Spatial Analysis of Time of Flight−Secondary Ion Mass Spectrometric Images by Ordinary Kriging and Inverse Distance Weighted Interpolation Techniques

Abstract

Ordinary kriging and inverse distance weighted (IDW) are two interpolation methods for spatial analysis of data and are commonly used to analyze macroscopic spatial data in the fields of remote sensing, geography, and geology. In this study, these two interpolation techniques were compared and used to analyze microscopic chemical images created from time of flight-secondary ion mass spectrometry images from a patterned polymer sample of fluorocarbon (C(x)F(y)) and poly(aminopropyl siloxane) (APS, a.k.a. siloxane). Data was eliminated from the original high-resolution data set by successive random removal, and the image file was interpolated and reconstructed with a random subset of points using both methods. The statistical validity of the reconstructed image was determined by both standard geographic information system (GIS) validation statistics and evaluating the resolution across an image boundary using ASTM depth and image resolution methodology. The results show that both ordinary kriging and IDW techniques can be used to accurately reconstruct an image using substantially fewer sample points than the original data set. Ordinary kriging performed better than the IDW technique, resulting in fewer errors in predicted intensities and greater retention of original image features. The size of the data set required for the most accurate reconstruction of the original image is directly related to the autocorrelation present within the data set. When 10% of the original siloxane data set was used for an ordinary kriging interpolation, the resulting image still retained the characteristic gridlike pattern. The C(x)F(y) data set exhibited stronger spatial correlation, resulting in reconstruction of the image with only 1% of the original data set. The removal of data points does result in a loss of image resolution; however, the resolution loss is not directly related to the percentage of sample points removed.

Fine Particulate Matter Induces Childhood Asthma Attacks via Extracellular Vesicle‐Packaged Let‐7i‐5p‐Mediated Modulation of the MAPK Signaling Pathway

“…Inverse distance weighted interpolation (IDW) is an important spatial interpolation method in ArcGIS software (version 10.2), that was employed to evaluate the individual PM 2.5 exposure concentrations. [ 45 , 46 ] The details are explained as follows: in Equation ( 1 ), Z ( u ) denotes the PM 2.5 exposure concentration of subjects, z ( u i ) is the observed value at the n measured sites, and d a represents the inverse distance weighted interpolation (IDW) weight distance.…”

“…Inverse distance weighted interpolation (IDW) is an important spatial interpolation method in ArcGIS software (version 10.2), that was employed to evaluate the individual PM 2.5 exposure concentrations. [ 45,46 ] The details are explained as follows: $$\begin{equation}Z\left( u \right){\rm{\ }} = {\rm{\ }}\frac{{\mathop \sum \nolimits_{i{\rm{\ }} = {\rm{\ }}1}^n \frac{1}{{{d^a}}}{\rm{\ }}z\left( {{u_i}} \right)}}{{\mathop \sum \nolimits_{i{\rm{\ }} = {\rm{\ }}1}^n \frac{1}{{{d^a}}}}}\end{equation}$$in Equation (), Z ( u ) denotes the PM 2.5 exposure concentration of subjects, z ( u i ) is the observed value at the n measured sites, and d a represents the inverse distance weighted interpolation (IDW) weight distance.…”

Hydrochemical variations of the springs on Jinfo Mountain, Chongqing, China

“…The most common methods for spatial interpolation are Inverse Distance weighting (IDw) and the Kriging method. Previous research has determined that the Kriging method is more accurate in its retention of original image features (Milillo & Gardella 2008), and in estimating radioactive contamination (Mabit & Bernard 2007) and soil mercury content (Hu et al 2004). On the other hand, the IDw method is superior for estimating whole landfill methane flux (Spokas et al 2003).…”

Does underweight amplify the relationship between short-term particulate matter exposure and blood pressure in children and adolescents: a large cross-sectional study in a metropolis of China

“…Then, inverse distance weighted (IDW) method was applied to deduce daily PM 10 , O 3 , and PM 2.5 exposure levels of each school based on daily air pollutant concentrations from neighboring air monitoring stations. As we know, IDW was a commonly used simulation method to perform spatial and temporal distribution of ambient air pollutants (Milillo and Gardella 2008). In total, individual short-term exposures (0-6-day previous BP measurements) to PM 2.5 and PM 10 were assessed.…”