Shape and size characterization of crystals using image analysis and neural networks

The characteristic properties of potash (KC1) crystals depend not only upon their chemical composition but on their morphological attributes as well. Hence, to determine the quality or grade of the crystalline product, it is necessary to be able to precisely quantify the size as well as the shape parameters of a sample population of the crystal product. Moreover, as process parameters during crystallization influence the size and shape of the crystal product obtained, accurately quantifying the size and shape parameters can serve to provide feedback information for on-line control of the crystallization process itself in order to obtain a better grade of crystalline product. This thesis presents a pattern recognition scheme that uses image analysis to acquire size features and Fourier descriptors to effectively describe the shape of a particle and neural networks for shape classification. Image analysis is presented as a viable, accurate, and time-efficient method that can be used to simultaneously and objectively characterize size and shape of crystal particles. The Zahn and Roskies Fourier descriptors, evaluated from the Fourier series expansion of angular bend as a function of arclength, are used to effectively describe the shape of a particle contour, and are considered to be ideal shape parameters. A pattern recognition system that comprises of a machine vision system and a neural network classifier is introduced. The shape features, which are the Fourier harmonic amplitudes, are the input vectors to competitive and backpropagation neural networks, which act as shape classifiers. The ideal number of Fourier harmonic amplitudes required for crystal shape discrimination is also studied. 15 to 20 harmonics are found to be ideal. Unsupervised competitive neural networks were used to cluster input vectors into classes without providing any feedback or supervision. In spite of successful clustering, competitive networks were not an ideal choice due to the constantly shifting clustering with increased training of the network. However, this unsupervised clustering made it possible to generate input and target vectors for training a multi-layered neural network using the backpropagation learning algorithm. Crystal shapes were classified into five classes corresponding to "excellent", "good", "fair", "poor", and "bad" crystal shapes by the backpropagation network. It was observed that all particles used for training the backpropagation network were correctly classified. 42% of particles not used to train the network were correctly classified and 48% were classified into classes adjacent to the desired class, which is acceptable considering the subjectivity involved in selecting input and target vector pairs. The remaining 10% were classified into classes farther than the adjacent class. Thus, an effective accuracy of 90% was achieved in grade classification of crystal shapes. The entire system was developed to behave like a "black box", with a single application package being developed to capture crystal images and analyze size information as well as the ZR Fourier descriptors, which are fed into the feedforward neural network that classifies the crystal shapes. The system is an objective alternative to the subjective decision making process of human inspectors in determining the grade of the crystalline product