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It is well accepted that both humans and non-human animals are able to make approximate judgments of relative numerosity (Dehaene, 2011). Discriminability of two visual numerosities can be characterized, at least approximately, as a function of their ratio, in accordance with Weber's law (Dehaene, 2003). Notably, ratio-dependent performance has been observed also

This paper addresses the challenge of establishing a bridge between deep convolutional neural networks and conventional object detection frameworks for accurate and efficient generic object detection. We introduce Dense Neural Patterns, short for DNPs, which are dense local features derived from discriminatively trained deep convolutional neural networks. DNPs can be easily plugged into conventional detection frameworks in the same way as other dense local features(like HOG or LBP). The effectiveness of the proposed approach is demonstrated with the Regionlets object detection framework. It is the first approach efficiently applying deep convolutional features for conventional object detection models.Detecting generic objects in high-resolution images is one of the most valuable pattern recognition tasks, useful for large-scale image labeling, scene understanding, action recognition, self-driving vehicles and robotics. At the same time, accurate detection is a highly challenging task due to cluttered backgrounds, occlusions, and perspective changes. Predominant approaches use deformable template matching with hand-designed features. However, these methods are not flexible when dealing with variable aspect ratios. Wang et al. recently proposed a radically different approach, named Regionlets, for generic object detection [4]. It extends classic cascaded boosting classifiers with a two-layer feature extraction hierarchy , and is dedicatedly designed for region based object detection. Despite the success of these sophisticated detection methods, the features employed in these frameworks are still traditional features based on lowlevel cues such as histogram of oriented gradients(HOG), local binary patterns(LBP) or covariance [3] built on image gradients.With the success in large scale image classification [1], object detection using a deep convolutional neural network also shows promising performance [2]. The dramatic improvements from the application of deep neural networks are believed to be attributable to their capability to learn hierarchically more complex features from large data-sets. Despite their excellent performance, the application of deep CNNs has been centered around image classification, which is computationally expensive when transferred to perform object detection. Furthermore, their formulation does not take advantage of venerable and successful object detection frameworks such as DPM or Regionlets which are powerful designs for modeling object deformation, sub-categories and multiple aspect ratios.These observations motivate us to propose an approach to efficiently incorporate a deep neural network into conventional object detection frameworks. To that end, we introduce the Dense Neural Pattern (DNP), a local feature densely extracted from an image with an arbitrary resolution using a deep convolutional neural network trained with image classification datasets. The DNPs not only encode high-level features learned from a large image data-set, but are also local and flexible like other dense local...

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