Cloud detection can be formally considered as a binary supervised classification problem. As such, methods for its solution need a representative set of data with labels considered to be “certain” (training dataset). They evaluate patterns in different features and assign data into one of the two classes (Clear or Cloudy). The classification procedure also involves collection and evaluation of a validation dataset. Once trained, each classifier applies a decision rule to determine if validation data are more likely to have originated from one class or another. This rule partitions the n-dimensional feature space into 2 regions corresponding to the Clear and Cloudy conditions.

Among the different approaches reported in the literature, we consider and compare for the present study seven different supervised classifiers. They fall into the categories usually labelled as Statistical and Machine Learning and are based on different principles, as Discriminant Analysis, Neural Networks, Nearest Neighbour. In the following we briefly describe them.

1. Linear Discriminant Analysis (LDA). It applies the Bayes rule to each scene to select the Clear/Cloudy class so to maximize the posterior probability of the class for a scene given the actual reflectance in that scene. LDA assumes that reflectance follows Gaussian distributions for the Clear and Cloudy classes sharing the same covariance matrix;
2. Quadratic Discriminant Analysis (QDA), that generalizes LDA assuming that also covariance matrix depends on the class (Clear or Cloudy);
3. Principal Component Discriminant Analysis (PCDA): the hypothesis of Gaussian distribution of reflectance is released in favour of a generic distribution estimated by nonparametric regression; in addition the original reflectances are transformed into uncorrelated Principal Components before classification;
4. Independent Component Discriminant Analysis (ICDA): similar to PCDA, but with the original reflectances transformed into Independent Components before nonparametric estimation of the densities; this makes such components independent also for non Gaussian distributions;
5. Cumulative Discriminant Analysis (CDA): the decision rule for classification depends on a single threshold for each feature (spectral band), based on the empirical distribution function, that discriminates scenes belonging to the Clear and Cloudy classes; the threshold is estimated so to minimize at the same time the false positive and false negative rates on the training or on a validation dataset.
6. Artificial Neural Networks (ANN). We use a two-layer feed-forward network, with sigmoid hidden and softmax output neurons for pattern recognition. The network is trained with scaled conjugate gradient backpropagation.
7. k-Nearest Neighbour (KNN) that labels each considered scene based on a voting strategy among the labels assigned to the K closest neighboring scenes belonging to the training dataset.

Methods LDA, QDA, PCDA, ICDA and CDA require estimate of the statistical distribution of radiance. We mention that other methods are available in the literature; results of some of them have not been  reported because of poor accuracy on other sensors (Logistic Regression) or unfeasible computational time (Support Vector Machine). All the above methods are pixel-wise, that is they treat pixels separately without taking account of spatial correlations among them or local features that are instead typical of images.