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Stanley Osher

Publications and source records attributed to Stanley Osher.

2 recordsLinked to original sources

Noise removal using smoothed normals and surface fitting.

In this work, we use partial differential equation techniques to remove noise from digital images. The removal is done in two steps. We first use a total-variation filter to smooth the normal vectors of the level curves of a noise image. After this, we try to find a surface to fit the smoothed normal vectors. For each of these two stages, the problem is reduced to a nonlinear partial differential equation. Finite difference schemes are used to solve these equations. A broad range of numerical examples are given in the paper.

Algorithms↗

Precursor tissue analogs as a tissue-engineering strategy.

Natural tissues are composed of functionally diverse cell types that are organized in spatially complex arrangements. Organogenesis of complex tissues requires a coordinated sequential transformation process, with individual stages involving time-dependent expression of cell-cell, cell-matrix, and cell-signal interactions in three dimensions. The common theme of temporal-spatial patterning of these cellular interactions is also observed in other physiological processes, such as growth and development, wound healing, and tumor migration. The "precursor tissue analog" (PTA) applies the temporal-spatial patterning theme to tissue engineering. The goal of PTA in tissue engineering is not to fabricate the final transplantable tissue but rather to guide the dynamic organization, maturation, and remodeling leading to the formation of normal and functional tissues. We describe the critical design principles of PTA. First, structural, mechanical, and physiological requirements of the PTA as a temporary scaffold must be met by a fabrication method with flexibility. The fabrication potential incorporating biological materials such as living cells and plasmid DNA has been addressed. Second, the PTA concept is considered suitable for future tissue engineering in light of the use of undifferentiated stem cells, and may possess a capability to guide stem cells toward diverse differentiation characteristics in situ. To this end, the behavior of the engineered cell and tissue must be monitored in detail. The development of a practical phenotype monitoring system such as a DNA microarray may be integral to the fabrication strategies of PTA. Third, the microtopographical and microenvironmental control on the liquid-solid interaction may lead to a critical design for PTA to provide soluble factors, nutrients, and gases to the cells embedded within the scaffold. We suggest that the level set numerical simulation method may be utilized to engineer the consistent circulation of bioactive liquid throughout the PTA microenvironment.

Animals↗