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13
An Active Contour Model For Mapping The Cortex
 IEEE TRANS. ON MEDICAL IMAGING
, 1995
"... A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approac ..."
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Cited by 67 (13 self)
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A new active contour model for finding and mapping the outer cortex in brain images is developed. A crosssection of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approach are proposed to achieve this goal. The primary difference between this formulation and that of snakes is in the specification of the external force acting on the active contour. A study of the uniqueness and fidelity of solutions is made through convexity and frequency domain analyses, and a criterion for selection of the regularization coefficient is developed. Examples demonstrating the performance of this method on simulated and real data are provided.
Efficient Multiresolution Counterparts to Variational Methods for Surface Reconstruction
, 1998
"... : Variational methods have been employed with considerable success in computer vision, particularly for surface reconstruction problems. Formulations of this type require the solution of computationally complex EulerLagrange partial differential equations (PDEs) to obtain the desired reconstruc ..."
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Cited by 24 (13 self)
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: Variational methods have been employed with considerable success in computer vision, particularly for surface reconstruction problems. Formulations of this type require the solution of computationally complex EulerLagrange partial differential equations (PDEs) to obtain the desired reconstructions. Further, the calculation of reconstruction error covariances for such approaches are usually neglected. In this paper we describe a computationally efficient multiscale approach to surface reconstruction which differs fundamentally from other multiresolution methods that are used to solve the EulerLagrange PDEs. Instead, we interpret the variational problem as a statistical estimation problem in order to define a nearby, but slightly different, multiscale estimation problem that admits efficient solutions for both surface reconstruction and the calculation of error statistics. In particular, the membrane and thinplate variational models for surfaces are interpreted as 1=f 2...
Image Denoising And Segmentation Via Nonlinear Diffusion
 Comput. Math. Appl
, 2000
"... . Image dnoising and segmentation are fundamental problems in the field of image processing and computer vision with numerous applications. In this paper we present a novel nonlinear diffusion model augmented with reactive terms that yields quality denoising and segmentation results on a variety of ..."
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Cited by 12 (1 self)
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. Image dnoising and segmentation are fundamental problems in the field of image processing and computer vision with numerous applications. In this paper we present a novel nonlinear diffusion model augmented with reactive terms that yields quality denoising and segmentation results on a variety of images. We present a proof for the existence, uniqueness and stability of the viscosity solution of this PDEbased model. To achieve a faster implementation, we embed the the model in a scale space and the solution is achieved via a dynamic system governed by a coupled system of first order differential equations. The dynamic system finds the solution at a coarse scale and tracks it continuously to a desired fine scale. We implement this scalespace tracking using a multigrid technique and demonstrate the smoothing and segmentation results on several images. Key words. Nonlinear Diffusion, Image Processing, Segmentation, PDEs, Scalespace 1. Introduction. Image denoising and segmentation ...
Robust Shape from Shading
 Image and Vision Computing
, 1994
"... Existing Shape from Shading algorithms are not robust enough to work reliably with real images. We present a new paradigm for Shape from Shading based upon & scale space surface representation. Using this representation, the Shape from Shading problem becomes one of forming a surface from gaussi ..."
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Cited by 5 (1 self)
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Existing Shape from Shading algorithms are not robust enough to work reliably with real images. We present a new paradigm for Shape from Shading based upon & scale space surface representation. Using this representation, the Shape from Shading problem becomes one of forming a surface from gaussian basis functions in such a way that the shading in the original image is explained. The algorithm is both fast and robust, producing convincing results. In its current form, the algorithm requires the reflectance function to be approximately circularly symmetric. We show results for synthetic images, both with and without added noise, and for real Scanning Electron Microscope images. 1
SOLVING INVERSE PROBLEMS IN COMPUTER VISION BY SCALE SPACE RECONSTRUCTION
"... Illposed inverse problems are widely encountered in computer vision. examples include shape from shading, surface reconstruction from sparse data and optic flow. Unique solutions to these problems are conventionally found by minimizing an objective function regularized by a smoothness constraint. H ..."
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Cited by 4 (0 self)
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Illposed inverse problems are widely encountered in computer vision. examples include shape from shading, surface reconstruction from sparse data and optic flow. Unique solutions to these problems are conventionally found by minimizing an objective function regularized by a smoothness constraint. However, objective functions of this form often contain many local minima, making it difficult to find an adequate solution by standard numerical methods. We describe an algorithm for solving inverse problems using scale space tracking which is robust, provably convergent and avoids local minima. The algorithm generates a hierarchy of solutions at different scales, forming a scale space from which a final solution can be selected at a later stage. We show how the use of gaussian basis functions to construct solutions can result in scale space behaviour without the need to blur the input data. Results are shown for shape from shading and surface reconstruction from stereo data, using both real and synthetic images.
Physicallybased Adaptive Preconditioning for Early Vision
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Several problems in early vision have been formulated in the past in a regularization framework. These problems when discretized lead to large sparse linear systems. In this paper, we present a novel physicallybased adaptive preconditioning technique which can be used in conjunction with a conju ..."
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Cited by 4 (2 self)
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Several problems in early vision have been formulated in the past in a regularization framework. These problems when discretized lead to large sparse linear systems. In this paper, we present a novel physicallybased adaptive preconditioning technique which can be used in conjunction with a conjugate gradient algorithm to drastically improve the speed of convergence for solving the aforementioned linear systems. A preconditioner based on the membrane spline or the thin plate spline or a convex combination of the two is termed as a physicallybased preconditioner for obvious reasons. The adaptation of the preconditioner to an early vision problem is achieved via the explicit use of the spectral characteristics of the regularization filter in conjunction with the data. This spectral function is used to modulate the frequency characteristics of a chosen wavelet basis leading to the construction of our preconditioner. The preconditioning technique is demonstrated for the surface ...
Hierarchical Calculation of 3dStructure
, 1994
"... this paper with algorithms processing only small areas at one time, thus reducing this effect. In addition, the algorithms used can cope with stereo pictures taken at a small baseline, thus reducing the effects of the other discussed problems. 2 Calculating disparities ..."
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Cited by 2 (0 self)
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this paper with algorithms processing only small areas at one time, thus reducing this effect. In addition, the algorithms used can cope with stereo pictures taken at a small baseline, thus reducing the effects of the other discussed problems. 2 Calculating disparities
ARTICLE NO. IV970630 Efficient Multiresolution Counterparts to Variational Methods for Surface Reconstruction ∗
"... Variational methods have been employed with considerable success in computer vision, particularly for surface reconstruction problems. Formulations of this type require the solution of computationally complex Euler–Lagrange partial differential equations (PDEs) to obtain the desired reconstructions. ..."
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Variational methods have been employed with considerable success in computer vision, particularly for surface reconstruction problems. Formulations of this type require the solution of computationally complex Euler–Lagrange partial differential equations (PDEs) to obtain the desired reconstructions. Further, the calculation of reconstruction error covariances for such approaches are usually neglected. In this paper we describe a computationally efficient multiscale approach to surface reconstruction which differs fundamentally from other multiresolution methods that are used to solve the Euler– Lagrange PDEs. Instead, we interpret the variational problem as a statistical estimation problem in order to define a nearby, but slightly different, multiscale estimation problem that admits efficient solutions for both surface reconstruction and the calculation of error statistics. In particular, the membrane and thinplate variational models for surfaces are interpreted as 1/f 2 prior statistical models for the surface and its gradients, respectively. Such 1/f 2 behavior is then achieved using a recently introduced class of multiresolution models that admits algorithms with constant perpixel computational complexity. c ○ 1998 Academic Press
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"... www.scielo.br/cam Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters ..."
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www.scielo.br/cam Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters