text: Learning to count is a learning strategy that has been recently proposed in the literature for dealing with problems where estimating the number of object instances in a scene is the final objective. In this framework, the task of learning to detect and localize individual object instances is seen as a harder task that can be evaded by casting the problem as that of computing a regression value from hand-crafted image features. In this paper we explore the features that are learned when training a counting convolutional neural network in order to understand their underlying representation. To this end we define a counting problem for MNIST data and show that the internal representation of the network is able to classify digits in spite of the fact that no direct supervision was provided for them during training. We also present preliminary results about a deep network that is able to count the number of pedestrians in a scene.
  @cite_19: We present a privacy-preserving system for estimating the size of inhomogeneous crowds, composed of pedestrians that travel in different directions, without using explicit object segmentation or tracking. First, the crowd is segmented into components of homogeneous motion, using the mixture of dynamic textures motion model. Second, a set of simple holistic features is extracted from each segmented region, and the correspondence between features and the number of people per segment is learned with Gaussian process regression. We validate both the crowd segmentation algorithm, and the crowd counting system, on a large pedestrian dataset (2000 frames of video, containing 49,885 total pedestrian instances). Finally, we present results of the system running on a full hour of video.
  @cite_5: 
  @cite_14: We propose a new supervised learning framework for visual object counting tasks, such as estimating the number of cells in a microscopic image or the number of humans in surveillance video frames. We focus on the practically-attractive case when the training images are annotated with dots (one dot per object). Our goal is to accurately estimate the count. However, we evade the hard task of learning to detect and localize individual object instances. Instead, we cast the problem as that of estimating an image density whose integral over any image region gives the count of objects within that region. Learning to infer such density can be formulated as a minimization of a regularized risk quadratic cost function. We introduce a new loss function, which is well-suited for such learning, and at the same time can be computed efficiently via a maximum subarray algorithm. The learning can then be posed as a convex quadratic program solvable with cutting-plane optimization. The proposed framework is very flexible as it can accept any domain-specific visual features. Once trained, our system provides accurate object counts and requires a very small time overhead over the feature extraction step, making it a good candidate for applications involving real-time processing or dealing with huge amount of visual data.
summary: Because we are casting the problem of object description as learning to count, it is worthy to check the similarities with counting strategies in literature. From this point of view, counting has been tackled in different domains, such as cell counting @cite_5 or pedestrian counting @cite_14 @cite_19 . The most common approach for counting firstly segments the objects of interest and then appropriate features are manually defined, automatically extracted, and then a supervised learner infers the final counting value @cite_5 , @cite_19 . Contrary to other approaches where bounding boxes or prototypes of the object of interest are used, in @cite_14 the annotation tasks is reduced to dotting (pointing) and the counting process is casted as a problem of estimating image densities. From the point of view of counting approaches and to the best of our knowledge the proposed approach is the first one where the counting problem is handled by learning deep features. Additionally, different from previous approaches we are not giving any hint on the object we are counting besides the occurrence multiplicity.