Geomatic Methods for the Analysis of Data in the Earth Sciences,9783540674764

Geomatic Methods for the Analysis of Data in the Earth Sciences

by ; ;
ISBN13: 9783540674764
ISBN10: 3540674764
Format: Paperback
Pub. Date: 2000-06-01
Publisher(s): Springer Nature
List Price: $199.99

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Summary

Geomatics is an amalgam of methods, algorithms and practices in handling data referred to the Earth by informatic tools. This book is an attempt to identify and rationally organize the statistical-mathematical methods which are common in many fields where geomatics is applied, like geodesy, geophysics and, in particular, the field of inverse problems and image analysis as it enters into photogrammetry and remote sensing.These lecture notes aim at creating a bridge between people working in different disciplines and making them aware of a common methodological basis.

Table of Contents

An overview of data analysis methods in geomatics
1(17)
A. Dermanis
F. Sanso
A. Grun
Data analysis methods in geodesy
17(76)
A. Dermanis
R. Rummel
Introduction
17(2)
The art of modeling
19(5)
Parameter estimation as an inverse problem
24(23)
The general case: Overdetermined and underdetermined system without full rank (r < min(n,m)
29(10)
The regular case (r=m=n)
39(1)
The full-rank overdetermined case (r=m<n)
40(1)
The full-rank underdetermined case (r=n<m)
41(2)
The hybrid solution (Tikhonov regularization)
43(3)
The full rank factorization
46(1)
The statistical approach to parameter determination: Estimation and prediction
47(6)
From finite to infinite-dimensional models (or from discrete to continuous models)
53(22)
Continuous observations without errors
58(7)
Discrete observations affected by noise
65(8)
The stochastic approach
73(2)
Beyond the standard formulation: Two examples from satellite geodesy
75(18)
Determination of gravity potential coefficients
75(3)
GPS observations and integer unknowns
78(5)
References
83(3)
The Singular Value Decomposition
86(7)
Linear and nonlinear inverse problems
93(72)
R. Snieder
J. Trampert
Introduction
93(3)
Solving finite linear systems of equations
96(24)
Linear model estimation
96(3)
Least-squares estimation
99(1)
Minimum norm estimation
100(2)
Mixed determined problems
102(1)
The consistency problem for the least-squares solution
103(3)
The consistency problem for the minimum-norm solution
106(2)
The need for a more general regularization
108(2)
The transformation rules for the weight matrices
110(2)
Solving the system of linear equations
112(1)
Singular value decomposition
113(4)
Interative least-squares
117(3)
Linear inverse problems with continuous models
120(11)
Continuous models and basis functions
122(1)
Spectral leakage, the problem
123(4)
Spectral leakage, the cure
127(2)
Spectral leakage and global tomography
129(2)
The single scattering approximation and linearized waveform inversion
131(10)
The Born approximation
131(2)
Inversion and migration
133(3)
The Born approximation for transmission data
136(3)
Surface wave inversion of the structure under North-America
139(2)
Rayleigh's principle and perturbed eigenfrequencies
141(4)
Rayleigh-Schrodinger perturbation theory
141(2)
The phase velocity perturbation of Love waves
143(2)
Fermat's theorem and seismic tomography
145(5)
Fermat's theorem, the eikonal equation and seismic tomography
146(2)
Surface wave tomography
148(2)
Nonlinearity and ill-posedness
150(5)
Example 1: Non-linearity and the inverse problem for the Schrodinger equation
151(2)
Example 2: Non-linearity and seismic tomography
153(2)
Model appraisal for nonlinear inverse problems
155(4)
Nonlinear Backus-Gilbert theory
155(2)
Generation of populations of models that fit the data
157(2)
Using different inversion methods
159(1)
Epilogue
159(6)
References
160(5)
Image Preprocessing for Feature Extraction in Digital Intensity, Color and Range Image
165(25)
W. Forstner
Motivation
165(2)
The image model
167(4)
Intensity images
168(1)
Color images
169(1)
Range images
169(2)
Noise variance estimation
171(5)
Estimation of the noise variance in intensity images
172(3)
Noise estimation in range images
175(1)
Variance equalization
176(1)
Principle
176(1)
Linear variance function
177(1)
General variance function
177(1)
Information preserving filtering
177(5)
The Wiener filter
177(1)
Approximation of the auto covariance function
178(1)
An adaptive Wiener filter for intensity images
179(2)
An adaptive Wiener filter for range images
181(1)
Fusing channels: Extraction of linear features
182(5)
Detecting edge pixels
182(5)
Localizing edge pixels
187(1)
Outlook
187(3)
References
188(2)
Optimization-Based Approaches to Feature Extraction from Aerial Images
190(39)
P. Fua
A. Gruen
H. Li
Introduction
190(1)
Dynamic programming
191(5)
Generic road model
192(1)
Road delineation
193(3)
Model based optimization
196(19)
Generalized snakes
198(11)
Enforcing consistency
209(3)
Consistent site modeling
212(3)
LSB-snakes
215(10)
Photometric observation equations
215(3)
Geometric observation equations
218(1)
Solution of LSB-snakes
219(1)
LSB-snakes with multiple images
220(2)
Road extraction experiments
222(3)
Conclusion
225(4)
References
226(3)
Diffraction tomography through phase back-projection
229(26)
S. Valle
F. Rocca
L. Zanzi
Introduction
229(2)
Born approximation and Fourier diffraction theorem
231(4)
Diffraction tomography through phase back-projection
235(4)
Theory
235(4)
Diffraction tomography and pre-stack migration
239(7)
Diffraction tomography wavepath
239(2)
Migration wavepath
241(4)
Diffraction tomography and migration: wavepath and inversion process comparison
245(1)
Numerical and experimental results
246(9)
Data pre-processing
246(1)
Numerical examples
247(1)
Laboratory model and real case examples
248(5)
The Green Functions
253(1)
Implementation details
254(1)
DT inversion including the source/receiver directivity function
254(1)
References
255

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