The confocal images contain not only information about the gene expression inside nuclei, but besides the nuisance information about null expression in internuclear space. We apply the simple segmentation procedure allowing to exclude the internuclear areas from consideration. Primarily the image is filtered by the multi-valued nonlinear filter (MVF) [11] for the elimination of noise, and subjected to image equalization in order to amplify the details and contrast range. Then it is thresholded by the following rule: every pixel whose brightness is lower than a given threshold is replaced by 0 and every pixel larger than or equal to the threshold is replaced by 255. The output of the procedure is a binary image in which contiguous groups of 'on' pixels, separated from other groups by 'off' pixels, define the intranuclear regions. Now the numerical data is read off the binary image and presented as an ASCII table.

All the quantitative data at our disposal are relative values, as in confocal imaging maximal fluorescence and background levels were defined visually by a human expert. Due to the difference in their background level gene expression data obtained under different experimental conditions could not be directly compared and simultaneously processed. The problem is to bring the data to the unified standard form with a zero background and to get rid of distortions of gene expression patterns caused by the presence of a background signal. Our method for removal of background signal is based on the observation that the level of a given gene expression in a null mutant embryo for that gene is well fit by a very broad two dimensional paraboloid. The background paraboloid is automatically determined from the areas of wild type embryos in which a given gene is not expressed and the whole image is then normalized by this paraboloid to remove background from the entire embryo.

The development of the method can be subdivided into two major stages, of which the first is the extraction of characteristic features from the expression pattern of eve gene in embryos of different age, and the second is the standardization of this pattern against experimentally determined developmental time. The developmental time of an embryo is obtained by experimentally measuring the degree of membrane invagination and using the standard curve, which gives membrane invagination as a function of developmental time [12]. Precise developmental age was experimentally determined for 120 embryos belonging to cleavage cycle 14A from our dataset. These embryos were used as a training set for temporal analysis.

• Extraction of characteristic features To detect the age of an embryo on the basis of knowledge about its eve expression pattern it is necessary to present the pattern in terms of a small number of parameters which well characterize temporal changes in eve expression domains. It has been shown in our previous study [11] that the frequency domain representation of images may be used to detect the characteristic features, which mark the development of expression patterns over time. The Fourier spectrum is extracted from the images by means of the Fast Fourier Transform, and the phases of low frequency coefficients of Fourier spectra are considered as parameters for the age detection algorithm.

• Training set At the next stage we use the group of 120 embryos in which the precise developmental age was determined as training data for creating the regression function with characteristic features used as independent variables. However, the spectral phases cannot be directly involved into the regression analysis for two reasons: first, phases are periodic values and, second, number of independent parameters is too big as compared with the size of the training set. To get rid of periodicity for each parameter the standard range of values is defined so that the maximal in absolute value pair-wise difference between values, which the parameter takes over the training set, is set to minimum.
  The problem of high dimensionality of the feature space often arises in the regression prediction. As the spectral phases are strongly correlated and hence the feature set is redundant, it makes possible to reduce the dimension of the feature vector by the principal component analysis (PCA). Applying PCA we construct a new set of uncorrelated features, which are linear combinations of the initial variables, and in case of their high correlation just few first new features may hold almost all the information originally contained in the whole initial set.

• Construction of the regression function Each embryo of the training set is now characterized by a multidimensional vector containing as components the value of developmental age together with 'new' parameters of gene expression patterns. The regression function for the age prediction is created from the training data applying the Support Vector (SV) regression method [13].

• Age prediction To determine the age of a new embryo the confocal image of eve expression pattern in this embryo is subjected to the same preprocessing and feature extraction procedures as the members of the training set were. Periodicity of the spectral phases is overcome by bringing their values to the standard range defined over the training set. Then applying the PCA the number of features is reduced to the required in the SV regression number, and the embryo age is defined using the regression function constructed for the training set. For the predicted age 95% confidence interval is constructed. The cleavage cycle 14A is divided into 8 temporal classes [14] and according to the predicted value the embryo is assigned to one of these classes.