Geological Image Analysis Software - GIAS v1.0
Nearest Neighbor Panel
THe Nearest Neighbor (NN) panel consists of the four graphical areas (Distance histogram, R and c statistical graphs, Skew vs. kurtosis plot) and a text summary of the statistical properties of five different fitting models. It is always active (i.e. input data is an image file, an NN image or NN Centroid List). Note that previously processed data is stored in memory until it is overwritten. This application is primarily written to test the object distance distribution for spatial randomness or other types of organisation, to examine if there are underlying processes which may be influencing the placement of the objects.
Objects may exhibit a spatial organization along a continuum that includes three classes

1. Regular spacing, which in an extreme sense manifests in an equal distance between all objects;
2. Random distributions, where the location of each object is independent of all other objects; and
3. Aggregated distributions, which in an end-member scenario results in objects being tightly clustered within a single group.

By examining the NN distances, such models can be tested. NN distances are determined by calculating the Euclidean distance between each interior object and all other objects within the dataset, including the vertices of the surrounding convex hull. The results for each interior point are sorted in ascending order to identify the minimum NN distance and calculate the actual mean NN distance.
All graphs are for visualisation purposes only. You cannot export any of the figures directly (other than screenshot capture). The data to reproduce the graphs can be saved to a spreadsheet-readable text file. See Input Panel Help.
NN Distance Histogram
The NN Histogram outputs the binned frequency of object distances. The bin size defaults to 10 equally-spaced bins. All updates take place immediately.
However, depending on the distribution of the object areas, the user can change the bin size by selecting Custom and entering the required bin size (which are correctly scaled). The starting and ending size bins on the X axis can be chaged by selecting Custom and typing in the green boxes marked 'Min' and 'Max'. If you do not do this correctly, the Custom box will flash the word 'Value >' to remind you to enter the required values.
The Y axis can be displayed in either Linear or Logarithmic spacing. When the Log button is clicked, the bars of the histogram become single points. The Maximum frequency displayed on the Y axis can also be clipped.
To reset the values to Default, click on the Bin Size: Default button.. In the Y Axis (green) text box, type 'Max' to reset the frequency axis.
R and c parameters
Using sample-size dependant values of R, c, and their respective thresholds of significance, we may define the following scenarios:

- If the values of R and c fall within ± 2 σ of their expected values, then one can confidently assume that the model correctly describes the input distribution.
- If the value of c is outside the range of ± 2 σ, then the model can be confidently rejected, regardless of the value of R.
- If c is outside ± 2 σ, and R is greater than the +2 σ threshold, then the input distribution exhibits a statistically significant repelling relative to the model. Conversely, if c is outside ± 2 σ range, and R less then than the -2 σ threshold, then the input distribution is clustered relative to the model.
- Lastly, if R is outside ± 2 σ, and c is within the ± 2 σ range, then the test results are ambiguous, which generally indicates that there is insufficient data to perform the analysis and/or the standard error (σ_e) of the input distribution is large.

Model Selection
One of the novel contributions of our application is the introduction of an automated calculation of the sample-size dependant biases in NN statistics. Baloga et al. (2007) proposed how finite sampling would affect several NN models; however, they only implemented a solution for the Poisson NN case. In our application, we have automated the Poisson NN procedure, extended it to include the three other models of Baloga et al. (2007), and derived the k = 2 case for the scavenged NN distribution (Appendix 1). Automation of the NN method within GIAS enables users to rapidly determine if their data fulfills the size-dependant criteria of statistical significance for the following five spatial distribution models: (1) Poisson; (2) Normalized Poisson; (3) Scavenged, k = 1; (4) and Scavenged k = 2; (Note the Logistic Distribution has been removed in Version 1.1). See the mauscript for summaries and discussion of the properties of these models.
Skew versus Kurtosis Plot
In addition to sample-size dependant R and c statistics, we expand upon the methods of Baloga et al. (2007) by simulating the sample-size dependant range of expected skewness and kurtosis values for each NN hypothesis. Calculated confidence intervals—at 90%, 95% and 99%—are plotted within GIAS to illustrate range of acceptable skewness versus kurtosis for each model. Plots of skewness versus kurtosis are also useful for discriminating between populations with otherwise similar R and c values, such as rootless cones and pingos (Bruno et al., 2006).
Nearest Neighbor Results
The nearest neighbor distances and other statistical properties of each model, (e.g. minimum, maximum, mean, R and c fit and expected mean etc of the data ) can be selected by clicking the appropriate button. All the data is output to the CSV file.
References:

Baloga SM., Glaze LS, Bruno BC, 2007, Nearest-neighbor analysis of small features on Mars: Applications to tumuli and rootless cones. Journal of Geophysical Research 112, E03002.