Understanding the Ability of Deep Neural Networks to Count Connected Components in Images

Humans can count very fast by subitizing, but slow substantially as the number of objects increases. Previous studies have shown a trained deep neural network (DNN) detector can count the number of objects in an amount of time that increases slowly with the number of objects. Such a phenomenon suggests the subitizing ability of DNNs, and unlike humans, it works equally well for large numbers. Many existing studies have successfully applied DNNs to object counting, but few studies have studied the subitizing ability of DNNs and its interpretation. In this paper, we found DNNs do not have the ability to generally count connected components. We provided experiments to support our conclusions and explanations to understand the results and phenomena of these experiments. We proposed three ML-learnable characteristics to verify learnable problems for ML models, such as DNNs, and explain why DNNs work for specific counting problems but cannot generally count connected components.