Uncertainty propagation: Avoiding the expensive sampling process for real-time image-based measurements

A common way of evaluating the quality of a measuring device is to use it to measure the properties of some test objects, thus obtaining a large number of samples whose values are then compared to a known ground truth. Such a process tends to be labor intensive and time-consuming. A more convenient and elegant alternative is to statistically propagate the uncertainty of the measurement process throughout the computation chain. A clear advantage of such an approach over the conventional sampling-based method is its practical nature: it allows the continuous changes in input parameter values and sampling conditions, which are common in real-time applications, to be instantly taken into account. In order to demonstrate the benefits of using uncertainty propagation in real-time image metrology applications, we describe a method for automatic computation of box dimensions from single perspective projection images in real time. For this, we derive expressions for the uncertainty in the measurements based on the uncertainties present in all variables used in the computational flow. Our results show that these estimates are in accordance with the ones obtained using the conventional sampling process, thus safely replacing them. We also show that the uncertainty propagation approach is computationally efficient. This approach can be incorporated into applications that aim to make real-time measurements directly from images, and should also be useful in many other time-critical applications.