Optimisation of an Image Analytical System for Bulk Materials Using the Theory of Sampling

Optimisation of a real-time at-line monitoring system for control of industrial granule coating quality is presented. The system is based on a fluorescence imaging system, because fluorescence originates in the interiors of enzyme granules but is significantly quenched by a polymer coating (which is needed due to environmental precautions). We have developed an image analytical system for direct prediction of coating quality, which is based on application of the Angle Measure Technique (AMT) for image complexity characterisation; AMT is briefly described. The first part of the presentation addresses pixel sampling strategies within a digital industrial image, inherent in application of AMT, in which the unfolded image is regarded as a one-dimensional object in analogy with 1D process sampling in Theory of Sampling (TOS). The effects of random, stratified and systematic pixel selections in the unfolded image are evaluated. Also factors such as the fraction of image pixels and the effects of specific unfolding strategies (there are three principal strategies, termed æchopÆ, æsnakeÆ and æspiralÆ respectively) are investigated. It turns out that unsuspected artifacts are sometimes produced, related to the specifics of the unfolding procedure, which interferes with a straightforward 1D TOS process sampling analogy. These artifacts have a wider interest û among others, for 2D sampling û and therefore receive special attention in this presentation. The optimal pixel selection strategy for the AMT algorithm is found to be systematic or stratified sampling (not surprising according to TOS) of 500+ initiating points, but need to be unfolded in the novel spiral- or snake-wise fashions in order to effectively counteract these artifacts. This also has a general impact on various suggested standard schemes for 2D grid-sampling, among others, from the geoscience realms. The second part of the presentation is directed towards optimal image analytical sampling of a continuous series of fluorescent images (imaging of conveyor belts of æinfinite lengthÆ), ie optimisation of process image sampling. The minimum number of images needed to uphold a sufficiently good on-line estimate of the quality control (QC) parameter in question is found to correspond to the relatively high sampling rate of 15 - 20 per cent, which can be shown to be related to an intrinsic very high measurement error level (25 per cent) of a mandated analytical reference method.