## 5 Conclusions  
We addressed a scientific problem that has also been the focus of our earlier investigations (i.e., the initial exploratory analysis [29; 30] and the first refined study [31; 32]) to a transition to the petroleum industry's operational application--i.e., the use of simple, mathematically-robust linear discriminant analysis (LDA) applied to SAR measurements to discriminate the oil-slick category (oil seeps vs. oil spills). This need continues to increase with time, as new offshore fossil fuel discoveries continue to be made, but with the requirement to assist ecological monitoring and response. In fact, the Brazilian Petroleum Corporation (Petrobras) is currently exploring our proven seep-spill discrimination methodology. Our exploratory data analysis has focused on oil-slick category discrimination exploiting different SAR backscatter coefficients (i.e., sigma-naught (\(\sigma^{\circ}\)), beta-naught (\(\beta^{\circ}\)), and gamma-naught (\(\gamma^{\circ}\))) calculated from various SAR calibrated products (i.e., amplitude (_amp_) or decibel (_dB_) measures of the back-scattered radar beam, with or without a despeckle filter (_FF_; for Frost filter [62])) applied to three data transformations (none, cube root, and \(\log_{10}\)). This resulted in 61-data combinations using several oil-slicks' signature (i.e., size information and SAR basic qualitative-quantitative statistics). The worst overall accuracy of all is found with the original data of the size only combination (63.90%), whereas the best one is the log-transformed _GAM.dB_ (68.85%). We explore 244 RADARSAR-2 images containing 4562 slicks (1994 seeps and 2568 spills) observed in Campeche Bay, Gulf of Mexico, to address our four scientific questions:  
1. Although the three backscatter coefficients have similar success at categorizing seeped and spilled oil (independently of the applied calibrated product or data transformation), \(\gamma^{\circ}\) is somewhat superior. 2. The discrimination power of the four calibrated products is rather independent of backscatter coefficient but varies to some extent within data transformation. When \(\log_{10}\) is applied, _dB_ (68.85%: _GAM_) is followed by _dB.FF_ (68.72%: _GAM_) and by two _amp_ forms. A baffling pecking order is observed with cube root, but even though it lacks a defined hierarchy pattern, _amp.FF_ reaches better accuracy levels (68.35%: _GAM_) and _amp_ the lowest (67.98%: _GAM_). With the not-transformed original data, _dB.FF_ effectiveness is followed by _dB_, then by the two _amp_ forms with no definite pattern; however, these have little practical meaning--see point 3 below. 3. The data transformation exerts the most influence over the seep-spill discrimination, dictating the performance of our optimal linear models. Among the tested ones, the highest overall accuracy is the log-transformed (68.85%: _GAM.dB_), though the cube root has slightly more balanced seep-spill discrimination capabilities and is as successful: 68.35% (_GAM.amp.FF_). If the data is not normalized, the top overall accuracy is 65.67% (_GAM.dB.FF_); nevertheless, its LDAs are incapable of separating seeps from spills, as its specificity and positive predictive values are void (\(\sim\)50%). 4. Concerning the use of different attributes describing the oil-slicks' signature, a comparison with the first refined study (_SIG.amp_) demonstrates that even though different size and SAR signatures have been used between both of our investigations (AVG and SKW against VAR and KUR; and PtoA and Compact against PtoA, Compact, and Fractal, respectively, for the refined study and our research), the discrimination improvement is disappointingly small. Although, there is an improvement once other backscatter coefficients and calibrated products are investigated--e.g., cube root size only (67.62%) against cube root _GAM.amp.FF_ (68.35%); the latter accounts for the same size information as the former, plus VAR and KUR.