Statistical Shape Analysis, 2nd Edition

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 (2^g − 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 ...