Disclaimer: these examples are mostly taken from my pre-Eikomagos career
The ice in frozen foodstuffs, including ice cream, might be thought to be stable, but in fact it is continuously changing and therefore changing product structure over time. Although at a fixed temperature the total amount of ice is constant, ice melts from crystals with a highly curved surface (smaller) and regrows onto lesser curved (bigger) crystals. As a result the product becomes coarser. A second process is accretion: crystal joining together. One way of studying these processes is to look at a model system under the microscope. A description of how these experiments are run can be found here.
The first step in the analysis is identifying the ice crystals. The image can be partioned using a watershed; this finds all the “basins” in if you interpret the image as a height map (fig 1). The shape of the basins (mostly convex for a crystal) is used to distinguish crystal and solution.
Once the individual crystals have been identified, the simplest and most common measurement is size. These measurements can be used to estimate the model parameters of the underpinning LSW theory of Ostwald ripening.
More “exciting” perhaps, is a study into a model of neck growth between accreting crystals which requires more advanced measurements. These measurements are: neck width and dihedral angle. Detection of a neck and measuring its width is straightforward. The dihedral angle is trickier.
If an image has low noise, the isophote curvature (an isophote is a height line in the surface representation, figure 1) can be accurately computed using:
There is ample theory on how to properly estimate the derivatives involved and the equation can be applied straightforwardly.
The curvature measurements are used to identify the osculating (tangent) circle on either side of a cusp. The intersection between these circles can be computed as can the angle at the intersection thus yielding the dihedral angle.