# Particle and Particle Agglomerate Size Monitoring by Scanning Probe Microscope
## 3 Size-Monitoring Method with the Use of the SPM
There are more advanced methods for segmentation such as the parametric (with the estimation of the parameters of the grey-level distribution of each class of objects in an image [28; 29]), variational [30], neuronet [31] and correlation methods [32]. All the above methods are limited in application and they are not always available in open-ended libraries such as OpenCV. In addition, the parametric and variational methods are distinguished by their considerable computational complexity and complexity of implementation; regarding the neuronet methods, sometimes it is difficult to provide a sufficient amount of the training material. The investigations of the segmentation methods with the use of open freeware (ImageAnalysis, ImageJ, WSxM) show the following: The images segmentation using conventional methods based on the intensity function is rather difficult for complex images with particle agglomerate. The difficulty of segmentation leads to the impossibility of accurately determining the size and coordinates of particles and the implementation of the proposed monitoring method. In  
Figure 1: Options of the SPM operation in the process of the size monitoring: (**a**) uniform scanning; (**b**) tracking scanning. the present study, we consider the approach of image segmentation based on the surface curvature function. For solving the second task, motorized sample platforms are used; as a rule, microscopes for studying large-size samples are equipped with such platforms. In this case, the larger the platform travel range is, the larger the minimal step of positioning is (Table 1). Judging by the value of the minimal step, the sample-positioning platforms in a commercial SPM are designed for use with an optical microscope (resolution of about 1 \(\upmu\)m). The use of such systems with a scanner having a travel range of less than 1 \(\upmu\)m is difficult. The presence of an error in the positioning of the motorized platform causes an uncertainty in the value of the scan overlapping, which makes difficult the solution of the third task, the determination of the probe and particles coordinates in a single global coordinate system. To solve the task, in an SPM the sensor values or the tools for the overlapping-image processing can be used. When sensors are used, each image and each particle have their unique coordinates, which allows for excluding repeating results in the overlap region. In this case, the main problems are as follows:  
* Sensors are not always present in the SPM positioning system, and sometimes their integration in this system is constructively impossible and impractical;
* The sensor accuracy may be insufficient for the unambiguous establishment of the correspondence of the centres of the particles. Software (algorithm) for stitching or coordinate coupling of overlapping images can be an alternative to sensors. When algorithmic methods are used, the accuracy of the coordinate determination depends on the resolution of the scanner and image and not on the precision of the platform or sensor. When the images are stitched, a single image is formed, and each particle is unique within the image. At the coordinate coupling, the mutual shift (displacement) and rotation of the images are determined. Using these values, the local coordinates of particles in each image can be combined into a common coordinate system. The cases are known of the combined use of the sensor values and the images for high-precision probe positioning. For example, in the SPM NEXT II [23], the sample positioning by the motorized platform is additionally controlled by a high-resolution video camera. Detectors and descriptors of key points are widely used for matching and stitching of images. Binary descriptors (BRIEF, ORB and BRISK) refer to low-level ones and they are sensitive to distortions associated with the change in scale, shape, and point of view [35] which are quite probable in an SPM. The SPMimages can contain distortions even after processing, which influence the result of the measurement of object sizes.