Fig 1.
Experimental setup (a), adapted from [6]. Light is emitted from behind the camera and light rays are reflected twice, leading to the characteristic interference patterns (b). Parameters d and p have a strong impact on the appearance of the ring-shaped patterns (simulation results).
Table 1.
Overview of parameters.
Fig 2.
Processing steps of an (experimental) image containing one particle. The result includes the particle position, particle size, and its contact area.
Fig 3.
Workflow of the detection process.
The processing steps of template creation and image processing.
Fig 4.
Deformations or menisci (yellow) can occur and vary depending on material properties (a). We assume a simpler geometric model (b), which is independent of such material properties but, however, could lead to deviations along the border of the contact area (hatched yellow area in the simulated image (c)).
Fig 5.
Increasing performance by reducing the search-space.
A pre-processing step aims to reduce the search space. To achieve this, the gradient is calculated (glyphs in Fig c, with color-coding based on their orientation) and lines are drawn along the gradient for every pixel (line image). Overlapping lines lead to intensity peaks in the center of radial profiles (d). These peaks are extracted with thresholding and they form the search space for the template matching process (e). Images a and b are experimental results (acquired as described in section 2.3) and their contrast was enhanced for presentation purposes.
Fig 6.
Sampling and fitting of profiles.
Fig a shows a RICM image and sampling at an exemplary position (brightness increased for presentation). Fig b demonstrates the fitting procedure of the obtained profile. Our basic template fit for this example shows good Pearson correlation of 0.91, however, adding an exponential decay for higher radii improves correlation to 0.99. To determine particle size, we fit the template regarding optimized extrema overlap (note the better match especially of low peaks for radius positions 5 μm and higher).
Fig 7.
Evaluation of particle detection, particle radius and contact radius.
The histogram (Fig a) displays the deviation for the location of the profiles compared to manually labeled reference data (total of 265 samples). The scatterplot (Fig b) shows results for particle radius determination compared to manually labeled reference data (total of 47 samples). It can be seen that the optimized version, in which particle size is determined on basis of a second extrema-focused matching, works notably better (mean absolute error 1.3 μm) than our naive approach (mean absolute error 3.8 μm). The bottom row shows the results for the comparison between the model-based contact radius and the reference data created by region growing. Plot c presents an evaluation for various region growing thresholds between 1% and 40% of the profile amplitude. Plot d shows detailed results for the lowest threshold (30%) that was free of erroneous stops during region growing, and the regression line (R2 = 0.9856). The plot reveals an overestimation of the contact radius by the threshold-based approach, which is a consequence of the relatively high threshold. Lower thresholds would lead to earlier stops (and thus smaller radii) but also to erroneous stops (see Fig c). Further details are given in section 4.3.