Many thousands of women die needlessly each year from breast cancer, a cancer from which there is theoretically a high probability of survival if detected sufficiently early.  If the presence of cancerous tissue is missed in a sample, then, by the time the next test is undertaken, the cancer may have progressed and the chance of survival significantly reduced.  The importance of detecting cancerous tissue in the samples can therefore not be over-emphasised. 
A typical national breast screening programme uses mammography for the early detection of impalpable lesions.  Once a lesion indicative of breast cancer is detected, then tissue samples are taken and examined by a trained histopathologist to establish a diagnosis and prognosis.  More particularly, one of the principal prognostic factors for breast cancer is the extent of mitotic activity, that is to say the degree of epithelial cell division that is taking place.  A histopathological slide is effectively a “snapshot” representing a very short time interval in a cell division process, so the chance of a particular slide showing a particular phase of mitotic activity is very small; if such a phase is in fact present in a slide, that is a good indicator of how fast a potential tumour is growing. 
In the existing manual procedure for scoring mitotic activity a histopathologist places a slide under a microscope and examines a region of it (referred to as a tile) at a magnification of ×40 for indications of mitoses.  Typically ten different tiles from the tissue sample are examined and a total count is made of the number of cell divisions which, in the histopathologist's opinion, are seen to be taking place in the ten tiles.  This is then converted to an indication of cancer grade typically in accordance with the following table:
Number of Mitotic Cellsper Ten TilesCancer Grade0 to NGrade 1(N + 1) to MGrade 2>MGrade 3where Grade 1 is the least serious and Grade 3 is the most serious.  Values of N and M are typically 5 and 10 but will vary in different schemes depending on the size of the tiles being observed. 
This is, however, a time consuming, labour intensive and expensive process.  Qualification to perform such examination is not easy to obtain and requires frequent review.  The examination itself requires the interpretation of colour images by eye, a highly subjective process characterised by considerable variations in both inter, and intra-observer analysis, i.e. variances in observation may occur for the same sample by different histopathologists, and by the same histopathologist at different times.  For example, studies have shown that two different histopathologists examining the same ten samples may give different opinions on three of them, an error of 30%.  This problem is exacerbated by the complexity of some samples, especially in marginal cases where there may not be a definitive conclusion.  If sufficient trained staff are not available this impacts upon pressures to complete the analysis, potentially leading to erroneous assessments and delays in diagnosis. 
These problems mean that there are practical limitations on the extent and effectiveness of screening for breast cancer with the consequence that some women are not being correctly identified as having the disease and, on some occasions, this failure may result in premature death.  Conversely, others are being incorrectly diagnosed with breast cancer and are therefore undergoing potentially traumatic treatment unnecessarily. 
It is thus an aim of the invention to provide an automated method of image analysis which can be embodied in a robust, objective and cost-effective tool to assist in the diagnosis and prognosis of breast cancer, although as previously indicated the invention may also find application in other fields. 
In one aspect the invention accordingly resides in a method for the automated analysis of a digital image comprising an array of pixels, including the steps of: identifying the locations of objects within the image which have specified intensity and size characteristics; defining regions of specified extent within the image which contain respective said objects; deriving from the data within respective said regions one or more respective closed contours comprising points of equal intensities; and estimating the curvature of at least one respective said contour within respective said regions at least to produce a measure of any concavity thereof. 
As will be understood from the ensuing detailed description of a preferred embodiment, such a method is of use in identifying mitotic cell nuclei in digital images of histopathological slides. 
The invention also resides in apparatus for the automated analysis of a digital image comprising means to perform the foregoing method and in a computer program product comprising a computer readable medium having thereon computer program code means adapted to cause a computer to execute the foregoing method and in a computer program comprising instructions so to do. 
These and other aspects of the invention will now be more particularly described, by way of example, with reference to the accompanying drawings and in the context of an automated system for grading cancer on the basis of the numbers of mitotic epithelial cell nuclei in digital images of histopathological slides of potential carcinomas of the breast.