An optimization-based approach to extract faceted crystal shapes from stereoscopic images

Abstract

a b s t r a c tThe size and shape of particles crucially influences the characteristics of solid products. Until recently these quantities were evaluated using light microscopy. However, extracting the three-dimensional shape of a faceted crystal from a single image is a formidable computer vision challenge. In this work we combine stereoscopic imaging devices (e.g., commercial stereoscopic microscopes or the stereoscopic flow through cell that continuously draws samples from a crystallizer ) with a model-based approach in which parametric polytopes are used to describe faceted crystals (Hours et al., 2014). In the shape reconstruction algorithm these parametric polytopes are scaled and rotated until their projections closely match the measured stereoscopic images, which is formulated as a nonlinear optimization problem. The proposed approach is assessed using simulated images and experimental data. We also assess in which cases the proposed approach does or does not provide advantages over concepts using generic particle shapes (Schorsch et al., 2012).

Disorientation angle distribution of primary particles in potash alum aggregates

“…Classification techniques such as discriminant factorial analysis or support vector machine can be combined with twodimensional (2D) image-based shape factor analysis to measure the degree of agglomeration [11,12,13], or to track the aggregate volume [14]. Threedimensional (3D) and stereo imaging techniques enable a full description of the particle shape [15,16,17,18,19]. They can be used to obtain the size, shape, and orientation of each primary particle in an aggregate [20].…”

Simulations of crystal aggregation and growth: Towards correct crystal area

“…Crystals may change the set of visible faces through growth and dissolution, as well as undergo breakage or form aggregates of several crystals. While two‐dimensional (2D), as well as three‐dimensional (3D) imaging methods have recently been established for characterizing complex particle shapes, simplifications are typically undertaken in order to model these processes. In this contribution, we focus on growth and aggregation while neglecting breakage.…”

Real-Time Characterization of Crystal Shape and Size Distribution Based on Moving Window and 3D Imaging in a Stirred Tank

“…However, in their later work, they turned to two cameras rather than a single camera plus mirrors [12]. More recently, they developed an optimization method to obtain crystal shape from stereoscopic images in a hot-stage reactor [13]. It needs to point out that in their work the crystals were also static.…”