visual support, an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance. The resulting motion equations are implemented using a levelset approach and a fast and stable numerical approximation scheme, the Additive Operator Splitting. Encouraging experimental results are provided using real data.
We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functiona...
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We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes. We propose a closed-form, parameter-free solution for incorporating invariance with respect to similarity transformations in the variational framework. We show segmentation results on artificial and real-world images with and without prior shape information. In the cases of noise, occlusion or strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by a levelset implementation of geodesic active contours.
We propose a new multiphase levelset framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization...
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We propose a new multiphase levelset framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2-phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In Scale-Space'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141-151) and T. Chan and L. Vese (2001. ieee-IP, 10(2):266-277). The multiphase levelset formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap;it needs only log n levelset functions for n phases in the piecewise constant case;it can represent boundaries with complex topologies, including triple junctions;in the piecewise smooth case, only two levelset functions formally suffice to represent any partition, based on The Four-Color Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and sethian levelset method.
Matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations. Handling complex, nonrigid deformations in thi...
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Matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations. Handling complex, nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years. The thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities (e. g. SSD) can be extended to the multimodal case where more complex intensity similarity measures are necessary. To this end, we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures, and use the results to generalize a recently proposed and very effective optical flow algorithm (L. Alvarez, J. Weickert, and J. Sanchez, 2000, Technical Report, and IJCV 39(1):41-56) to the case of multimodal image registration. Our method readily extends to the case of locally computed similarity measures, thus providing the flexibility to cope with spatial non-stationarities in the way the intensities in the two images are related. The well posedness of the resulting equations is proved in a complementary work (O.D. Faugeras and G. Hermosillo, 2001, Technical Report 4235, INRIA) using well established techniques in functional analysis. We briefly describe our numerical implementation of these equations and show results on real and synthetic data.
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