Dataset Information

Extending Ripley's K-Function to Quantify Aggregation in 2-D Grayscale Images.

ABSTRACT: In this work, we describe the extension of Ripley's K-function to allow for overlapping events at very high event densities. We show that problematic edge effects introduce significant bias to the function at very high densities and small radii, and propose a simple correction method that successfully restores the function's centralization. Using simulations of homogeneous Poisson distributions of events, as well as simulations of event clustering under different conditions, we investigate various aspects of the function, including its shape-dependence and correspondence between true cluster radius and radius at which the K-function is maximized. Furthermore, we validate the utility of the function in quantifying clustering in 2-D grayscale images using three modalities: (i) Simulations of particle clustering; (ii) Experimental co-expression of soluble and diffuse protein at varying ratios; (iii) Quantifying chromatin clustering in the nuclei of wt and crwn1 crwn2 mutant Arabidopsis plant cells, using a previously-published image dataset. Overall, our work shows that Ripley's K-function is a valid abstract statistical measure whose utility extends beyond the quantification of clustering of non-overlapping events. Potential benefits of this work include the quantification of protein and chromatin aggregation in fluorescent microscopic images. Furthermore, this function has the potential to become one of various abstract texture descriptors that are utilized in computer-assisted diagnostics in anatomic pathology and diagnostic radiology.

SUBMITTER: Amgad M

PROVIDER: S-EPMC4670231 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Publications

Extending Ripley's K-Function to Quantify Aggregation in 2-D Grayscale Images.

Amgad Mohamed M Itoh Anri A Tsui Marco Man Kin MM

PloS one 20151204 12

In this work, we describe the extension of Ripley's K-function to allow for overlapping events at very high event densities. We show that problematic edge effects introduce significant bias to the function at very high densities and small radii, and propose a simple correction method that successfully restores the function's centralization. Using simulations of homogeneous Poisson distributions of events, as well as simulations of event clustering under different conditions, we investigate vario ...[more]

PMID: 26636680

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Project description:PurposeQuantitative assessment of white matter hyperintensities (WMH) on structural Magnetic Resonance Imaging (MRI) is challenging. It is important to harmonise results from different software tools considering not only the volume but also the signal intensity. Here we propose and evaluate a metric of white matter (WM) damage that addresses this need.MethodsWe obtained WMH and normal-appearing white matter (NAWM) volumes from brain structural MRI from community dwelling older individuals and stroke patients enrolled in three different studies, using two automatic methods followed by manual editing by two to four observers blind to each other. We calculated the average intensity values on brain structural fluid-attenuation inversion recovery (FLAIR) MRI for the NAWM and WMH. The white matter damage metric is calculated as the proportion of WMH in brain tissue weighted by the relative image contrast of the WMH-to-NAWM. The new metric was evaluated using tissue microstructure parameters and visual ratings of small vessel disease burden and WMH: Fazekas score for WMH burden and Prins scale for WMH change.ResultsThe correlation between the WM damage metric and the visual rating scores (Spearman ρ > =0.74, p < 0.0001) was slightly stronger than between the latter and WMH volumes (Spearman ρ > =0.72, p < 0.0001). The repeatability of the WM damage metric was better than WM volume (average median difference between measurements 3.26% (IQR 2.76%) and 5.88% (IQR 5.32%) respectively). The follow-up WM damage was highly related to total Prins score even when adjusted for baseline WM damage (ANCOVA, p < 0.0001), which was not always the case for WMH volume, as total Prins was highly associated with the change in the intense WMH volume (p = 0.0079, increase of 4.42 ml per unit change in total Prins, 95%CI [1.17 7.67]), but not with the change in less-intense, subtle WMH, which determined the volumetric change.ConclusionThe new metric is practical and simple to calculate. It is robust to variations in image processing methods and scanning protocols, and sensitive to subtle and severe white matter damage.

Project description:We present an analytical method using correlation functions to quantify clustering in super-resolution fluorescence localization images and electron microscopy images of static surfaces in two dimensions. We use this method to quantify how over-counting of labeled molecules contributes to apparent self-clustering and to calculate the effective lateral resolution of an image. This treatment applies to distributions of proteins and lipids in cell membranes, where there is significant interest in using electron microscopy and super-resolution fluorescence localization techniques to probe membrane heterogeneity. When images are quantified using pair auto-correlation functions, the magnitude of apparent clustering arising from over-counting varies inversely with the surface density of labeled molecules and does not depend on the number of times an average molecule is counted. In contrast, we demonstrate that over-counting does not give rise to apparent co-clustering in double label experiments when pair cross-correlation functions are measured. We apply our analytical method to quantify the distribution of the IgE receptor (FcεRI) on the plasma membranes of chemically fixed RBL-2H3 mast cells from images acquired using stochastic optical reconstruction microscopy (STORM/dSTORM) and scanning electron microscopy (SEM). We find that apparent clustering of FcεRI-bound IgE is dominated by over-counting labels on individual complexes when IgE is directly conjugated to organic fluorophores. We verify this observation by measuring pair cross-correlation functions between two distinguishably labeled pools of IgE-FcεRI on the cell surface using both imaging methods. After correcting for over-counting, we observe weak but significant self-clustering of IgE-FcεRI in fluorescence localization measurements, and no residual self-clustering as detected with SEM. We also apply this method to quantify IgE-FcεRI redistribution after deliberate clustering by crosslinking with two distinct trivalent ligands of defined architectures, and we evaluate contributions from both over-counting of labels and redistribution of proteins.

Dataset Information

Extending Ripley's K-Function to Quantify Aggregation in 2-D Grayscale Images.

Publications

Extending Ripley's K-Function to Quantify Aggregation in 2-D Grayscale Images.

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