# Diesel Spray Macroscopic Parameter Estimation Using a Synthetic Shapes Database
## 2 Algorithm  
Regardless of the considered segmentation technique, the desired output is not the description of the actual spray boundary but rather an overall description of the spray shape, given by penetration and cone angle. The latter can be outlined as a conical region, surmounted by a semi-elliptical or by a circular head [18; 19]. Therefore, the goal of the macroscopic spray characterization is to obtain such simplified description. The technique proposed in the present paper aims at obtaining the abovementioned shape. A similar approach is followed in [9; 20] where the cone angle definition is associated to those of a symmetrical triangular shape, whose area is proportional to the binarized spray image one. Therefore, this method does not imply that the shape of the resulting model is close to the actual one or that the obtained value is independent on the used segmentation algorithm. The proposed method is rooted on the technique described in [21] where a basic face recognition algorithm is used to select the threshold level \(T\) in order to perform image segmentation and obtain the spray boundary. In this method, a database of binary images is created case by case, by thresholding the original image with different intensity levels. The images are hence represented as vectors, and then, the closest match between the original image and the best black and white version is obtained. The macroscopic spray parameters are than evaluated by processing the resulting boundary in accordance to one of the possible definitions of such parameters. In the present paper, the database is no longer created image by image but is made up of artificial binary spray images just once. The method looks for the closest match between the original image and its simplified binary version and, given that the parameters of such images are a priory known, no further analysis is required to evaluate the spray parameters. The database must be representative of all of the possible spray shapes. Considering the whole injection event, it is clear that a database containing all of the significant angles, penetrations and shapes of the leading edge becomes so wide to be unmanageable. In order to reduce the database dimensions, while maintaining its representativeness, the penetration length of the artificial sprays can vary within a range centered around half of the image height. Then, a scaling step of the original spray is introduced in order to make the real image and the artificial ones comparable. Figure 2: Transverse (**a**–**c**) and longitudinal (**d**) intensity profile of a typical diesel spray image. The goal is to characterize the volume of the spray through one of its projections (e.g., an image). Therefore, only symmetrical spray shapes have been considered. The asymmetries encountered in a single image, which are often due to the illumination pattern rather than to the spray itself, cannot be extended to the entire spray. Figure 3 shows a sketch of the artificial images, which constitute the database. Sprays are obtained by varying the penetration \(S\), the angle \(\theta\) and the ellipse semi-axes \(\xi\). It is worth mentioning that the size of the artificial images must be the same as that of the real spray images. This is not a limiting factor: The tested image is simply to be resized to be compared to an existing database afore starting the processing. Still, images must have the same aspect ratio (e.g., the same ratio between pixel height \(h\) and width \(w\)). An image of size \(N\ =\ (h\ \times\ w)\) can be represented as a column vector of dimensions \((h\cdot w)\ \times\ 1\). By following this representation, any image can be considered as a point in the N-dimensional images space. This high dimensionality space is representative of images depicting whatever subject. Images showing similar features, like sprays, are located into a sub-space, i.e., into a smaller region of this space. The idea behind the method is to compute the coordinate system that efficiently describes such cluster.