@article {576, title = {Multiscale statistical methods for the segmentation of signals and images}, journal = {IEEE Transactions on Image Processing}, volume = {9}, year = {2000}, pages = {456 - 468}, abstract = {

This paper addresses the problem of both segmenting and reconstructing a noisy signal or image. The work is motivated by large problems arising in certain scientific applications, such as medical imaging. Two objectives for a segmentation and denoising algorithm are laid out: it should be computationally efficient and capable of generating statistics for the errors in the reconstruction and estimates of the boundary locations. The starting point for the development of a suitable algorithm is a variational approach to segmentation (Shah 1992). This paper then develops a precise statistical interpretation of a one dimensional (1-D) version of this variational approach to segmentation. The 1-D algorithm that arises as a result of this analysis is computationally efficient and capable of generating error statistics. A straightforward extension of this algorithm to two dimensions would incorporate recursive procedures for computing estimates of inhomogeneous Gaussian Markov random fields. Such procedures require an unacceptably large number of operations. To meet the objective of developing a computationally efficient algorithm, the use of previously developed multiscale statistical methods is investigated. This results in the development of an algorithm for segmenting and denoising which is not only computationally efficient but also capable of generating error statistics, as desired

}, keywords = {biomedical MRI, boundary locations, brain, denoising, error statistics, Gaussian processes, image reconstruction, image segmentation, images, inhomogeneous Gaussian Markov random fields, interference suppression, Markov processes, medical image processing, medical imaging, multiscale methods, noisy image, noisy signal, reconstruction, recursive procedures, scientific applications, Segmentation, signal reconstruction, signals, statistical interpretation, variational approach, variational techniques}, issn = {1057-7149}, doi = {http://dx.doi.org/10.1109/83.826782}, author = {M Schneider and P Fieguth and W C. Karl and A S. Willsky} } @inproceedings {490, title = {A general multiresolution approach to the estimation of dense fields in remote sensing}, booktitle = {International Conference on Image Processing}, year = {1996}, address = {Lausanne, Switzerland}, abstract = {

A fast multiscale optimal interpolation algorithm has been adapted to the mapping of hydrographic and other oceanographic data. This multiscale algorithm produces solution and error estimates which are consistent with those obtained from exact least-squares methods, but at a small fraction of the computational cost. Problems whose solution would be completely impractical using exact least-squares, that is problems with tens or hundreds of thousands of measurements and estimation grid points, can easily be solved on a small workstation using the multiscale algorithm. Contrary to methods previously proposed for solving large least-squares problems, the multiscale approach provides error statistics while permitting long-range correlations, using all measurements, and permitting arbitrary measurement locations

}, keywords = {arbitrary measurement locations, computational cost, correlation methods, dense fields estimation, error estimates, error statistics, exact least-squares methods, fast multiscale optimal interpolation algorithm, general multiresolution approach, geophysical signal processing, hydrographic data mapping, hydrological techniques, image resolution, interpolation, least squares approximations, long-range correlations, measurements, multiscale algorithm, oceanographic data mapping, oceanographic techniques, Remote Sensing, workstation}, doi = {http://dx.doi.org/10.1109/ICIP.1996.560937}, author = {P Fieguth and A S. Willsky and D Menemenlis and C Wunsch} } @inproceedings {491, title = {Multiscale Methods for the Segmentation of Images}, booktitle = {ICASSP {\textquoteright}96}, year = {1996}, abstract = {

This work presents a method for segmenting images based on gradients in the intensity function. Past approaches have centered on formulating the problem in the context of variational calculus as the minimization of a functional involving the image intensity and edge functions. Computational methods for finding the minima of such variational problems are prone to two shortfalls: they are often computationally intensive and almost always incapable of computing error statistics associated with the segmentation. Using a particular variational formulation as a starting point, this paper presents a derivation of an associated statistical formulation using multiscale models. The result is an algorithm which is fast and capable of computing error statistics

}, keywords = {error statistics, functional, functional equations, gradients, image segmentation, images, intensity function, minimisation, minimization, multiscale models, Segmentation, statistical formulation, variational calculus, variational techniques}, doi = {http://dx.doi.org/10.1109/ICASSP.1996.545869}, author = {M Schneider and P Fieguth and W C. Karl and A S. Willsky} } @inproceedings {459, title = {Multiresolution stochastic imaging of satellite oceanographic altimetric data}, booktitle = {Image Processing, 1994. Proceedings. ICIP-94., IEEE International Conference}, year = {1994}, abstract = {

Large data assimilation problems present a number of challenges, many of which the authors\&$\#$39; multiscale estimation framework is capable of addressing. They demonstrate the application of their estimation framework to an oceanographic data assimilation problem of considerable interest: the smoothing of Topex/Poseidon ocean altimetric data. they produce surface estimates and error statistics on a 512 times;512 grid in one minute on a Sparc-10. Using a generic surface reconstruction problem they demonstrate alternative uses of the multiscale framework: higher order state models, combining estimates from an ensemble of trees, and overlapping tree models

}, keywords = {error statistics, geophysical signal processing, higher order state models, image reconstruction, large data assimilation problems, multiresolution stochastic imaging, multiscale estimation framework, multiscale framework, oceanographic techniques, overlapping tree models, radar altimetry, radar imaging, remote sensing by radar, satellite oceanographic altimetric data, smoothing methods, state estimation, stochastic processes, surface estimates, surface reconstruction problem, Topex/Poseidon ocean altimetric data, trees, trees (mathematics)}, doi = {http://dx.doi.org/10.1109/ICIP.1994.413519}, author = {P Fieguth and A S. Willsky and W C. Karl} } @inproceedings {460, title = {Multiresolution stochastic imaging of satellite oceanographic altimetric data}, booktitle = {Image Processing, 1994. Proceedings. ICIP-94., IEEE International Conference}, year = {1994}, abstract = {

Large data assimilation problems present a number of challenges, many of which the authors\&$\#$39; multiscale estimation framework is capable of addressing. They demonstrate the application of their estimation framework to an oceanographic data assimilation problem of considerable interest: the smoothing of Topex/Poseidon ocean altimetric data. they produce surface estimates and error statistics on a 512 times;512 grid in one minute on a Sparc-10. Using a generic surface reconstruction problem they demonstrate alternative uses of the multiscale framework: higher order state models, combining estimates from an ensemble of trees, and overlapping tree models

}, keywords = {error statistics, geophysical signal processing, higher order state models, image reconstruction, large data assimilation problems, multiresolution stochastic imaging, multiscale estimation framework, multiscale framework, oceanographic techniques, overlapping tree models, radar altimetry, radar imaging, remote sensing by radar, satellite oceanographic altimetric data, smoothing methods, state estimation, stochastic processes, surface estimates, surface reconstruction problem, Topex/Poseidon ocean altimetric data, trees, trees (mathematics)}, doi = {http://dx.doi.org/10.1109/ICIP.1994.413519}, author = {P Fieguth and A S. Willsky and W C. Karl} }