Ensemble-Based Uncertainty Estimation for Deep-Learning Measurement Systems in Vision Applications

Deep-learning-based vision systems are increasingly employed as measuring instruments, for example to estimate dimensional or positional quantities from images. However, such systems are typically characterized by the absence of explicit quantification of the uncertainty associated with each individual measurement. This paper presents a practical framework to treat a deep neural network as a measuring device and to estimate its uncertainty using an ensemble of object detectors. Concretely, an ensemble of ten nominally identical YOLOv12s detectors is trained on the same microscopy dataset, using the same architecture and hyperparameters but different random seeds. Each trained network is interpreted as a feasible realization of the associated measurement task. At inference time, all ensemble members are applied to the same image; their bounding boxes are clustered by Intersection-over-Union (IoU) and class label, so that each physical object is associated with a cloud of bounding boxes provided by different models. The mean bounding box of the cloud is interpreted as the measurement result, while the dispersion of the cloud provides a per-object uncertainty estimate in the image domain. A simple scalar calibration factor obtained from the microscope allows these quantities to be directly expressed in physical units. The proposed approach requires no modification of the network architecture or loss function and can be described in the language of measurement science: the bounding box is measured as the average of repeated "readings", and the spread of those readings quantifies the uncertainty.