Training and evaluating object detection pipelines with connected components

This paper describes methods to evaluate (and train) pixel classifiers when connected components is used as a post-processing step. In previous work the method was used to train a convolutional neural network for image segmentation and we provided pseudo-code for a disjoint-set based algorithm that efficiently calculates the Rand Error and its gradient. This paper describes the modifications we have found useful for applying the same approach to small (moving) object detection in low-frame rate, low spatial resolution video where objects of interest have low probability, and are spatially small and compact. We suggest the Rand Error is a suitable error for evaluating these detectors compared to centroid based error measures because of its monotonic receiver-operator characteristics (ROC curve).