Download Stochastic geometry for image analysis by Xavier Descombes PDF

By Xavier Descombes

ISBN-10: 1118601238

ISBN-13: 9781118601235

ISBN-10: 1118601327

ISBN-13: 9781118601327

"This e-book develops the stochastic geometry framework for photo research goal. major frameworks are defined: marked aspect technique and random closed units types. We derive the most matters for outlining a suitable version. The algorithms for sampling and optimizing the types in addition to for estimating parameters are reviewed. various functions, protecting distant sensing pictures, organic and medical Read more...

content material: bankruptcy 1. advent / X. Descombes --
bankruptcy 2. Marked element methods for item Detection / X. Descombes --
2.1. imperative definitions --
2.2. Density of some degree procedure --
2.3. Marked aspect tactics --
2.4. aspect methods and snapshot research --
2.4.1. Bayesian as opposed to non-Bayesian --
2.4.2. A priori as opposed to reference degree --
bankruptcy three. Random units for Texture research / C. Lantǔjoul, M. Schmitt --
3.1. creation --
3.2. Random units --
3.2.1. Insufficiency of the spatial legislation --
3.2.2. creation of a topological context --
3.2.3. the idea of random closed units (RACS) --
3.2.4. a few examples --
3.2.5. Stationarity and isotropy --
3.3. a few geostatistical features --
3.3.1. The ergodicity assumption --
3.3.2. Inference of the DF of a desk bound ergodic RACS --
3.3.2.1. development of the estimator --
3.3.2.2. On sampling --
3.3.3. person research of gadgets --
3.4. a few morphological points --
3.4.1. Geometric interpretation --
3.4.1.1. aspect --
3.4.1.2. Pair of issues --
3.4.1.3. phase --
3.4.1.4. Ball --
3.4.2. Filtering --
3.4.2.1. beginning and shutting --
3.4.2.2. Sequential trade filtering --
3.5. Appendix: demonstration of Miles' formulae for the Boolean version --
bankruptcy four. Simulation and Optimization / F. Lafarge, X. Descombes, E. Zhizhina, R. Minlos --
4.1. Discrete simulations: Markov chain Monte Carlo algorithms --
4.1.1. Irreducibility, recurrence, and ergodicity --
4.1.1.1. Definitions --
4.1.1.2. Stationarity --
4.1.1.3. Convergence --
4.1.1.4. Irreducibility --
4.1.1.5. Aperiodicity --
4.1.1.6. Harris recurrence --
4.1.1.7. Ergodicity --
4.1.1.8. Geometric ergodicity --
4.1.1.9. important restrict theorem --
4.1.2. Metropolis-Hastings set of rules --
4.1.3. Dimensional jumps --
4.1.3.1. mix of kernels --
4.1.3.2. π-reversibility --
4.1.4. ordinary proposition kernels --
4.1.4.1. uncomplicated perturbations --
4.1.4.2. version swap --
4.1.4.3. start and loss of life --
4.1.5. particular proposition kernels --
4.1.5.1. developing advanced transitions from regular transitions --
4.1.5.2. Data-driven perturbations --
4.1.5.3. Perturbations directed by means of the present kingdom --
4.1.5.4. Composition of kernels --
4.2. non-stop simulations --
4.2.1. Diffusion set of rules --
4.2.2. start and loss of life set of rules --
4.2.3. Muliple births and deaths set of rules --
4.2.3.1. Convergence of the distributions --
4.2.3.2. start and loss of life procedure --
4.2.4. Discrete approximation --
4.2.4.1. Acceleration of the a number of births and deaths set of rules --
4.3. combined simulations --
4.3.1. leap strategy --
4.3.2. Diffusion technique --
4.3.3. Coordination of jumps and diffusions --
4.4. Simulated annealing --
4.4.1. Cooling time table --
4.4.2. preliminary temperature T0 --
4.4.3. Logarithmic reduce --
4.4.4. Geometric reduce --
4.4.5. Adaptive relief --
4.4.6. preventing criterion/final temperature --
bankruptcy five. Parametric Inference for Marked aspect tactics in photograph research / R. Stoica, F. Chatelain, M. Sigelle --
5.1. advent --
5.2. First query: what and the place are the items within the picture? --
5.3. moment query: what are the parameters of the purpose method that versions the items saw within the photo? --
5.3.1. entire info --
5.3.1.1. greatest probability --
5.3.1.2. greatest pseudolikelihood --
5.3.2. Incomplete facts: EM set of rules --
5.4. end and views --
5.5. Acknowledgments --
bankruptcy 6. the way to arrange some degree procedure? / X. Descombes --
6.1. From disks to polygons, through a dialogue of segments --
6.2. From no overlap to alignment --
6.3. From the chance to a speculation try out --
6.4. From Metropolis-Hastings to a number of births and deaths --
bankruptcy 7. inhabitants Counting / X. Descombes --
7.1. Detection of Virchow-Robin areas --
7.1.1. info modeling --
7.1.2. Marked element strategy --
7.1.3. Reversible leap MCMC set of rules --
7.1.4. effects --
7.2. review of forestry assets --
7.2.1. second version --
7.2.1.1. past --
7.2.1.2. info time period --
7.2.1.3. Optimization --
7.2.1.4. effects --
7.2.2. 3D version --
7.2.2.1. effects --
7.3. Counting a inhabitants of flamingos --
7.3.1. Estimation of the flamingo colour --
7.3.2. Simulation and optimization via a number of births and deaths --
7.3.3. effects --
7.4. Counting the boats at a port --
7.4.1. Initialization of the optimization set of rules --
7.4.1.1. Parameter γd --
7.4.1.2. Calibration of the do parameter --
7.4.2. preliminary effects --
7.4.3. amendment of the information strength --
7.4.3.1. First amendment of the past strength --
7.4.3.2. moment amendment of the earlier strength --
bankruptcy eight. constitution Extraction / F. Lafarge, X. Descombes --
8.1. Detection of the line community --
8.2. Extraction of establishing footprints --
8.3. illustration of usual textures --
8.3.1. basic version --
8.3.1.1. facts time period --
8.3.1.2. Sampling through leap diffusion --
8.3.1.3. effects --
8.3.2. types with advanced interactions --
bankruptcy nine. form reputation / F. Lafarge, C. Mallet --
9.1. Modeling of a LIDAR sign --
9.1.1. Motivation --
9.1.2. version library --
9.1.2.1. power formula --
9.1.3. Sampling --
9.1.4. effects --
9.1.4.1. Simulated information --
9.1.4.2. satellite tv for pc facts: huge footprint waveforms --
9.1.4.3. Airborne information: small footprint waveforms --
9.1.4.4. program to the class of 3D element clouds --
9.2. 3D reconstruction of constructions --
9.2.1. Library of 3D versions --
9.2.2. Bayesian formula --
9.2.2.1. probability --
9.2.2.2. A priori --
9.2.3. Optimization --
9.2.4. effects and dialogue --
Bibliography --
record of Authors --
Index.
summary:

This ebook develops the stochastic geometry framework for picture research objective. major frameworks are defined: marked aspect strategy and random closed units versions. We derive the most concerns for Read more...

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Extra resources for Stochastic geometry for image analysis

Example text

The approach adopted in this chapter relies on interpreting the image and its texture as realizations of a random stationary ergodic set in a limited field. 2. This tool is to the random set what a distribution function is to a random variable. 2, that Random Sets for Texture Analysis 31 the estimator for this distribution function can be written simply in terms of morphological dilations and erosions. We will demonstrate that this estimator is unbiased, and an asymptotic calculation of the variance will allow us to quantify the image size necessary to obtain an estimate with a given precision.

Point Suppose that K is reduced to a point. Owing to the stationarity, there is no disadvantage in assuming that this point is the origin. 12], the ergodic assumption is written as: vd (X ∩ Br ) r−→∞ vd (Br ) T ({o}) = lim vd (X ∩ Br ) r−→∞ vd (Br ) Q({o}) = lim Thus, p and q represent the proportions of points contained, respectively, in X and X. 2. Pair of points Here, K is the pair of points {x, y}. By stationarity, T (K) and Q(K) do not depend explicitly on x and y but only on the vector h = y − x, which separates them.

11] 1 as estimators of E{ψ(A)}. – Compensated estimators. We reconsider estimation of the mean radius of a Boolean model of circles. 11] have instead Random Sets for Texture Analysis 51 been applied empirically. One thousand simulations of the model (with Poisson density 1) were carried out for a field with radius 10. For each simulation, we estimated the mean radius of the objects for several sizes of field. We then took the average of the estimated values. 13. The bias in plus sampling appears to be significantly attenuated for small field sizes.

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