350.

[Cover] [Contents] [Index]

Page viii

they can be identified in terms of phenomena of interest. In a sense, this procedure is akin to exploring the data (and visualisation methods can help considerably in the process), whereas the supervised approach is inductive.

This book is about pattern recognition for remotely sensed data. We prefer the term ‘pattern recognition’ to ‘classification’, because the latter term can be misleading, as noted above. However, the two terms are used in this book, partly for reasons of tradition. A pattern is a set of measurements made on an object. It can be described as a mathematical vector of measurements. For example, a person’s height and weight can be represented by the vector [192, 50] (in cm and kg, respectively). If a supervised approach is used, then the pattern is compared in some way to members of the sets of patterns that define the categories of interest, and the given pattern is assigned to one of these categories (one of which may be ‘unknown’). This approach can be described as inductive. Alternatively, a clustering strategy may be used, based on the similarity between patterns, in order to determine whether any distinct groups of patterns exist in the data.

In Earth observation by remote sensing, the objects to be labelled are normally the individual pixels forming a multispectral or hyperspectral image. Each pixel is represented by a pattern vector consisting of a set of measurements, one per image band plus, possibly, other measurements such as texture. If each spectral band is represented by one axis of a multidimensional space (the feature space), then the pixel can be represented as a point in that space. For simplicity, let the number of features be two, and let the x-axis represent the first feature and the y-axis represent the second. A pixel with a feature vector of [1, 5] can therefore be shown on a graph as a point with cartesian coordinates [1, 5]. Now imagine that all the pixels in the two-band image have been plotted on the graph, and that they fall into clearly defined groups. We can separate these groups by lines or curves. These lines or curves are called ‘decision boundaries’, for they show the positions of the boundaries of individual categories. If a point lies on one side of the boundary, it is given a label such as ‘A’, whereas if it lies at the other side of the boundary it is given the label ‘B’. In higher-dimensional problems, the lines and curves become hyperplanes and hypersurfaces. So the labelling problem can be thought of as one that involves the positioning of hyperplanes or hypersurfaces, representing decision boundaries, in a multi-dimensional feature space. The algorithm that determines the position of the pixel with respect to the decision boundaries, and thus allocates a specific label to that pixel, is called a decision rule. The word classifier is widely used as a synonym for the term decision rule.

The use of pattern recognition methods in remote sensing has a long history. Air photo-interpreters were perhaps the first to use intuitive methods to determine the information contained in reconnaissance photographs, and these methods continue to be of great importance, particularly in the gathering of military intelligence, as the human eye/brain combi

[Cover] [Contents] [Index]