We address an ill-posed inverse problem of image estimation from sparse samples of its Fourier transform. The problem is formulated as joint estimation of the supports of unknown sparse objects in the image, and pixel...
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We address an ill-posed inverse problem of image estimation from sparse samples of its Fourier transform. The problem is formulated as joint estimation of the supports of unknown sparse objects in the image, and pixel values on these supports. The domain and the pixel values are alternately estimated using the level-set method and the conjugate gradient method, respectively. Our level-set evolution shows a unique switching behavior, which stabilizes the level-set evolution. Furthermore, the trade-off between the stability and the speed of evolution can be easily controlled by the number of the conjugate gradient steps, thus avoiding the re-initialization steps in conventional levelset approaches.
In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape....
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In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape. The model provides the segmentation and the transformation that maps the segmented contour to the prior shape. The active contour is able to find boundaries that are similar in shape to the prior, even when the entire boundary is not visible in the image (i.e., when the boundary has gaps). A levelset formulation of the active contour is presented. The existence of the solution to the energy minimization is also established. We also report experimental results of the use of this contour on 2d synthetic images, ultrasound images and fMRI images. Classical active contours cannot be used in many of these images.
We use the geometric Beltrami framework to incorporate and explain some of the known invariant flows e.g. the equi-affine invariant flow. It is also demonstrated that the tint, concepts put forward in this framework e...
ISBN:
(纸本)076951278X
We use the geometric Beltrami framework to incorporate and explain some of the known invariant flows e.g. the equi-affine invariant flow. It is also demonstrated that the tint, concepts put forward in this framework enable us to construct new invariant flows for the case where the codimension is greater than one e.g. for color images and video.
An automatic cortical gray matter segmentation from a three-dimensional brain images (MR or CT) is a well known problem in medical image processing. In this paper we formulate it as geometric variational problem for p...
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ISBN:
(纸本)076951278X
An automatic cortical gray matter segmentation from a three-dimensional brain images (MR or CT) is a well known problem in medical image processing. In this paper we formulate it as geometric variational problem for propagation of two coupled bounding surfaces. An efficient numerical scheme is used to implement the geodesic active surface model. Experimental results of cortex segmentation on real three-dimensional MR data are provided.
The minimization of the Total Variation is an important toot of image processing. A lot of authors have addressed the problem and developed algorithms for image denoising. In a previous paper we gave an alternative ap...
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ISBN:
(纸本)076951278X
The minimization of the Total Variation is an important toot of image processing. A lot of authors have addressed the problem and developed algorithms for image denoising. In a previous paper we gave an alternative approach of the Total Variation minimization problem based on the Coarea formula. The aim of this paper is to present a new efficient algorithm for the Coarea formula approach, based on the Fast levelsets Transform.
We address image estimation from sparse Fourier samples. The problem is formulated as joint estimation of the supports of unknown sparse objects in the image, and pixel values on these supports. The domain and the pix...
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We present a modification of the Mumford-Shah Junctional and its cartoon limit which allows the incorporation of statistical shape knowledge in a single energy functional. We show segmentation results on artificial an...
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ISBN:
(纸本)076951278X
We present a modification of the Mumford-Shah Junctional and its cartoon limit which allows the incorporation of statistical shape knowledge in a single energy functional. We show segmentation results on artificial and real-world images with and without prior shape information. In the case of occlusion and strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by, a level-set implementation of geodesic active contours.
We address the problem of nonparametric multi-modal image matching. We propose a generic framework which relies on a global variational formulation and show its versatility through three different multi-modal registra...
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In this paper we propose to study different smoothness measures of planar contours or surfaces. We first define a smoothness measure as a functional that follows three types of invariance : invariance to changes of co...
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ISBN:
(纸本)076951278X
In this paper we propose to study different smoothness measures of planar contours or surfaces. We first define a smoothness measure as a functional that follows three types of invariance : invariance to changes of contour parameterization, invariance to contour rotations and translations and invariance to the contour sizes. We then introduce different smoothness measures that can be classified into local or global functionals but also that can be of geometric or algebraic nature. We finally discuss their implementation by observing the advantages and disadvantages of explicit and implicit Contour representations.
In this paper, 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 acheived by minimi...
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ISBN:
(纸本)076951278X
In this paper, 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 acheived 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 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.
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