scholarly journals A general rice formula, palm measures, and horizontal-window conditioning for random fields

1984 ◽  
Vol 17 (2) ◽  
pp. 265-283 ◽  
Author(s):  
Ulrich Zähle
Keyword(s):  
Random Fields ◽  
Rice Formula

scholarly journals Level Sets of Random Fields and Applications: Specular Points and Wave Crests

2010 ◽  
Vol 2010 ◽  
pp. 1-22
Author(s):  
Esteban Flores ◽  
José R. León R
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Fields ◽  
Level Sets ◽  
Two Dimensions ◽  
Level Curve ◽  
Curvilinear Integral ◽  
The Waves ◽  
Rice Formula

We apply Rice's multidimensional formulas, in a mathematically rigorous way, to several problems which appear in random sea modeling. As a first example, the probability density function of the velocity of the specular points is obtained in one or two dimensions as well as the expectation of the number of specular points in two dimensions. We also consider, based on a multidimensional Rice formula, a curvilinear integral with respect to the level curve. It follows that its expected value allows defining the Palm distribution of the angle of the normal of the curve that defines the waves crest. Finally, we give a new proof of a general multidimensional Rice formula, valid for all levels, for a stationary and smooth enough random fields X:ℝd→ℝj(d>j).

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

PRNU-based Image Manipulation Localization with Discriminative Random Fields

2017 ◽  
Vol 2017 (7) ◽  
pp. 113-120 ◽  
Author(s):  
Sujoy Chakraborty ◽  
Matthias Kirchner
Keyword(s):  
Random Fields ◽  
Image Manipulation

Detection Approach of DDoS Attacks Based on Conditional Random Fields

2011 ◽  
Vol 22 (8) ◽  
pp. 1897-1910 ◽  
Author(s):  
Yun LIU ◽  
Zhi-Ping CAI ◽  
Ping ZHONG ◽  
Jian-Ping YIN ◽  
Jie-Ren CHENG
Keyword(s):  
Random Fields ◽  
Conditional Random Fields ◽  
Ddos Attacks ◽  
Detection Approach
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