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

• Faceted crystal shapes are extracted from stereoscopic images.
• This is accomplished by solving a nonlinear nonconvex optimization problem.
• The approach is assessed thoroughly using simulated and experimental images.
• Advantages and disadvantages in comparison to simpler approaches are highlighted.

The 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 (Schorsch et al., 2014)) 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).