Introduction To The Special Issue On Partial Differential Equations And Geometry-driven Diffusion In Image Processing And Analysis

1998 ◽  
Vol 7 (3) ◽  
pp. 269-273 ◽  
Author(s):  
V. Caselles ◽  
J. Morel
Keyword(s):  
Image Processing ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Special Issue ◽  
Partial Differential ◽  
Image Processing And Analysis

Automatically interpreting all faults, unconformities, and horizons from 3D seismic images

2016 ◽  
Vol 4 (2) ◽  
pp. T227-T237 ◽  
Author(s):  
Xinming Wu ◽  
Dave Hale
Keyword(s):  
Image Processing ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Array Processing ◽  
3D Seismic ◽  
Partial Differential ◽  
Seismic Image ◽  
Processing Procedure ◽  
Seismic Images

Extracting fault, unconformity, and horizon surfaces from a seismic image is useful for interpretation of geologic structures and stratigraphic features. Although others automate the extraction of each type of these surfaces to some extent, it is difficult to automatically interpret a seismic image with all three types of surfaces because they could intersect with each other. For example, horizons can be especially difficult to extract from a seismic image complicated by faults and unconformities because a horizon surface can be dislocated at faults and terminated at unconformities. We have proposed a processing procedure to automatically extract all the faults, unconformities, and horizon surfaces from a 3D seismic image. In our processing, we first extracted fault surfaces, estimated fault slips, and undid the faulting in the seismic image. Then, we extracted unconformities from the unfaulted image with continuous reflectors across faults. Finally, we used the unconformities as constraints for image flattening and horizon extraction. Most of the processing was image processing or array processing and was achieved by efficiently solving partial differential equations. We used a 3D real example with faults and unconformities to demonstrate the entire image processing.

scholarly journals Special issue on complex partial differential equations and higher dimensional versions

2017 ◽  
Vol 62 (10) ◽  
pp. 1411-1412
Author(s):  
Heinrich Begehr ◽  
Ahmet Okay Celebi ◽  
Tynysbek Kalmenov ◽  
Abdelhamid Meziani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Special Issue ◽  
Partial Differential ◽  
Higher Dimensional

Soliton Kernels for Solving PDEs

2016 ◽  
Vol 13 (02) ◽  
pp. 1640009 ◽  
Author(s):  
Marjan Uddin ◽  
H. U. Jan ◽  
Amjad Ali ◽  
I. A. Shah
Keyword(s):  
Image Processing ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Response Surface ◽  
Computer Experiments ◽  
Time Dependent ◽  
Response Surface Modeling ◽  
Partial Differential ◽  
Special Solutions ◽  
Better Than

There are many important applications in the fields of computer experiments, response surface modeling, finance and image processing, where some special types of nonstandard kernels performed better than standard kernels. These kernels are more appropriate than standard kernels when looking at special solutions of partial differential equations (PDEs). For example some nonlinear time-dependent PDEs have soliton like solutions, so soliton kernels would more suit to approximate the solution. In this work, we recover the solution of equal width equation using soliton kernels.

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