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Hyper Spectral Image Processing
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Simulated Spot-Equivalent Reflectance
Characteristics of Common Reef Features
Analysis of Variance
A statistical procedure for analyzing data with a quantitative dependent variable and a categorical
independent variable, as is the case here, is analysis of variance (ANOVA). The variance of means is compared
to the background variance of the data from which the means are determined. In the following one-way
ANOVA, the null hypothesis of equal sample means is tested against the alternative hypothesis that each bottom
type category comprises a separate population. ANOVA procedures compare differences in means such that
within- and between-group variability are compared and referenced to the grand mean of the dataset.
An analysis of variance was performed on the entire dataset consisting of 596 SPOT 1 reflectance values
(dependent variable) separated into 5 groups (healthy coral, bleached coral, algae, rubble and sea grass) with the
null hypothesis that the means of all 5 groups are equal. In performing the ANOVA, the goal is to determine
what part of the variance should be attributed to randomness and what part can be attributed to other factors.
The Mean Square (MS) column reveals the sum of squares divided by the degrees of freedom, which indicates
variance. The first value, 0.09, measures the variance between groups, while the second value, 0.00, measures
the variance within groups. Since the variance between groups is larger than the variance within groups, then
the average bottom reflectance is not the same for each group.
The F-value, 21.03, is the ratio of the two variances and is used to choose between the two hypotheses
where the null hypothesis will be rejected if the F-ratio is in the upper 5% of the F distribution. The p-value is
0.00, which is less than the alpha value of 0.05 specified as the confidence level. The null hypothesis that the
group means are equal must therefore be rejected at the 5% level. The calculated F-statistic, 21.03, is greater
than the F-critical value, 2.39, indicating that the calculated F-statistic is in the upper 5% of the F-distribution.
Therefore, although the qualitative assessment and comparison of population means suggested that there were
no discernible differences, the statistical results of ANOVA suggest that the reflectance measurements were
taken from 5 different or unique populations.
4. Conclusions
There is little qualitative difference between in situ reflectance values of various substrates collected at
depth in a coral reef environment. This indicates that visual interpretation of remotely sensed imagery will yield
inaccurate classification results. Significant mixing of several different substrate types within the relatively
large pixels of SPOT HRV images (20x20m) compounds the issues of classification inaccuracy. Other
complicating factors include the effects of attenuation and multiple scattering from the overlying water column,
refraction of light at the air-water interface, scattering and absorption in the atmosphere, and effects of the
variable morphology of the substrate with respect to slopes and self-shading.
The results of the statistical analysis of the simulated SPOT HRV reflectance values are encouraging since
the populations can be considered significantly and sufficiently different to allow discrimination. While the
populations defined for this study are admittedly broad, the categorization will still be useful for a change
detection study of a large geographic region. Due to the natural variation of reflectance values both within and
between populations, accurate and definite identification of substrate type may not be advisable especially
considering the additional sources of error when the values are sensed remotely rather than in situ, as in this
study. Alternatively, the fact that the in situ data reveals statistical separability between populations suggests
that change detection is the most appropriate use of currently available satellite imagery.
Although the satellite imagery available has significant limitations in the accuracy and precision with which
it can be used to map and monitor changes in coral reef ecosystems, the overt changes that are occurring warrant
the use of the technology in an attempt to further our understanding of coral reefs. The currently available
passive satellite imagery with appropriate spectral band locations (visible wavelengths for water penetration)
should therefore be utilized to map the geographic extent of coral reefs and investigate changes in ecosystem
health. The errors associated with the coarse spatial, spectral and temporal resolution should not be ignored, but
rather, attempts should be made to minimize the associated errors and communicate the limitations of the digital
image analysis results.
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