Classification of Crystal Shape Using Fourier Descriptors and Mathematical Morphology

Abstract

The performances of two image analysis methods for the classification of some randomly selected KCl crystals from a crystallization experiment into four two‐dimensional classes (nearly circular, square, rectangular and irregular) are compared. The first method uses the first 15 Fourier descriptors of the angular bend as a function of arc length of the periphery of the particles, whereas the second method is based on a combination of seven geometrical and morphological parameters of the crystals using a commercially available image analysis system (Visilog, Noesis, Orsay, France). The feedforward neural network with back‐propagation learning algorithm and discriminant factorial analysis (STATlab, SLP, Ivry sur Seine. France) were found to classify the crystals with similar success.

A Random Angular Bend Algorithm for Two- Dimensional Discrete Modeling of Granular Materials

“…The summation of all the angular bends from the initial starting point and the point generated in the previous step is φ ( φ =∑Δ φ i ). In case of the generation of spiral polygon (a spiral polygon is a simple polygon whose boundary chain contains exactly one concave subchain [38]), φ should equal to 2π [39]. Consequently, repeat steps 2, 3, and 4 until the value of φ is larger than or equal to 2π.…”

Control of Product Quality in Batch Crystallization of Pharmaceuticals and Fine Chemicals. Part 2: External Control

“…To classify the crystals into several shape classes, a supervised neural network was used. The technique was compared with the mathematical morphology algorithms and the principal component analysis for classification. , Recently, Mettler Toledo has introduced an image analyzer, PVM, for online monitoring of the crystal habit…”

Advances in On-line Monitoring and Control of the Morphological and Polymorphic Forms of Organic Crystals Grown from Solution

“…They concluded that Fourier descriptors based on spectral transforms provide robust performance, accuracy, compact features and low computation complexity, as well as being the most promising method to overcome noise. Fourier descriptors have been used by several researchers for the contour analysis of particles 35,36) . This technique is popular due to its invariance under two-dimensional transformations, i.e.…”

“…ART2 is a neural network that adopts a learning mechanism that is both unsupervised and recursive. Since it is unsupervised learning, unlike back propagation neural networks that require training using pairs of predefined shape clusters and descriptors 36) , ART2 automatically determines the number of clusters and the assignment of data patterns in a way that patterns in a cluster are more similar than those in a different cluster. The recursive learning feature is a mechanism that can continuously update the knowledge with new data available, without corrupting the existing knowledge already learned using previous data and without the need to make up the new data with previous data for re-training or re-learning, also very important for on-line use (in some literature it is called incremental learning).…”