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.
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.
@cite_19 @cite_5 @cite_14
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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. 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. We are interested in counting the number of instances of object classes in natural, everyday images. Previous counting approaches tackle the problem in restricted domains such as counting pedestrians in surveillance videos. Counts can also be estimated from outputs of other vision tasks like object detection. In this work, we build dedicated models for counting designed to tackle the large variance in counts, appearances, and scales of objects found in natural scenes. Our approach is inspired by the phenomenon of subitizing &#x2013; the ability of humans to make quick assessments of counts given a perceptual signal, for small count values. Given a natural scene, we employ a divide and conquer strategy while incorporating context across the scene to adapt the subitizing idea to counting. Our approach offers consistent improvements over numerous baseline approaches for counting on the PASCAL VOC 2007 and COCO datasets. Subsequently, we study how counting can be used to improve object detection. We then show a proof of concept application of our counting methods to the task of Visual Question Answering, by studying the how many? questions in the VQA and COCO-QA datasets. We propose a deep learning method for people counting.We provide a new crowd dataset called AHU-CROWD.We test our method on UCSD and UCF-CROWD and compare with the state-of-the-art. For reasons of public security, modeling large crowd distributions for counting or density estimation has attracted significant research interests in recent years. Existing crowd counting algorithms rely on predefined features and regression to estimate the crowd size. However, most of them are constrained by such limitations: (1) they can handle crowds with a few tens individuals, but for crowds of hundreds or thousands, they can only be used to estimate the crowd density rather than the crowd count; (2) they usually rely on temporal sequence in crowd videos which is not applicable to still images. Addressing these problems, in this paper, we investigate the use of a deep-learning approach to estimate the number of individuals presented in a mid-level or high-level crowd visible in a single image. Firstly, a ConvNet structure is used to extract crowd features. Then two supervisory signals, i.e., crowd count and crowd density, are employed to learn crowd features and estimate the specific counting. We test our approach on a dataset containing 107 crowd images with 45,000 annotated humans inside, and each with head counts ranging from 58 to 2201. The efficacy of the proposed approach is demonstrated in extensive experiments by quantifying the counting performance through multiple evaluation criteria. The ability to accurately quantitate specific populations of cells is important for precision diagnostics in laboratory medicine. For example, the quantization of positive tumor cells can be used clinically to determine the need for chemotherapy in a cancer patient. In this paper, we describe a supervised learning framework with Convolutional Neural Network (CNN) and cast the cell counting task as a regression problem, where the global cell count is taken as the annotation to supervise training, instead of following the classification or detection framework. To further decrease the prediction error of counting, we tune several cutting-edge CNN architectures (e.g. Deep Residual Network) into the regression model. As the final output, not only the cell count is estimated for an image, but also its spatial density map is provided. The proposed method is evaluated with three state-of-the-art approaches on three cell image datasets and obtain superior performance. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. In this paper, we propose a deep Convolutional Neural Network (CNN) for counting the number of people across a line-of-interest (LOI) in surveillance videos. It is a challenging problem and has many potential applications. Observing the limitations of temporal slices used by state-of-the-art LOI crowd counting methods, our proposed CNN directly estimates the crowd counts with pairs of video frames as inputs and is trained with pixel-level supervision maps. Such rich supervision information helps our CNN learn more discriminative feature representations. A two-phase training scheme is adopted, which decomposes the original counting problem into two easier sub-problems, estimating crowd density map and estimating crowd velocity map. Learning to solve the sub-problems provides a good initial point for our CNN model, which is then fine-tuned to solve the original counting problem. A new dataset with pedestrian trajectory annotations is introduced for evaluating LOI crowd counting methods and has more annotations than any existing one. Our extensive experiments show that our proposed method is robust to variations of crowd density, crowd velocity, and directions of the LOI, and outperforms state-of-the-art LOI counting methods. We investigate the complexity of approximately counting stable matchings in the k-attribute model, where the preference lists are determined by dot products of ''preference vectors'' with ''attribute vectors'', or by Euclidean distances between ''preference points ''and ''attribute points''. Irving and Leather (1986) [14] proved that counting the number of stable matchings in the general case is #P-complete. Counting the number of stable matchings is reducible to counting the number of downsets in a (related) partial order [14] and is interreducible, in an approximation-preserving sense, to a class of problems that includes counting the number of independent sets in a bipartite graph (#BIS) ( (2004) [6]). It is conjectured that no FPRAS exists for this class of problems. We show this approximation-preserving interreducibility remains even in the restricted k-attribute setting when k>=3 (dot products) or k>=2 (Euclidean distances). Finally, we show it is easy to count the number of stable matchings in the 1-attribute dot-product setting. We propose a novel object detection framework for partially-occluded small instances, such as pedestrians in low resolution surveillance video, cells under a microscope, flocks of small animals (e.g. birds, fishes), or even tiny insects like honeybees and flies. These scenarios are very challenging for traditional detectors, which are typically trained on individual instances. In our approach, we first estimate the object density map of the input image, and then divide it into local regions. For each region, a sliding window (ROI) is passed over the density map to calculate the instance count within each ROI. 2D integer programming is used to recover the locations of object instances from the set of ROI counts, and the global count estimate of the density map is used as a constraint to regularize the detection performance. Finally, the bounding box for each instance is estimated using the local density map. Compared with current small-instance detection methods, our proposed approach achieves state-of-the-art performance on several challenging datasets including fluorescence microscopy cell images, UCSD pedestrians, small animals and insects. We propose a new method to count objects of specific categories that are significantly smaller than the ground sampling distance of a satellite image. This task is hard due to the cluttered nature of scenes where different object categories occur. Target objects can be partially occluded, vary in appearance within the same class and look alike to different categories. Since traditional object detection is infeasible due to the small size of objects with respect to the pixel size, we cast object counting as a density estimation problem. To distinguish objects of different classes, our approach combines density estimation with semantic segmentation in an end-to-end learnable convolutional neural network (CNN). Experiments show that deep semantic density estimation can robustly count objects of various classes in cluttered scenes. Experiments also suggest that we need specific CNN architectures in remote sensing instead of blindly applying existing ones from computer vision. An approach to the problem of estimating the size of inhomogeneous crowds, which are composed of pedestrians that travel in different directions, without using explicit object segmentation or tracking is proposed. Instead, the crowd is segmented into components of homogeneous motion, using the mixture of dynamic-texture motion model. A set of holistic low-level features is extracted from each segmented region, and a function that maps features into estimates of the number of people per segment is learned with Bayesian regression. Two Bayesian regression models are examined. The first is a combination of Gaussian process regression with a compound kernel, which accounts for both the global and local trends of the count mapping but is limited by the real-valued outputs that do not match the discrete counts. We address this limitation with a second model, which is based on a Bayesian treatment of Poisson regression that introduces a prior distribution on the linear weights of the model. Since exact inference is analytically intractable, a closed-form approximation is derived that is computationally efficient and kernelizable, enabling the representation of nonlinear functions. An approximate marginal likelihood is also derived for kernel hyperparameter learning. The two regression-based crowd counting methods are evaluated on a large pedestrian data set, containing very distinct camera views, pedestrian traffic, and outliers, such as bikes or skateboarders. Experimental results show that regression-based counts are accurate regardless of the crowd size, outperforming the count estimates produced by state-of-the-art pedestrian detectors. Results on 2 h of video demonstrate the efficiency and robustness of the regression-based crowd size estimation over long periods of time. The popular h-index used to measure scientific output can be described in terms of a pool of evaluated objects (the papers), a quality function on the evaluated objects (the number of citations received by each paper) and a sentencing line crossing the origin, whose intersection with the graph of the quality function yields the index value (in the h-index this is a line with slope 1). Based on this abstraction, we present a new index, the c-index, in which the evaluated objects are the citations received by an author, a group of authors, a journal, etc., the quality function of a citation is the collaboration distance between the authors of the cited and the citing papers, and the sentencing line can take slopes between 0 and ∞. As a result, the new index counts only those citations which are significant enough, where significance is proportional to collaboration distance. Several advantages of the new c-index with respect to previous proposals are discussed. Cross-scene crowd counting is a challenging task where no laborious data annotation is required for counting people in new target surveillance crowd scenes unseen in the training set. The performance of most existing crowd counting methods drops significantly when they are applied to an unseen scene. To address this problem, we propose a deep convolutional neural network (CNN) for crowd counting, and it is trained alternatively with two related learning objectives, crowd density and crowd count. This proposed switchable learning approach is able to obtain better local optimum for both objectives. To handle an unseen target crowd scene, we present a data-driven method to finetune the trained CNN model for the target scene. A new dataset including 108 crowd scenes with nearly 200,000 head annotations is introduced to better evaluate the accuracy of cross-scene crowd counting methods. Extensive experiments on the proposed and another two existing datasets demonstrate the effectiveness and reliability of our approach. Counting the number of leaves in plants is important for plant phenotyping, since it can be used to assess plant growth stages. We propose a learning-based approach for counting leaves in rosette (model) plants. We relate image-based descriptors learned in an unsupervised fashion to leaf counts using a supervised regression model. To take advantage of the circular and coplanar arrangement of leaves and also to introduce scale and rotation invariance, we learn features in a log-polar representation. Image patches extracted in this log-polar domain are provided to K-means, which builds a codebook in a unsupervised manner. Feature codes are obtained by projecting patches on the codebook using the triangle encoding, introducing both sparsity and specifically designed representation. A global, per-plant image descriptor is obtained by pooling local features in specific regions of the image. Finally, we provide the global descriptors to a support vector regression framework to estimate the number of leaves in a plant. We evaluate our method on datasets of the (LCC), containing images of Arabidopsis and tobacco plants. Experimental results show that on average we reduce absolute counting error by 40 w.r.t. the winner of the 2014 edition of the challenge -a counting via segmentation method. When compared to state-of-the-art density-based approaches to counting, on Arabidopsis image data 75 less counting errors are observed. Our findings suggest that it is possible to treat leaf counting as a regression problem, requiring as input only the total leaf count per training image. We address the problem of counting cells in time-lapse microscopy images of developing human embryos. Cell counting is considered as an important step in analyzing biological phenomenon such as embryo viability. Traditional approaches to counting cells rely on hand crafted features and cannot fully take advantage of the growth in data set sizes. In this paper, we propose a framework to automatically count the number of cells in developing human embryos. The framework employs a deep convolutional neural network model trained to count cells from raw microscopy images. We demonstrate the effectiveness of our approach on a data set of 265 human embryos. The results show that the proposed framework provides robust estimates of the number of cells in a developing embryo up to the 5-cell stage (i.e., 48 h post fertilization). In this paper we address the problem of counting objects instances in images. Our models are able to precisely estimate the number of vehicles in a traffic congestion, or to count the humans in a very crowded scene. Our first contribution is the proposal of a novel convolutional neural network solution, named Counting CNN (CCNN). Essentially, the CCNN is formulated as a regression model where the network learns how to map the appearance of the image patches to their corresponding object density maps. Our second contribution consists in a scale-aware counting model, the Hydra CNN, able to estimate object densities in different very crowded scenarios where no geometric information of the scene can be provided. Hydra CNN learns a multiscale non-linear regression model which uses a pyramid of image patches extracted at multiple scales to perform the final density prediction. We report an extensive experimental evaluation, using up to three different object counting benchmarks, where we show how our solutions achieve a state-of-the-art performance. Crowd counting, for estimating the number of people in a crowd using vision-based computer techniques, has attracted much interest in the research community. Although many attempts have been reported, real-world problems, such as huge variation in subjects' sizes in images and serious occlusion among people, make it still a challenging problem. In this paper, we propose an Adaptive Counting Convolutional Neural Network (A-CCNN) and consider the scale variation of objects in a frame adaptively so as to improve the accuracy of counting. Our method takes advantages of contextual information to provide more accurate and adaptive density maps and crowd counting in a scene. Extensively experimental evaluation is conducted using different benchmark datasets for object-counting and shows that the proposed approach is effective and outperforms state-of-the-art approaches. There are several computational problems that can be formulated as problems of counting the number of objects having a certain property. Valiant [22] has introduced the class #P which includes a variety of counting problems such as counting the number of perfect matchings in a graph, computing the permanent of a matrix [22], finding the size of a backtrack search tree [14], and computing the probability that a network remains connected when links can fail with a certain probability [23]. We define and study a class of restricted, but very natural, probabilistic sampling methods motivated by the particular counting problems mentioned above. Instead of “singleton sampling” the algorithm is allowed to sample a large set S ample; U in one step; the information returned from the sample is whether S contains any element having the property being counted. We attempt to classify the complexity of computing approximate solutions to problems in #P. The classification is done in terms of the polynomial-time hierarchy (for short, P-hierarchy) [21]. We give a relativization result that complements a recent result of Sipser and Gaacute;c [19] that BPP is contained in the second level of the P-hierarchy. We propose an integer programming method for estimating the instantaneous count of pedestrians crossing a line of interest (LOI) in a video sequence. Through a line sampling process, the video is first converted into a temporal slice image. Next, the number of people is estimated in a set of overlapping sliding windows on the temporal slice image, using a regression function that maps from local features to a count. Given that the count in a sliding window is the sum of the instantaneous counts in the corresponding time interval, an integer programming method is proposed to recover the number of pedestrians crossing the LOI in each frame. Integrating over a specific time interval yields the cumulative count of pedestrians crossing the line. Compared with current methods for line counting, our proposed approach achieves state-of-the-art performance on several challenging crowd video data sets. For crowded scenes, the accuracy of object-based computer vision methods declines when the images are low-resolution and objects have severe occlusions. Taking counting methods for example, almost all the recent state-of-the-art counting methods bypass explicit detection and adopt regression-based methods to directly count the objects of interest. Among regression-based methods, density map estimation, where the number of objects inside a subregion is the integral of the density map over that subregion, is especially promising because it preserves spatial information, which makes it useful for both counting and localization (detection and tracking). With the power of deep convolutional neural networks (CNNs) the counting performance has improved steadily. The goal of this paper is to evaluate density maps generated by density estimation methods on a variety of crowd analysis tasks, including counting, detection, and tracking. Most existing CNN methods produce density maps with resolution that is smaller than the original images, due to the downsample strides in the convolution pooling operations. To produce an original-resolution density map, we also evaluate a classical CNN that uses a sliding window regressor to predict the density for every pixel in the image. We also consider a fully convolutional adaptation, with skip connections from lower convolutional layers to compensate for loss in spatial information during upsampling. In our experiments, we found that the lower-resolution density maps sometimes have better counting performance. In contrast, the original-resolution density maps improved localization tasks, such as detection and tracking, compared with bilinear upsampling the lower-resolution density maps. Finally, we also propose several metrics for measuring the quality of a density map, and relate them to experiment results on counting and localization.