Showing papers by "Stanley Osher published in 1992"
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.
15,225 citations
TL;DR: The Hamilton-Jacobi level set formulation of the equations of motion for propagating interfaces has been introduced recently by Osher and Sethian as mentioned in this paper, which allows fronts to self-intersect, develop singularities, and change topology.
430 citations
TL;DR: In this paper, a triangle-based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures.
140 citations
TL;DR: In this article, high order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2D and 3D compressible Euler and Navier-Stokes equations.
105 citations
01 Jun 1992
TL;DR: The algorithm performed well in phantom experiments, demonstrating an average four-fold reduction in the error associated with estimating the radius of a small bone although the standard deviation of the estimate was almost twice that of the edge detection techniques.
Abstract: This paper tests a new, fully automated image segmentation algorithm and compares its results with conventional threshold-based edge detection techniques. A CT phantom-based method is used to measure the precision and accuracy of the new algorithm in comparison to two edge detection variants. These algorithms offer a high degree of noise and differential lighting immunity and allow multi-channel image data, making them ideal candidates for multi-echo MRI sequences. The algorithm considered in this paper employs a fast numerical method for energy minimization of the free boundary problem that can incorporate regional image characteristics such as texture or other scale-specific features. It relies on a recursive region merge operation, thus providing a series of nested segmentations. In addition to the phantom testing, we discuss the results of this fast, multiscale, pyramidal segmentation algorithm applied to MRI images. The CT phantom segmentation is measured by the geometric fidelity of the extracted measurements to the geometry of the original bone components. The algorithm performed well in phantom experiments, demonstrating an average four-fold reduction in the error associated with estimating the radius of a small bone although the standard deviation of the estimate was almost twice that of the edge detection techniques. Modifications are proposed which further improve the geometric measurements. Finally, the results on soft-tissue discrimination are promising, and we are continuing to enhance the core formulation to improve the segmentation of complex shaped regions.
5 citations
01 Jan 1992
TL;DR: In this article, a successful nonlinear partial differential equation based approach to restoration was carried out, ENO least squares, shock filters, feature detectors and total variation based deconvolution techniques were combined.
Abstract: : A successful nonlinear partial differential equation based approach to restoration was carried out, ENO least squares, shock filters, feature detectors and total variation based deconvolution techniques were combined. Also rigorous morphological methods and wavelet analysis were developed and used to restore noisy, blurry images.
1 citations