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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This work proposes a new method to classify multi-spectral satellite images based on multivariate adaptive regression splines (MARS) and compares this classification system with the more common parallelepiped and maximum likelihood (ML) methods. We apply the classification methods to the land cover classification of a test zone located in southwestern Spain. The basis of the MARS method and its associated procedures are explained in detail, and the area under the ROC curve (AUC) is compared for the three methods. The results show that the MARS method provides better results than the parallelepiped method in all cases, and it provides better results than the maximum likelihood method in 13 cases out of 17. These results demonstrate that the MARS method can be used in isolation or in combination with other methods to improve the accuracy of soil cover classification. The improvement is statistically significant according to the Wilcoxon signed rank test.

Conventional classification methods used in remote sensing have some basic problems due to the fact that they are not adapted to the real characteristics of image data. In addition, they lack proper configurations, and there is generally minimal user interaction.

Traditional remote sensing classification methods are divided into two large families. The first family is parametric, and includes the ML, bayesian methods,

According to [

In addition to the assumption of a probability distribution that may be inappropriate for the data under analysis, parametric methods have added another substantial problem. Namely, if the data have a high dimensionality, many samples are required for the learning stage of these methods. Overall, the assumption of a normal spectral distribution is often violated, especially in complex landscapes. In addition, insufficient, non-representative, or multimode distributed training samples can further introduce uncertainty to the image classification procedure [

Many studies have shown that non-parametric methods provide better classification results. In studies such as [

MARS is a non-parametric regression method in which no assumption is made regarding the functional relationship between dependent and independent variables. Instead, MARS builds this relationship from a set of coefficients and basic functions, which in turn are heavily influenced by the regression of the data. The operating method involves partitioning the area of entry into regions, each with its own regression equation [

This method was proposed by [

As shown in [

It should be emphasised that [

Only [

The ASTER sensor was developed in an attempt to use detailed geological data to understand phenomena such as volcanic activities that can significantly impact the global environment [

On the other hand, on how to evaluate the accuracy of the classification, a receiver operating characteristic (ROC) curve is a 2D graph representing both the specificity and the sensitivity of a binary (

AUC provides a measure of how well a classification algorithm performs. [

ROC curves are generated by varying a threshold across the output range of a scoring model and then observing the corresponding classification performances. This graph is necessary to obtain the AUC statistic. The AUC statistic has an important property; namely, the AUC of a classifier is equivalent to the probability that classifier will rank a randomly chosen positive instance higher than a randomly chosen negative instance [

[

In brief, the aim of this study is to evaluate the MARS algorithm as a remote sensing classifier. For this purpose, the same TERRA-ASTER scene was classified by MARS and by two classical remote sensing classifiers (the ML and parallelepiped methods) to compare class probabilities derived from the AUC statistic. Section 2 describes the study's framework and data processing methods. Section 3 introduces the classification methods, and section 4 analyses and discusses the results.

The test area was a roughly 60 × 60 km area in the Spanish province of Badajoz, which is located in Extremadura in southeastern Spain (

The platform is composed of three different subsystems. First, the visible and near-infrared (VNIR) has three bands with a spatial resolution of 15 m and an additional backward telescope for stereoscopic use. Second, the shortwave infrared (SWIR) has six bands with a spatial resolution of 30 m. Finally, the thermal infrared (TIR) has five bands with a spatial resolution of 90 m. Each subsystem operates in a different spectral region with its own telescope [

The ASTER data can be downloaded free of cost from the website

The Regions of Interest (ROIs) used in the classification process were obtained from the Spain forest map (see

All operations were performed using a variety of softwares as ENVI (image processing), ArcView and ArcGIS (geographic information systems), SPSS (statistical analysis), and MARS (predictive modelling).

In this study, the data were pre-processed prior to any classification procedures (see Section 3.1). A brief introduction to the MARS algorithm is presented before developing different classifications (see Section 3.2.). Two different processes were performed in this study. On the one hand, we generated three traditional classification maps using the ML, parallelepiped and MARS algorithms (see Section 3.3.). On the other hand, class probability maps were also obtained using these three algorithms; their accuracies were calculated using the AUC statistic (see Section 3.4.).

Two different operations were implemented on the original image before starting classification processes. First, regardless of whether the data included L1-B images, that is, radiometrically calibrated and geometrically registered images, an additional geometric registration was performed using nine ground control points. These points were previously measured using GPS techniques.

Second, we re-sampled the SWIR and TIR bands to obtain the same geometric resolution for the entire image. With this action, no alteration was introduced to the original pixel information because the re-sampling was performed from a larger pixel resolution up to a smaller pixel resolution (see

After these two processes, the image data were ready for classification.

The MARS model is a spline regression model that uses a specific class of base functions as predictors in place of the original data [

A spline is a special function defined piecewise by polynomials, and it is used to refer to a wide class of functions that are used in applications requiring data interpolation. [

On the other hand, basic functions have a key attribute known as a “knot”. A knot marks the end of one region of data and the beginning of another [

Basis functions are used to search for knots; these functions serve as a set of functions representing the relationship between the predictor variables (

This function consists of an interceptor parameter _{0}_{m}(X)

MARS uses what [_{+} and _{+}, with

The MARS procedure is divided into three steps. First, a forward algorithm selects all possible basic functions and their corresponding knots. Second, a backward algorithm eliminates all basic functions in order to generate the best combinations of existing knots, and finally, a smoothing operation is performed to obtain continuous partition borders.

The selection of basic functions from the initial set is achieved by determining a constant function _{0}

The backward removal is performed by suppressing those model terms that contribute to a minimal residual error. This stage consists of reducing the complexity of the model complexity by increasing its generalisability [

With this GCV function, the optimum number of model terms (

The value

The process stops when the number of model terms reaches

Finally, smoothing is necessary for removing discontinuities within regional borders and ensuring the continuity of first and second derivatives.

[

In this process, 17 out of the total 18 categories were considered for classification. The “agricultural cultivations” class (cod 534) was excluded due to its heterogeneity. All the crops of dry regions and irrigated regions are incorporated into this EFM category so that very different spectral responses are included. Considering this class would cause serious errors in classification processes.

The original format of the EFM categories was the ArcInfo exchange coverage extension “*.e00”. Thus, an import operation became necessary to convert all classes into “shp” format. This process was performed using both ArcInfo and ArcView software.

The second preliminary operation, as referred to above, was to reduce all “shp” polygons through a buffer of −100 m in order to purify the ROIs. Not all polygons were chosen for the classification task. As shown in

Thus, we relied on a variety of ROI sizes to confirm whether there was relationship between training size and final classification results. As shown in

This study uses the ML, parallelepiped, and MARS methods. A brief summary of the properties of each of these classifiers is given in the next section.

ML is the most popular parametric classification method used in remote sensing. This method assigns observation X to class ωI if the function gi(X) is larger than any other _{j}(X)

The parallelepiped classification method is a non-parametric method. It is one of the simplest classification methods based on a radiometric model rather than on the measurement of distances or probabilities [

In order to monitor the whole battery process more effectively, a chart diagram is displayed, summarizing the methodology for MARS classifications (

For MARS classification, it is necessary to know the digital numbers (DNs) of pixel values at all 14 bands. Thus, once all shp ROI polygons were superimposed onto the ASTER scene, we performed an ASCII exportation using ENVI software. The 17 resulting files contained image and map coordinates of all pixels inside the corresponding ROI and their corresponding DN values for all bands. See

First, the image must be classified by discriminating each class from the rest. The class with which all other classes were compared was called the “fixed class”, and the fixed class was compared with the “comparing class”. Next, these classifications were merged into a unique probability image per class, and finally, the probabilities per class were joined into a final classification map. Based on this premise, the classification process was designed as follows.

As discussed in [

The pairwise combinations of ROI files were developed using SPSS. A new variable was introduced to distinguish between the fixed and comparing classes. This variable was assigned the value 1 for the fixed class and 0 for the comparing class. Overall, 272 training files were obtained, for a total of 16 ROI class combinations.

All 272 training files were introduced into the MARS software, and basic functions were obtained by defining a partition border between the two classes. Before validating these basic functions, they were applied to the input data again to verify that they could discriminate between class training data and that they could consistently extrapolate image holes for discriminating classes. This validation process was developed using the AUC statistic, and it was assumed to show the degree of adjustment of the MARS model relative to the input data.

Once the basic functions were obtained from the training data, the second stage consisted of applying them to the entire image in order to perform the actual classification.

Basic functions were introduced into an ArcInfo macro language (AML) file. This AML file was programmed to apply MARS basic functions to the image, resulting in a probability value for each pixel. This value indicated the probability of belonging to the fixed class (i.e., higher probability values) or to the comparing class (i.e., lower values).

Until now, we have used 272 probability files for the combinations of all working classes. Now, we intend to generate a binary map in which the value 1 represents “pixel belongs to the fixed class” and value 0 represents “pixel belongs to the comparing class”, or equivalently, “pixel does not belong to the fixed class”.

The suitability scores obtained from MARS were not in the standard [0,1] interval. Thus, it was necessary to improve the application to calculate what some authors have called a “cut for best classification”. In our study, this value had to fulfil two conditions:

Maximise correct classification probabilities

Minimise incorrect classification probabilities

The application was programmed using SPSS software, and it counted false positive and false negative frequencies and subsequently changed the cut-off point in probability space. The process was similar to the one used for the ROC curve.

Once the cut-off value was calculated for all 272 probability files, the binary grids were generated using ArcInfo software.

At this stage of the work, we had 16 binary grids per class. The purpose of the class probability image was to join all these binary grids.

All grids were added in ArcView, so the result was another grid with values ranging from 16 (if the pixel was always classified as the fixed class) to 0 (if the pixel had never been classified as belonging to the fixed class).

These values were transformed to the standard [0,1] interval dividing the grid by 16. Thus, the maximum probability value of 1 was assigned to those pixels that the MARS classifier always denoted with the same classification.

The final operation was to join the 17 grids using ArcInfo software. This operation determined the class with the maximum probability value among the 17 input grids for each pixel.

At the same time that the classifications were calculated, a probability map was generated for each class. This allowed us to conduct an exhaustive evaluation of the method's accuracy in predicting classifiers.

While performing classification processes, ENVI software allows for the calculation of rule images. Rule images for ML classifiers are grids containing the discriminant function expressed in [

The rule image obtained for this study contained values in the interval [−300,000, 100] with a heterogeneous distribution. This property impeded the use of rule images for the development of probability maps.

An alternative probability map was calculated by following the same pairwise method used for the MARS classification. We generated 272 binary ML classifications and combined them as explained in the MARS procedure to obtain the final probability map.

This option was also useful to validate the pairwise classification method because we did not stop at the class probabilities map but rather completed the entire process and thus obtained a final ML classification map; from now on, this will be called the pairwise ML classification map. If the pairwise classification process is valid, then the final pairwise ML classification map should be the same as the original ML classification map from Section 3.3.1.

The ENVI rule images for parallelepiped classification provides for each pixel the number of bands that fulfils the parallelepiped condition. These pixel values were considered as probabilities with no transformations because the AUC statistic can be calculated with values not in the [0, 1] interval.

Probability maps were calculated during the classification process, so it was not necessary to recalculate them.

These classification maps cannot be used in and of themselves to evaluate accuracy. It is necessary to perform a separate accuracy study, and thus as mentioned before, ROC curves and AUC statistics were calculated for this purpose.

Accuracy assessments of the probability maps were implemented;

Based on AUC statistics (

This paper has presented the novel application of the MARS classification method to a conventional multi-spectral image. The results show that this method can be useful to improve some classifications. The main advantages of this method are that MARS is a non-parametric method that can be used without prior assumptions regarding the statistical distribution of the data. In addition, MARS is not severely affected by data collinearity, a common issue in satellite multiband imagery, and its functions are clear and transparent, especially when compared to the “black box” functions of other methods.

We compared the accuracy of various methods using the AUC statistic, an independent and objective test that can be applied to very different classification methods and that is independent of the cut-off classification threshold. The AUC statistic is a tool for evaluating classification performance that has been widely used in other disciplines, but only infrequently employed in remote sensing.

As the main conclusion of this study, MARS is a robust classification method that can be used in remote sensing without any disadvantages or apparent problems: its non-parametric nature, its transparency in terms of the relevant variables, and its adaptability to the data give it great potential as a multi-spectral classifier.

Our future work will focus on the application of hyperspectral data to MARS in order to deepen our analysis of its performance by using highly correlated bands and very large numbers of data.

The authors are grateful for the wise suggestions by the two anonymous referees. This paper has been co-funded by the Junta de Extremadura (Consejería de Educación, Ciencia y Tecnología — II Plan Regional de Investigación, Desarrollo Tecnológico e Innovación de Extremadura) and FEDER (Fondo Europeo de Desarrollo Regional).

Location of the Extremadura test area in southeastern Spain.

Extremadura forest map (EFM).

Re-sampling example for TIR bands.

Work flow for the MARS process classification.

Fragment of the ROI ASCII export file.

(a) ML classification map, (b) Parallelepiped classification map, (c) MARS classification map.

Main characteristics of the ASTER sensor systems.

1 | 0.52–0.60 | 15 | 8 bits | |

2 | 0.63–0.69 | |||

3N | 0.78–0.86 | |||

3B | 0.78–0.86 | |||

| ||||

4 | 1.60–1.70 | 30 | 8 bits | |

5 | 2.145–2.185 | |||

6 | 2.185–2.225 | |||

7 | 2.235–2.285 | |||

8 | 2.295–2.365 | |||

9 | 2.360–2.430 | |||

| ||||

10 | 8.125–8.475 | 90 | 12 bits | |

11 | 8.475–8.825 | |||

12 | 8.925–9.275 | |||

13 | 10.25–10.95 | |||

14 | 10.95–11.65 |

Forest categories of area under study.

^{2}) |
|||
---|---|---|---|

Water | 49.6 | 1.3% | |

Mixed silicicolous scrubland | 47.5 | 1.2% | |

Agricultural land | 2,422.9 | 61.4% | |

Mixed riparian forest | 23.5 | 0.6% | |

Dense seasonal pasture | 135.6 | 3.4% | |

Open formation | 8.7 | 0.2% | |

Dense formation | 8.6 | 0.2% | |

Boulders | 2.1 | 0.1% | |

Rocky desert | 42.2 | 1.1% | |

109.2 | 2.8% | ||

22.0 | 0.6% | ||

10.4 | 0.3% | ||

194.7 | 4.9% | ||

10.1 | 0.3% | ||

53.5 | 1.4% | ||

786.0 | 19.9% | ||

1.4 | 0.0% | ||

17.8 | 0.5% |

Regions of interest (ROI) used in the classifications.

^{2}) |
^{2}) |
|||
---|---|---|---|---|

Water | 49.6 | 33.3 | 67.19% | |

Mixed silicicolous scrubland | 47.5 | 28.4 | 59.73% | |

Mixed riparian forest | 23.5 | 11.6 | 49.18% | |

Dense seasonal pasture | 135.6 | 52.2 | 38.47% | |

Open formation | 8.7 | 2.8 | 31.89% | |

Dense formation | 8.6 | 5.6 | 64.68% | |

Boulders | 2.1 | 0.8 | 36.22% | |

Rocky desert | 42.2 | 23.5 | 55.82% | |

109.2 | 69.6 | 63.69% | ||

22.0 | 10.6 | 48.33% | ||

10.4 | 8.1 | 78.18% | ||

194.7 | 140.6 | 72.25% | ||

10.1 | 5.7 | 55.93% | ||

53.5 | 26.0 | 48.48% | ||

786.0 | 544.2 | 69.23% | ||

1.4 | 0.7 | 52.24% | ||

17.8 | 12.1 | 67.92% |

Area under the ROC curve (AUC) statistics.

^{2}) |
|||||
---|---|---|---|---|---|

| |||||

AUC | AUC | AUC | |||

999 | Water | 33.3 | 0.945 | 0.793 | |

547 | Mixed silicicolous scrubland | 28.4 | 0.813 | 0.754 | |

507 | Mixed riparian forest | 11.6 | 0.814 | ||

458 | Dense seasonal pasture | 52.2 | 0.714 | 0.687 | |

454 | Open formation | 2.8 | 0.929 | 0.954 | |

453 | Dense formation | 5.6 | 0.961 | 0.971 | |

337 | Boulders | 0.8 | 0.963 | 0.791 | |

329 | Rocky desert | 23.5 | 0.884 | 0.701 | |

309 | 69.6 | 0.699 | 0.670 | ||

303 | 10.6 | 0.826 | 0.728 | ||

221 | 8.1 | 0.898 | 0.657 | ||

62 | 140.6 | 0.856 | 0.834 | ||

61 | 5.7 | 0.939 | 0.870 | ||

46 | 26.0 | 0.841 | 0.766 | ||

45 | 544.2 | 0.577 | 0.600 | ||

26 | 0.7 | 0.957 | 0.903 | ||

23 | 12.1 | 0.952 | 0.924 |