| 1. |
- Häbel, Henrike, 1987, et al.
(författare)
-
A three-dimensional anisotropic point process characterization for pharmaceutical coatings
- 2017
-
Ingår i: Spatial Statistics. - : Elsevier BV. - 2211-6753. ; 22:2, s. 306-320
-
Tidskriftsartikel (refereegranskat)abstract
- © 2017 Elsevier B.V. Spatial characterization and modeling of the structure of a material may provide valuable knowledge on its properties and function. Especially, for a drug formulation coated with a polymer film, understanding the relationship between pore structure and drug release properties is important to optimize the coating film design. Here, we use methods from image analysis and spatial statistics to characterize and model the pore structure in pharmaceutical coatings. More precisely, we use and develop point process theory to characterize the branching structure of a polymer blended film with data from confocal laser scanning microscopy. Point patterns, extracted by identifying branching points of pore channels, are both inhomogeneous and anisotropic. Therefore, we introduce a directional version of the inhomogeneous K-function to study the anisotropy and then suggest two alternative ways to model the anisotropic three-dimensional structure. First, we apply a linear transformation to the data such that it appears isotropic and subsequently fit isotropic inhomogeneous Strauss or Lennard-Jones models to the transformed pattern. Second, we include the anisotropy directly in a Lennard-Jones and a more flexible step-function model with anisotropic pair-potential functions. The methods presented will be useful for anisotropic inhomogeneous point patterns in general and for characterizing porous material in particular.
|
|
| 2. |
- Rajala, Tuomas, et al.
(författare)
-
A review on anisotropy analysis of spatial point patterns
- 2018
-
Ingår i: Spatial Statistics. - : Elsevier BV. - 2211-6753. ; 28, s. 141-168
-
Forskningsöversikt (refereegranskat)abstract
- A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for anisotropy analysis of (stationary) point patterns in ℝ2 andℝ3. We discuss methods based on nearest neighbour and second order summary statistics as well as spectral and wavelet analysis. All techniques are illustrated on both a clustered and a regular example. Finally, we discuss methods for testing for isotropy as well as for estimating preferred directions in a point pattern.
|
|
| 3. |
- Redenbach, Claudia, et al.
(författare)
-
Anisotropy analysis of pressed point processes
- 2009
-
Ingår i: Advances in Statistical Analysis. ; 93:3, s. 237-261
-
Tidskriftsartikel (refereegranskat)abstract
- This paper introduces methods for the detection of anisotropies which are caused by compression of regular three-dimensional point patterns. Isotropy tests base d on directional summary statistics and estimators for the compression factor are developed. These allow not only for the detection of anisotropies but also for the estimation of their strength. Using simulated data the power of the methods and the dependence of the power on the intensity, the degree of regularity, and the compression strength are studied. The motivation of this paper is the investigation of anisotropies in the structure of polar ice. Therefore, our methods a re applied to the point patterns of centres of air pores extracted from tomographic images of ice cores. This way the presence of anisotropies in the ice caused by the compression of the ice sheet as well as an increase of their strength with increasing depth are shown.
|
|
| 4. |
- Redenbach, Claudia, et al.
(författare)
-
Classification of Points in Superpositions of Strauss and Poisson Processes
- 2015
-
Ingår i: Spatial Statistics. - : Elsevier BV. - 2211-6753. ; 12, s. 81-95
-
Tidskriftsartikel (refereegranskat)abstract
- Consider a realisation of a point process which is formed as a superposition of a regular point process, here a Strauss process, and some Poisson noise. The aim of the current work is to decide which of the two processes each point belongs to. We construct an MCMC algorithm which estimates the parameters of the superposition model and obtains posterior probabilities for each point of being a Strauss point. The algorithm is evaluated in a simulation study. Finally, it is applied to our motivating data set containing the locations of air bubbles, some of which are noise, in an Antarctic ice core.
|
|
| 5. |
- Sormani, M., et al.
(författare)
-
Second order analysis of geometric anisotropic point processes revisited
- 2020
-
Ingår i: Spatial Statistics. - : Elsevier BV. - 2211-6753. ; 38
-
Tidskriftsartikel (refereegranskat)abstract
- Various methods for directional analysis of spatial point patterns have been introduced in the literature. In this paper, we formulate a unifying framework for methods based on integral transforms of the second order product density. Examples include directional versions of Ripley's K-function, wavelet transforms, and spectral analysis. Furthermore, we propose an additional method based on the projection of the Fry points of the point pattern on the unit sphere. This method solves some of the practical problems appearing in the application of the integral transform. In particular, it can be easily applied in 3D and provides a definition of an isotropy test without the need of replicated data. The method is evaluated in a simulation study.
|
|
