Simulation of microbiological objects fluorescent images
While modelling the process of image obtaining is divided into successive stages corresponding to a real experimental procedure using a fluorescence microscope. At the first stage an ideal image is generated which consists of specially labelled cells. The simulation result at this stage is an ideal object. Then the obtained image is distorted due to measurement system errors: uneven illumination of the object, background autofluorescence, optical errors, noise from the photomultiplier, etc. Thus, the output is an image which has properties similar to real fluorescent images [3].
Each type of cell is defined independently by an appropriate form of cells and their organelles, as well as by sets of markers that define the texture and colour of these forms. There can be set dependences between subpopulations which affect the position of cells, their shape and markers [4]. Then the effects of errors of the measurement system and the generated ideal image may overlay.
The first step towards obtaining synthetic images of cell populations is to define these populations and the objects they include. These objects are cells that may contain nuclei, cytoplasm, lipids and other components. To generate shapes of cells and their organelles a parametric model is used. The shape is defined as a polygon with a given number of vertices and then the position of certain vertices is modified. The final shape is obtained by smoothing the contour using cubic spline interpolation.
However, the peculiarity of this model is that the shape of each object is generated independently, thus it is necessary to specify the correspondence between objects belonging to the same cell. It is possible due to the definition of dependences while setting generation parameters [3]. For example, in order to make sure that the nucleus gets inside the corresponding cytoplasm, one should specify the dependence between this nucleus and the cytoplasm that has already been defined. Otherwise, one can create the shape of a nucleus independently, but one will have to determine the dependence on this nucleus when setting the parameters of the cytoplasm. Thus, there are two types of generated shapes: independent from other objects and associated ones, the position of which is determined by independent objects. For each of subpopulations only one type of objects is independent while the others should be determined.
One more important factor is how the generated form will look like. At least one marker able to describe the appearance of the object is required to solve this problem. The feature of this simulation model is that objects can be determined not only by some value of intensity of given colour and texture, but by a number of markers as well. This makes it possible to create visually complex objects and to generate images very similar to the real ones [3].
Markers definition occurs sequentially, thus it is important to take into consideration their order. Therefore, all these operations can be divided into two groups. The first group includes operations establishing the basic level of the object marker intensity. These markers should be set primarily [3]. This group includes: a) the marker of a constant intensity level that sets the same intensity for all pixels of the object based on the Gaussian distribution; b) the marker the intensity of which is constant, but depends on the density of objects in the surrounding area; c) the marker which sets a linear dependence of a constant intensity level on the intensity of another marker in the specified area; d) the marker which sets the intensity according to the position of the object on the image in which random texture for the whole image is determined first and then the average value for the object is calculated.
The second group of markers consists of those operations that do not determine the level of intensity themselves, but only redistribute their value. That is why these markers should be applied only after definition of baseline intensity using markers of the first group. The examples of markers changing the intensity level are angular and linear gradients in any direction; markers that define the intensity depending on the proximity of borders and other cell organelles; markers which specify texture with the help of Perlin [2, 5] and turbulent noise [6]. One more marker in the second group is the marker which can scale the intensity level in a given range, which may be very useful for enhancing image contrast.
After defining the objects properties separately it is important to consider the parameters that characterize the whole population. These parameters include the number and arrangement of cells.
Due to various biological causes cells can be combined into clusters. The determined number Nc of clusters is evenly randomly distributed in the image with the coordinates (xc,yc). Cells assigned to a cluster are arranged around the center of the cluster according to exponential distribution. Thus, cells will be combined into a cluster with probability pc and distributed uniformly randomly with probability (1-pc) [2, 3].
The level of different objects overlapping in this simulation model is defined as a set of rules that specify possible values of objects overlapping. The introduction of a number of rules allows not only acquiring images similar to real experimental ones, but is strongly needed when working with such a variety of subpopulations and their objects. Another characteristic related to overlapping is visibility of objects markers that are compared with the cell. This model provides defining weight coefficients that determine fractions of the object and the cell.
The final stage of the modelling process is to distort the generated ideal image by effects which are observed in a real measurement system. Within this simulation model such effects as image illumination distortion, optical aberrations, noise from the photomultiplier and improper cells staining when labelling [7] may be observed.
Image illumination distortion is usually caused by the influence of a light source which leads to an increase in the image intensity. This results in contrast reduction and displacement of a light source can introduce additional problems in segmenting objects [6]. In this model image illumination distortion is defined as an increase of illumination intensity of each image point by a certain value. Uneven image illumination can also be modelled. In this case image illumination can be represented by a linear gradient in any direction or by a radial gradient with the center of a light source at a random point.
Not all objects are located at the focal plane of the microscope because of three-dimensional structure of examined samples. This results in blurring some objects. To add a blurring effect two-dimensional Gaussian blurring is used in this simulation model which allows transferring data contained in pixels using Gaussian distribution to the outer zone [5]. This effect is observed as a result of the Gaussian filter with oversampling – a process of changing sampling frequency of a discrete (usually digital) signal [5].
To generate fluorescent images cells are labelled with special dyes called fluorophores. However, this treatment may make adjustments to the final image which is obtained with a microscope. For example, some cells may not be well processed by the substance, while others can absorb an unexpectedly large amount of a dye [7].
Thus, this simulation model allows generating images of cell populations, including many different types of cells. Taking into consideration the dependencies between the synthesized objects allows better recreating the real picture. In fact, cells and their organelles have a tremendous impact on lives of each other, which is reflected in the experimental images obtained using a fluorescence microscope and is the direct object of study. The determined simulation parameters make it possible to obtain a large number of different images from the viewpoint of cells and cell populations morphology. A new approach when setting markers allows generating diverse cellular populations of a complex visual representation, which is a big advantage of this simulation model. However, a comparatively short list of opportunities for modelling experimental conditions a little bit restricts the field where this model can be implemented.
The simulation algorithm of modelling fluorescent images of microbiological objects is based on the theory described earlier. It corresponds to the classical approach in modelling fluorescent images of cellular systems, i.e. the process of obtaining an image is divided into successive stages that occur in the real experiment. Thus, the first step is to create an ideal image of the cell population. The result is then deliberately distorted according to the impact of the measurement system and the environment [1, 2]. As a result of these actions the final synthetic image is obtained.
To generate an ideal image it is necessary to determine all objects of a given population, to define how these objects will look and be placed on the image. After completing these steps for each of the simulated subpopulations it is possible to move on to the second stage - the introduction of distortion. These stages are shown in Figure 1 which is worth considering in more detail.
