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Convolutional Neural Networks (CNN) have been successfully used to recognize and extract visual patterns in different tasks such as object detection, object classification, scene recognition, and image retrieval. The CNNs have also contributed in local features extraction by learning local representations. A representative approach is LIFT that generates keypoint descriptors more discriminative than handcrafted algorithms like SIFT, BRIEF, and SURF. In this paper, we investigate the binary tests selection problem, and we present an in-depth study of the limit of searching solutions with CNNs when the gradient is computed from the local neighborhood of the selected pixels. We performed several experiments with a Siamese Network trained with corresponding and non-corresponding patch pairs. Our results show the presence of Local Minima and also a problem that we called Incorrect Gradient Components. We pursued to understand the binary tests selection problem and even some limitations of Convolutional Neural Networks to avoid searching for solutions in unviable directions.

Exploring the Limitations of the Convolutional Neural Networks on Binary Tests Selection for Local Features