Statistical analysis of the image

For a statistical analysis to adequately characterize the distribution of a component, the data should first be processed to obtain the optimum selectivity for that component. In this application the PLS model produces a score image that effectively separates the spectral response of the API from the excipients. Even though there is very little observable contrast in the images of the well blended samples, the results from the poorly blended samples convey conhdence that the method is effective at tracking the API distribution. 

The interpretation of these metrics for a chemical image is somewhat dependent on the overall morphology of the sample. For a highly to moderately homogeneous sample (e.g. tablets D-F), the mean value indicates the bulk abundance of the component and the 

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Fig. 3.62 Statistical analysis of the tapping mode AFM phase image (5x5 gm2) for PMMA - PB 80 - 20 blend after 24 h of ambient conditioning [134] shown as inset. The distribution of pixel values can be deconvoluted into three components (the corresponding curves have been superimposed on the histogram), thus reflecting the presence of the two distinct phases and a contribution that may originate from possible from tip convolution (or an intermediate phase) at the phase boundaries...

Invariant moments are descriptors derived from a statistical analysis of the distribution and value of the pixels that make up the image to be compared [Hu, 1962 Robinson, Barlow et al, 1997b]. This distribution takes the form of the following equations ... 

The Multichannel ("Stroboscopic") Optical Spectrum Analyser (MOSA) allows us to carry out spatial Fourier analysis of the images of a ruffled water surface. One can show (see, Appendix) that the frequency spectrum s(co) = < i cof > (<...> denotes statistical averaging) of the MOSA signal i t) can be written in the form... 

Table 21.4 Quantification of elementary reaction processes through statistical analysis of AFM images of isolated 4-arm polystyrene comb stars (Reprinted with permission from M. Schappacher and A. Deffieux, AFM image analysis applied to the investigation of elementary reactions in the synthesis of comb star copolymers, Macromolecules, 38, 4942—4946, 2005 2005 American Chemical Society.)...

Scale bar 200 pm. Red arrows indicate the avascular zones. Quantification of digital analysis of the fluorescence angiography images number of branching points (mm2) (B) and mean mesh size (102 pm2) (C) as markers of vessel density for CAM. P < 0.05 was considered to be statistically significant. Error bars represent standard error of the mean. 

Precise thickness measurements by TEM require sections transverse to the basal lamellar surface. Conversely, only lamellae that can be identified as untilted "edge-on" or "flat-on" in AFM images are suitable for thickness analysis. The average thickness obtained by these techniques is based on sampling microscopic areas and will only be correct if the morphology is uniform in the sample. Micrographs taken from different areas of the specimen are usually studied, and statistical analysis of histograms used for quantitative analysis [255,256]. 

We conducted proteomic analysis of the KO mouse brain to identify proteins or peptides whose expression levels may change due to a lack of SCRAPPER. Imaging MS allowed us to statistically analyze location and expression intensities of many biomolecules and to extract molecules that exhibited region-specific expression. Groups of molecules whose expression patterns differed between WT mice and KO mice particularly attracted our attention. 

The mean sizes of windows, dw, and contacting cross sections, Dpc can be measured during analysis of the electron microscopy images as the relation of the first statistical moment to the zero one the sizes of dw can also be measured by adsorption methods (see Section 9.3). The direct interrelation between dw and, for example, Z)pc, is determined in view of a used model (e.g., in the framework of a model of isotropic deforming lattice of particles). Besides, also possible are correlations type of dwi dCi that relate the possible size of a cavity dCj to corresponding sizes of windows dWi from the cavity to the neighboring cavities. 

Dudewicz, E.J. Statistical Analysis of Magnetic Resonance Imaging Data in The Normal Brain, Part I Data, Screening, Normality, Discrimination, Variability" unpublished report, 1985. 

These same analysis techniques can be applied to chemical imaging data. Additionally, because of the huge number of spectra contained within a chemical imaging data set, and the power of statistical sampling, the PLS algorithm can also be applied in what is called classification mode as described in Section 8.4.5. When the model is applied to data from the sample, each spectrum is scored relative to its membership to a particular class (i.e. degree of purity relative to a chemical component). Higher scores indicate more similarity to the pure component spectra. While these scores are not indicative of the absolute concentration of a chemical component, the relative abundance between the components is maintained, and can be calculated. If all sample components are accounted for, the scores for each component can be normalized to unity, and a statistical assessment of the relative abundance of the components made. 

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