The Optimum Index Factor (OIF) in ArcGIS, and remote sensing generally, is a statistical metric used to identify the best three-band combination from a multi-spectral dataset that provides the most useful information for visualization or analysis.
Understanding the Optimum Index Factor
Based on the provided reference, the Optimum Index Factor (OIF) determines the three-band combination that maximizes the variability (information) in a multi-spectral scene. Multi-spectral satellite or aerial imagery captures data across multiple different wavelength bands, each revealing unique characteristics of the Earth's surface. Choosing which three of these bands to combine for display or analysis is crucial, as some combinations show more contrast and detail than others.
The OIF provides a quantitative way to make this choice. As the reference states, the index is calculated as a ratio of the total variance (standard deviation) within and the correlation between all possible band combinations. A higher OIF value indicates a better band combination because it suggests the chosen bands collectively contain more unique information (high variance) and less redundant information shared between them (low correlation).
Why is OIF Important?
Selecting the optimal band combination is vital for:
- Maximizing Information: Ensuring the displayed image or data used in analysis contains the most distinct features and variations present in the scene.
- Reducing Redundancy: Avoiding the use of bands that provide very similar information, which doesn't add significant value to the combination.
- Improving Visualization: Creating visually appealing and informative images where different surface features (like vegetation, water, urban areas, etc.) are clearly distinguishable.
- Enhancing Analysis: Providing input data that is rich in independent information, which can improve the results of subsequent analytical processes.
How OIF is Calculated (The Ratio)
The OIF for a specific three-band combination is typically calculated using the following ratio:
OIF = (Sum of the standard deviations of the three chosen bands) / (Sum of the absolute values of the correlation coefficients between the three pairs of bands)
Formula Concept:
- Numerator (Sum of Standard Deviations): Bands with high standard deviation have a wider range of values, indicating more variability or information within that band. Summing standard deviations favors bands rich in information.
- Denominator (Sum of Absolute Correlations): High correlation between two bands means they show similar patterns. Low correlation means they show different patterns. The OIF calculation uses the absolute correlation (ignoring whether it's positive or negative correlation, only caring about the strength of the relationship) because any strong correlation, positive or negative, signifies redundancy. Summing absolute correlations penalizes combinations with highly correlated bands.
A higher OIF score results from combinations that have high variability and low correlation among the selected bands.
Using OIF in ArcGIS (Practical Insight)
While ArcGIS Pro or ArcMap might not have a single "Calculate OIF" tool, the necessary steps can be performed using available geoprocessing tools to find the optimal combination:
- Calculate Statistics: Use tools like "Calculate Statistics" to find the standard deviation for each individual band in your multi-spectral dataset.
- Calculate Correlation Matrix: Use tools or scripting to compute the correlation coefficient between every pair of bands.
- Compute OIF: For every possible combination of three bands (e.g., bands 1, 2, 3; bands 1, 2, 4; bands 1, 3, 4; etc.), calculate the OIF using the formula above.
- Select the Best Combination: Identify the three-band combination that yields the highest calculated OIF value. This is statistically considered the most informative combination.
- Apply Combination: Use the band combination with the highest OIF when displaying the multi-spectral image in ArcGIS for better visualization or as input for further analysis.
For instance, applying OIF to Landsat or Sentinel imagery helps determine which bands to display as Red, Green, and Blue channels to best highlight urban features, vegetation health, or water bodies for a specific study area.
