**4.1 Digital
Imagery**

Different from Cartesian coordinate system, the origin and the axis in an image coordinate system takes the following form for printing and processing purposes:

Figure 4.1. An image coordinate system

Each picture element in an image, called a pixel, has coordinates of (x, y) in the discrete space representing a continuous sampling of the earth surface. Image pixel values represent the sampling of the surface radiance. Pixel value is also called image intensity, image brightness or grey level. In a multispectral image, a pixel has more than one grey level. Each grey level corresponds to a spectral band. These grey levels can be treated as grey-level vectors.

From the continuous physical space to the discrete image space, a quantization process is needed. The details of quantization is determined by how we do sampling and what kind of resolution we use. General concepts on sampling and resolution have been introduced in Chapter 1.

Two concepts are of particular importance;

image spaceandfeature space. Image space refers to the spatial coordinates of an image(s) which are denoted asIwithm x nelements, wheremandnare respectively the number of rows and the number of columns in the image(s). The elements in image space,I(i,j) (i = 1, 2,..., m; j = 1, 2,..., n)are imagepixels.They represent spatial sampling units from which electromagnetic energy or other phenomena are recorded. All possible image pixel values constitute the feature spaceV. One band of image constitutes a one-dimensional feature space.kbands in an image denoted asIkconstruct ak-dimensional feature spaceVk. Each element inVkis a unit hypercube whose coordinate is ak-dimensional vectorv = (v1, v2, ..., vk)T. Whenk = 1, 2, and 3the hypercube becomes a unit line, a unit area, and a real unit cube. Each pixel in image space has one and only one vector in feature space. Different pixels may have the same vector in feature space.Multispectral images construct a special feature space, a multispectral space

Sk. InS, each unit becomes agrey-level vectorg = (g1, g2, ..., gk)T. In multispectral images, each pixel has a grey-level vector. There are other types of images which add additional dimensions to the feature space. In the feature space, various operations can be performed. One of these operations is to classify feature space into groups with similar grey-level vectors, and give each group a same label that has a specific meaning. The classification decision made for each image pixel is in feature space and the classification result is represented in image space. Such an image is a thematic image which could also be used as an additional dimension in feature space for further analysis.