17 Shape in images

17.1 Introduction

There has been an explosion in the collection of image data in the last decade, especially with the availability of cheap high-quality cameras and smart-phones. An important area of study is the interpretation of images, and shape is a very important component. A wide ranging summary of measuring shape in images was given by Neale and Russ (2012).

A digital image is an r × c grid of pixels (picture elements) each of which is assigned an integer representing the brightness (or intensity) at that pixel. The pixel is coloured a particular shade of grey depending on the brightness at that position, and hence the integer representing brightness is called the grey level.

A common scale used is for the grey levels to range from 0 (black) through to 255 (white). So, for example, a grey level of 50 would be dark grey, 128 mid grey and 200 light grey. Such images are called grey-level or grey-scale images. The range of grey levels is usually on the scale 0 to (2g − 1), where g = 1 for binary images (black/white), g = 8 for 256 grey-scale (8 bit) images and g = 12 for 4096 grey-scale (12 bit) images. Colour images can be represented as three grey-level images – each image for the red, green and blue colour bands. For a 256 × 256 image a scene is represented by 216 = 65 536 integers, and hence the data are very high dimensional. Image analysis is involved with all aspects of analysing such image data. For an introduction to statistical image analysis ...

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