We address the problem of restoring, while presenting possible discontinuities, fields of noisy orthonormal vector sets, taking the orthonormal constraints explicity into account. We develop a variational solution for...
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ISBN:
(纸本)076951278X
We address the problem of restoring, while presenting possible discontinuities, fields of noisy orthonormal vector sets, taking the orthonormal constraints explicity into account. We develop a variational solution for the general case where each image feature may correspond to multiple n-D orthogonal vectors of unit norms. We first formulate the problem in a new variational framework, where discontinuities and orthonormal constraints are preserved by means of constrained minimization and /spl Phi/-function regularization, leading to a set of coupled anisotropic diffusion PDE. A geometric interpretation of the resulting equations, coming from the field of solid mechanics, is proposed for the 3D case. Two interesting restrictions of our framework are also tackled: the regularization of 30 rotation matrices and the direction diffusion (the parallel with previous works is made). Finally, we present a number of denoising results and applications.
Image registration is the process of establishing a common geometric reference frame between two or more data sets from the same or different imaging modalities possibly taken at different times. In the context of med...
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ISBN:
(纸本)076951278X
Image registration is the process of establishing a common geometric reference frame between two or more data sets from the same or different imaging modalities possibly taken at different times. In the context of medical imaging and in particular image-guided therapy, the registration problem consists of finding automated methods that align multiple data sets with each other and with the patient. We propose a method of elastic registration based on the Monge-Kantorovich problem of optimal mass transport.
We present a new approach for finding a set of contour curves in an image. We consider the problem of perceptual grouping and contour completion, where the data is a set of points in the image. A new method to find co...
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ISBN:
(纸本)076951278X
We present a new approach for finding a set of contour curves in an image. We consider the problem of perceptual grouping and contour completion, where the data is a set of points in the image. A new method to find complete curves from a set of contours or edge points is presented. Our approach is based on a previous work on finding contours as minimal paths between two end points using the fast marching algorithm (Cohen et al., 1997). Given a set of key points, we find the pairs of points that have to be linked. The paths that join them complete the initial set of contours and allow us to close them. In a second part, we propose a scheme that does not need key points for initialization. Key points are automatically selected from a larger set of admissible points. We illustrate the capability of our approach to close contours with synthetic examples.
We show how the piecewise-smooth Mumford-Shah segmentation problem can be solved using the levelset method of Osher and sethian (1988). The obtained algorithm can be simultaneously used to denoise, segment, detect-ex...
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ISBN:
(纸本)076951278X
We show how the piecewise-smooth Mumford-Shah segmentation problem can be solved using the levelset method of Osher and sethian (1988). The obtained algorithm can be simultaneously used to denoise, segment, detect-extract edges, and perform active contours. The proposed model is also a generalisation of a previous active contour model without edges, proposed by the authors in Chan et al., (2001), and of its extension to the case with more than two segments for piecewise-constant segmentation Chan et al., (2000). Based on the four color theorem, we can assume that in general, at most two levelset functions are sufficient to detect and represent distinct objects of distinct intensities, with triple junctions, or T-junctions.
We propose a new variational restoration method. We express the energy as the sum of a data attachment term. A contour smoothing term and an enhancement term. The contour smoothing is achieved by minimizing the square...
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ISBN:
(纸本)076951278X
We propose a new variational restoration method. We express the energy as the sum of a data attachment term. A contour smoothing term and an enhancement term. The contour smoothing is achieved by minimizing the square of the derivative of the intensity in the contour direction. The enhancement is obtained by minimizing the square of the gradient norm in each estimated region, and acts like shock filters. The minimization of the energy is then done using the conjugate gradient algorithm. We present an algorithm which allows us to compute easily the gradient of the energy in the discrete case, without calculating the Euler-Lagrange equations. Experiments have been carried out on both synthetic and real images applied to 3D angiographies.
A novel model for boundary determination that incorporates prior shape information into geometric active contours is presented. The basic idea of this model is to minimize the energy functional depending on the inform...
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ISBN:
(纸本)076951278X
A novel model for boundary determination that incorporates prior shape information into geometric active contours is presented. The basic idea of this model is to minimize the energy functional depending on the information of the image gradient and the shape of interest, so that the boundary of the object can be captured either by higher magnitude of the image gradient or by the prior knowledge of its shape. The levelset form of the proposed model is also provided. We present our experimental results on some synthetic images, functional MR brain images, and ultrasound images for which the existing active contour methods are not applicable. The existence of the solution to the proposed minimization problem is also discussed.
Edge completion is the interpolation of gaps between edge segments which are extracted from an image. We provide a new analytic solution to this problem within equi-affine plane geometry which is the natural framework...
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ISBN:
(纸本)076951278X
Edge completion is the interpolation of gaps between edge segments which are extracted from an image. We provide a new analytic solution to this problem within equi-affine plane geometry which is the natural framework for the interpolation of pairs of line segments. The desired curves are the geodesics of equi-affine plane geometry, namely parabolic arcs, which generalize the connection of points by straight lines in Euclidean geometry. Whereas most common methods of edge completion are invariant only under the group of Euclidean motions, SE(2), this solution has the advantage of being invariant under the larger group of equi-affine transformations, SA(2), that is more relevant to computervision. In addition to these geometric qualities, the parabola is a simple algebraic curve which renders it computationally attractive, especially in comparison to the popular elastica curves.
This paper treats the problem of tracking contours of flames captured by PLIF imaging using geodesic paths and levelsets. Successive images of the combustion process captured in controlled experiments are smoothed by...
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ISBN:
(纸本)076951278X
This paper treats the problem of tracking contours of flames captured by PLIF imaging using geodesic paths and levelsets. Successive images of the combustion process captured in controlled experiments are smoothed by nonlinear diffusion filtering then active contour models are used to obtain the curves that most accurately describe the frame boundary. These curves are matched using the concept of shortest path (geodesic) computation on a cost surface. The levelset representation is employed so that complex curve evolutions including those with topological changes in their structures could be handled. A critical point detection algorithm is used to identify important curve landmarks that are then used to modify the cost surface so as to improve the quality and stability of the matching. Accordingly, the propagation of curves representing successive flame contours within a sequence is obtained and used for studying the flame dynamics.
Geometric active contours (GAC) and surfaces (GAS) implemented via levelset techniques enjoy many advantages over parametric active contours (PAC) and surfaces (PAS), such as computational stability and the ability t...
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ISBN:
(纸本)076951278X
Geometric active contours (GAC) and surfaces (GAS) implemented via levelset techniques enjoy many advantages over parametric active contours (PAC) and surfaces (PAS), such as computational stability and the ability to change topology during deformation. While many capabilities of earlier PAC and PAS have been reproduced by various GAC and GAS, and while relationships have been discussed for a variety of specific cases, a comprehensive accounting of the connections between these two worlds (particularly regarding rigid forces) has not been consolidated thus far. We present the precise mathematical relationships between the two for an extensive family of both active contour and surface models, encompassing spatially varying coefficients, both tension and rigidity, and both conservative and non-conservative external forces. The result is a very general geometric formulation for which the intuitive design principles of PAC and PAS can be applied. We also point out which type of PAC and PAS methodologies cannot be adapted to the geometric levelset framework. We conclude by demonstrating several geometric adaptations of specific PAC and PAS in several simulations.
We present a theoretical study of the recovery of images x from noisy data y by minimizing a regularized cost-function F(x,y)=/spl Psi/(x,y)+/spl alpha//spl Phi/(x), where /spl Psi/ is a data-fidelity term, /spl Phi/ ...
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ISBN:
(纸本)076951278X
We present a theoretical study of the recovery of images x from noisy data y by minimizing a regularized cost-function F(x,y)=/spl Psi/(x,y)+/spl alpha//spl Phi/(x), where /spl Psi/ is a data-fidelity term, /spl Phi/ is a smooth regularisation term and /spl alpha/>0 is a parameter. Generally /spl Psi/ is a smooth function; only a few papers make an exception. Non-smooth data-fidelity terms are avoided in image processing. In spite of this, we consider both smooth and non-smooth data-fidelity terms. Our ambition is to catch essential features exhibited by the local minimizers of F in relation with the smoothness of /spl Psi/. Cost-functions with non-smooth data-fidelity exhibit a strong mathematical property which can be used in various ways. We then construct a cost-function allowing aberrant data to be detected and selectively smoothed. The obtained results advocate the use of non-smooth data-fidelity terms.
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