Methods in quantitative image analysis

Abstract

The main steps of image analysis are image capturing, image storage (compression), correcting imaging defects (e.g. non-uniform illumination, electronic noise, glare effect), image enhancement, segmentation of objects in the image and image measurements. Digitisation is made by a camera. The most modern types include a frame-grabber, converting the analog-to-digital signal into digital (numerical) information. The numerical information consists of the grey values describing the brightness of every point within the image, named a pixel. The information is stored in bits. Eight bits are summarised in one byte. Therefore, grey values can have a value between 0 and 256 (2⁸). The human eye seems to be quite content with a display of 5-bit images (corresponding to 64 different grey values). In a digitised image, the pixel grey values can vary within regions that are uniform in the original scene: the image is noisy. The noise is mainly manifested in the background of the image. For an optimal discrimination between different objects or features in an image, uniformity of illumination in the whole image is required. These defects can be minimised by shading correction [subtraction of a background (white) image from the original image, pixel per pixel, or division of the original image by the background image]. The brightness of an image represented by its grey values can be analysed for every single pixel or for a group of pixels. The most frequently used pixelbased image descriptors are optical density, integrated optical density, the histogram of the grey values, mean grey value and entropy. The distribution of the grey values existing within an image is one of the most important characteristics of the image. However, the histogram gives no information about the texture of the image. The simplest way to improve the contrast of an image is to expand the brightness scale by spreading the histogram out to the full available range. Rules for transforming the grey value histogram of an existing image (input image) into a new grey value histogram (output image) are most quickly handled by a look-up table (LUT). The histogram of an image can be influenced by gain, offset and gamma of the camera. Gain defines the voltage range, offset defines the reference voltage and gamma the slope of the regression line between the light intensity and the voltage of the camera. A very important descriptor of neighbourhood relations in an image is the co-occurrence matrix. The distance between the pixels (original pixel and its neighbouring pixel) can influence the various parameters calculated from the co-occurrence matrix. The main goals of image enhancement are climination of surface roughness in an image (smoothing), correction of defects (e.g. noise), extraction of edges, identification of points, strengthening texture elements and improving contrast. In enhancement, two types of operations can be distinguished: pixel-based (point operations) and neighbourhood-based (matrix operations). The most important pixel-based operations are linear stretching of grey values, application of pre-stored LUTs and histogram equalisation. The neighbourhood-based operations work with so-called filters. These are organising elements with an original or initial point in their centre. Filters can be used to accentuate or to suppress specific structures within the image. Filters can work either in the spatial or in the frequency domain. The method used for analysing alterations of grey value intensities in the frequency domain is the Hartley transform. Filter operations in the spatial domain can be based on averaging or ranking the grey values occurring in the organising element. The most important filters, which are usually applied, are the Gaussian filter and the Laplace filter (both averaging filters), and the median filter, the top hat filter and the range operator (all ranking filters). The principal advantage of ranking filters over averaging operators is that they do not reduce the brightness difference across steps. The edges remain in place and well-defined. Very important prerequisites for extracting quantitative information from digitised images are clearly identifiable segmented objects and knowledge about instrumental and technical influences on the results (glare effect and thickness of histological slides). Segmentation of objects is traditionally based on threshold grey values. The grey value histogram of the original or enhanced image is an important tool for setting threshold levels. For determining the threshold grey value, bidimensional histograms can be applied. Quantitative information can be extracted from images by mathematical operations on binary images or on grey scale images. Boolean operations on binary images are applied when one desires to combine the information contained in several binary images. The morphological operations on binary images mainly include erosion and dilation, and modifications of these operations. There are many methods allowing direct quantitation of segmented objects within grey scale images. They use different sets of parameters: planimetric, histogram-derived, densitometric, co-occurrence matrix-derived parameters, invariant moments, run lengths, parameters of quantitative immunohistochemistry and immunocytochemistry, parameters of silver-stained nucleolar organiser regions (AgNORs) and parameters of cellular sociology. Digital image analysis requires a distinction between two phases for the evaluation procedure: generation of fundamental data (x- andy-coordinates and grey values of the pixels, immediately after object segmentation) and calculation of parameters from these data. The data generated during segementation must remain always available and these data must be conceptually separated from the parameters deduced from them. With such a data organisation it is no longer necessary to repeat the object segmentation if new algorithms should be applied on objects which earlier were segmented. In dealing with methods or instruments for digital image analysis, it is always essential to know precisely the characteristics of both of them.