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Humans can count very fast by subitizing, but slow substantially as thenumber of objects increases. Previous studies have shown a trained deep neuralnetwork (DNN) detector can count the number of objects in an amount of timethat increases slowly with the number of objects. Such a phenomenon suggeststhe subitizing ability of DNNs, and unlike humans, it works equally well forlarge numbers. Many existing studies have successfully applied DNNs to objectcounting, but few studies have studied the subitizing ability of DNNs and itsinterpretation. In this paper, we found DNNs do not have the ability togenerally count connected components. We provided experiments to support ourconclusions and explanations to understand the results and phenomena of theseexperiments. We proposed three ML-learnable characteristics to verify learnableproblems for ML models, such as DNNs, and explain why DNNs work for specificcounting problems but cannot generally count connected components.

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