Differential Digital Image Tracking (DDIT)
The DDIT method exploits the shape of these powder particles when digitally imaged in the intensity domain as shown in Figure 2. The resemblance of the particles to mathematical functions that are adept at describing peak shapes with precise center locations and broadening (tails) allow them to be fit to a given function and thus tracked.
It is perhaps coincidental that the symmetric normal (Gauss) distribution function proficiently fits the intensity profiles of the particles, although many functions would be suitable as well (e.g., Pearson VII, Cauchy). This function can also be described in two dimensions. The quality of the Gaussian fit to a peak profile is shown in Figure 3.
The DDIT script works in the following fashion as schematically shown in Figure 4 (alongside, for comparison, the DIC code, see link, that was also developed). A detailed guide that describes the inner workings of both the DDIT and DIC code can be found below. First, images are captured during the course of a mechanical test. Second, a list of image filenames is generated and the image capture times are extracted from the original images in order to synchronize the DDIT data to that of the data acquisition system. The markers are then automatically detected in the first image (after undergoing automatic background subtraction) by an image processing algorithm that labels connected components in a binary image and subsequently, information regarding the size and shape of these components are extracted (e.g. area, bounding box, centroid, major axis length, minor axis length, etc.). Particles with properties that do not conform to specifications for “ideal” shapes are thrown out, and the remaining markers in the first image are fit to a Gaussian function (in this thesis work) using a nonlinear least-squares algorithm in both the longitudinal and transverse directions. The normalized residuals of the fit of the peak to the function are calculated for every peak (typically several hundred in an image such as Figure 5 ) and again, fits deemed “poor” as given by the value of the residual are removed from the analysis. This process now continues for every image in the sequence, and the result includes the position of the peak center, which is then post-processed using a visualization and data analysis script that allows visualization and output of the quantities of interest. Incidentally, the DDIT technique has also been successfully applied to the testing of brittle SiO2 and ductile Au thin films.
Read more about this topic: Digital Image Correlation
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