Experimental accessibility of crystal shape is still limited today. We present a new method for extracting three-dimensional (3D) crystal shape from measurement data. The algorithm is demonstrated on data obtained by microcomputed tomography (μCT) for potash alum, although the approach is applicable to any 3D imaging technique and any faceted crystal. First, the crystal face normals are identified using a 3D Hough transform. In a second step, the relationship between the identified and all potentially arising crystal face normals is matched to obtain the relative orientation between the measurement data and the crystal model. The final shape parameters guarantee maintainance of the symmetry of the geometric crystal model and, hence, are compatible with common approaches to model the growth of multifaceted crystals. The procedure can be automated, which opens the possibility of evaluating full particle size-and-shape distributions, within the discussed limitations concerning crystal quality and sample size.

Filamentous fungi are widely used in the production of biotechnological compounds.Since their morphology is strongly linked to productivity, it is a key parameter in industrial biotechnology. However, identifying the morphological properties of filamentous fungi is challenging. Owing to a lack of appropriate methods, the detailed three-dimensional morphology of filamentous pellets remains unexplored. In the present study, we used state-of-the-art X-ray microtomography (µCT) to develop a new method for detailed characterization of fungal pellets. µCT measurements were performed using freeze-dried pellets obtained from submerged cultivations. Threedimensional images were generated and analyzed to locate and quantify hyphal material, tips, and branches. As a result, morphological properties including hyphal length, tip number, branch number, hyphal growth unit, porosity, and hyphal average diameter were ascertained. To validate the potential of the new method, two fungal pellets were studied-one from Aspergillus niger and the other from Penicillium chrysogenum. We show here that µCT analysis is a promising tool to study the threedimensional structure of pellet-forming filamentous microorganisms in utmost detail.The knowledge gained can be used to understand and thus optimize pellet structures by means of appropriate process or genetic control in biotechnological applications. K E Y W O R D Sfilamentous fungi, image analysis, pellets, three-dimensional morphological quantification, X-ray microtomography

The degree of agglomeration and the aggregate shape influence the quality of crystalline products and the ease of downstream processing. Studying the shape of primary particles in an aggregate can lead to a better understanding of the underlying aggregation mechanism. We present an automatic image processing procedure for identifying the shape, size, and position of each primary particle in microcomputed tomography (μCT) images of potash alum aggregates. Splitting an aggregate into primary particles is based on recombining watershed-transform regions, where concavity points are considered as indicators of correct segmentation. The shape identification algorithm uses the Hough transform to identify visible face normals and matches them to the set of face normals defined by a crystal model. In principle, the algorithm is applicable to other crystalline compounds provided that sufficient symmetry is present to determine the shape of a primary particle from its visible part.

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In order to fully characterize crystal aggregates, the orientation of primary particles has to be analyzed. A procedure for extracting this information from three-dimensional microcomputed tomography (µCT) images was recently published by our group. We here extend this method for asymmetrical crystals and apply it for studying the disorientation angle distribution of four potash alum crystal samples that were obtained under various experimental conditions. The results show that for all considered supersaturation profiles, primary particle pairs tend to have the same orientation significantly more often than in theoretical considerations, in which the orientations of primary particles are assumed to be distributed randomly.