The performance of a binary classifier is described by a confusion matrix with four entries: the number of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN).  The Matthew’s Correlation Coefficient (MCC), F1, and Fowlkes–Mallows (FM) scores are scalars that summarize a confusion matrix. Both the F1 and FM scores are based on only three of the four entries in a confusion matrix (they ignore TN). In contrast, the MCC takes into account all four entries of a confusion matrix and thus can be seen as providing a more representative picture.  However, in object detection problems, measuring the number of true negatives is so large it is often intractable. Thus we ask, what happens to the MCC as the number of true negatives approaches infinity? This paper provides insight into the relationship between the MCC and FM score by proving that the FM-measure is equal to the limit of the MCC as the number of true negatives approaches infinity.

The MCC approaches the geometric mean of precision and recall as true negatives approach infinity.

In this thesis we address the problem of identifying individual animals using images in the context of assisting an ecologist in performing a population census. We are motivated by events like the “Great Zebra Count” where thousands of images of zebras and giraffes were collected in Nairobi National Park over two days. By grouping all images that contain the same individual we can census these populations. This problem is challenging because images are collected outdoors and contain occlusion, lighting, and quality variations and because the animals exhibit viewpoint and pose variations.

Our first contribution is an algorithm that ranks a database of images by their similarity to a query. A manual reviewer inspects only the top few results for each query — significantly reducing the search space — and determines if the animals match. Using this algorithm alone, we analyzed the images from the Great Zebra Count and performed a population census. Our second contribution is a verification algorithm that determines the probability that two images are from the same animal, that they are not, or that there is not enough to decide. This algorithm is used with the ranking algorithm to re-rank results and automatically verify high confidence image pairs.

Our third contribution is a semi-automatic graph identification algorithm. The approach represents each image as a node in the graph and incrementally forms edges between nodes determined to the same animal. The ranking and verification algorithms are used to search for candidate edges and estimate their probability of matching. Based on these probabilities, edges are prioritized for review and placed in the graph when they are automatically verified or manually reviewed. Redundant connections are added to detect and recover from errors. A termination criterion determines when identification is finished. Using the graph algorithm we perform a population census on the scale of the Great Zebra Count using less than 25% of the manual reviews required by the original method.