# Diesel Spray Macroscopic Parameter Estimation Using a Synthetic Shapes Database
## 1 Introduction  
The injection system aims at delivering fuel with the proper timing and quantity required by the combustion process and represents a fundamental element of the engine in contributing to emissions and performances [1]. Therefore, particular care must be taken with the injection process, mainly for compression ignition engines, whose essence lies in the introduction of finely atomized fuel into the compressed air inside the cylinder. For diesel engines, indeed, fuel spray plays a major role since its characteristics are strictly related to the combustion process [2]. Sprays can be characterized in terms of microscopic parameters, such as droplets size and velocity, or from a macroscopic perspective. In this latter case, the geometrical description of the overall jet is provided, namely, in terms of tip penetration length (\(S\)) and cone angle (\(\theta\)) as sketched in Figure 1.  
Figure 1: Generic definition of macroscopic spray parameters. While penetration is univocally defined and easily measured as the travelled distance by the tip of the spray into still air [3], the measurement of the cone angle is quite challenging and, among the scientific community, there is no agreement in defining such quantity. It can be measured as the angle formed by two straight lines emerging from the discharge hole and tangent to the spray contour, as a function of the penetration, or as a function of the nozzle diameter. Alternatively, it can be measured by fitting two straight lines to the spray contour or even as the apex angle of an isosceles triangle having the corresponding spray area at a given percentage of the penetration length. A comprehensive description and comparison of different spray angle definitions can be found in [4] where a variation up to 95% has been observed in the cone angle evaluated by different methods. This disagreement arises from the fact that the spray cone features irregular and faded boundaries, thus making it intrinsically difficult to discern what is to be considered as spray from the surrounding. Among different experimental approaches ranging from mechanical to electrical solutions [3], macroscopic spray characterization is mainly performed by means of optical techniques [5], being these methods non-intrusive and hence allowing for the study of the jet without affecting its own evolution. Amongst the optical approaches, direct visualization technique, such as high-speed photography, is widely used. The output of such technique is a time series of digital images, commonly in grey tones, of the evolving spray, which must be post-processed to extract the spray characteristic. The first step into the analysis is to isolate the spray from the background. The operation of separating a subject from the surrounding image is referred to as segmentation and represents one of the most challenging tasks in image processing [6]. Two main approaches can be followed in pursuing image segmentation: subdivide the image in regions according to a sudden change in the intensity of pixels (e.g., looking for edges); categorize the pixels showing similar properties into classes [6]. Thresholding belongs to the second group and plays a central role in image segmentation. In the image thresholding, every pixel is assigned either to the subject or to the background, by comparing its intensity to a given threshold \(T\). The resulting output is a binary image in which every pixel shows a 0 or 1 value depending on the assigned ensemble. Over the decades, a lot of solutions have been proposed to select the proper threshold and some of them have been applied to diesel spray images. The threshold is manually selected as a constant value for all of the image set on the basis of the visual quality of the result in [7; 8; 9]. This solution cannot be considered as a good choice as the illumination and, therefore, the pixel intensity varies between different images. In addition, results are sensitive to the experimenter interaction.