Regression tasks in computer vision such as age estimation or counting are often formulated into classification by quantizing the target space into classes. Yet real-world data is often imbalanced - the majority of training samples lie in a head range of target values while a minority of samples span a usually larger tail range. By selecting the class quantization one can adjust imbalanced re-gression targets into balanced classification outputs though there are trade-offs in balancing classification accuracy and quantization error. To improve regression performance over the entire range of data we propose to construct hierarchical classifiers for solving imbalanced regression tasks. The fine-grained classifiers limit the quantization error while being modulated by the coarse predictions to ensure high accuracy. Standard hierarchical classification approaches when applied to the regression problem fail to ensure that predicted ranges remain consistent across the hierarchy. As such we propose a range-preserving distillation process that effectively learns a single classifier from the set of hierarchical classifiers. Our novel hierarchical classification adjustment (HCA) for imbalanced regression shows superior results on three diverse tasks age estimation crowd counting and depth estimation. Code is available at https: / / gi thub. com/xhp-hust −2018-2011/HCA

In object counting, objects often exhibit different sizes at different scales, even if they have similar physical sizes in reality. This is particularly true when targeting crowd counting and vehicle counting in intelligent transportation. Failing to model such variations leads to the mismatch between the object size and image scale. To address this problem, existing methods often extract multi-scale features, but they either still generate the single-scale prediction or lack an explicit suppression mechanism to eliminate predictions engendered by inappropriate scales. Our scale analysis manifests that, the single-scale estimation only works well for objects of certain sizes, and a suppression operator is required to isolate the estimation of a specific scale. In this work, we propose a scale-aware counting network termed NSSNet. NSSNet has two key features: it not only i) generates multi-scale predictions but also ii) applies a novel non-scale suppression (NSS) operator to suppress scale-mismatched estimations. NSS is inspired by the widely-used non-maximum suppression (NMS). In contrast to NMS that only reserves the maximum response, NSS filters out those clearly wrong predictions (the remaining predictions may still be from multiple scales). We evaluate NSSNet on four standard crowd and vehicle counting benchmarks and report state-of-the-art performance. We also show the scale adaptability of NSSNet through a controlled multi-scale experiment. Code and pretrained models are available athttps://git.io/nssnet.

One of appealing approaches to counting dense objects, such as crowd, is density map estimation. Density maps, however, present ambiguous appearance cues in congested scenes, rendering infeasibility in identifying individuals and difficulties in diagnosing errors. Inspired by an observation that counting can be interpreted as a two-stage process, i.e., identifying possible object regions and counting exact object numbers, we introduce a probabilistic intermediate representation termed the probability map that depicts the probability of each pixel being an object. This representation allows us to decouple counting into probability map regression (PMR) and count map regression (CMR). We therefore propose a novel decoupled two-stage counting (D2C) framework that sequentially regresses the probability map and learns a counter conditioned on the probability map. Given the probability map and the count map, a peak point detection algorithm is derived to localize each object with a point under the guidance of local counts. An advantage of D2C is that the counter can be learned reliably with additional synthesized probability maps. This addresses important data deficiency and sample imbalanced problems in counting. Our framework also enables easy diagnoses and analyses of error patterns. For instance, we find that, the counter per se is sufficiently accurate, while the bottleneck appears to be PMR. We further instantiate a network D2CNet in our framework and report state-of-the-art counting and localization performance across 6 crowd counting benchmarks. Since the probability map is a representation independent of visual appearance, D2CNet also exhibits remarkable cross-dataset transferability. Code and pretrained models are made available at: https://git.io/d2cnet.

In this paper, we introduce the idea of blockwise classification to count objects. The current mainstream method for counting objects is to regress the density map or to regress the redundant count map via a deep convolutional neural network (CNN). However, these methods suffer from two critical issues: inaccurately generated regression targets and serious sample imbalances. First, the ground truth density map is generated by convolving the dot map using a Gaussian kernel. Because an inappropriate kernel can cover the background or uncover objects, this approach introduces a form of noise, and therefore results in ambiguities when training the networks. Second, inhomogeneously distributed objects often exist in images, which gives rise to a data collection bias. This leads to a long-tailed distribution of region counts, which is a typical characteristic that occurs with imbalanced samples; therefore, underestimations in high-density regions and overestimations in low-density regions are common. In this paper, we address these two issues within one framework-blockwise count level classification. The intuition behind this idea is that while it may not be possible to provide an exact count of pixels or patches, it is possible to provide a count of a region that falls within a certain interval with high confidence. Our method classifies the count levels of each block produced by nonlinearly quantizing the continuous counts, thus transforming the imbalance of sample patch counts into a class imbalance of count levels. Consequently, an information-entropy-inspired loss can be applied to alleviate this issue. Through ablative studies, we analyze the impact of imbalanced data, Gaussian kernel sizes, quantization errors, and the effectiveness of each module in our method. Without bells and whistles, our method outperforms or performs competitively with other state-of-the-art approaches on seven object-counting benchmarks, including four crowd-counting datasets from ShanghaiTech, WorldExpo'10, UCF-QNRF and UCF_CC_50, one vehicle-counting dataset (TRANCOS), one maize-tassel-counting dataset (MTC), and one challenging sonar fish-counting dataset that we constructed. The results suggest that our framework provides a strong and improved baseline for object counting.

Visual counting, a task that predicts the number of objects from an image/video, is an open-set problem by nature, i.e., the number of population can vary in [0,+∞) in theory. However, the collected images and labeled count values are limited in reality, which means only a small closed set is observed. Existing methods typically model this task in a regression manner, while they are likely to suffer from an unseen scene with counts out of the scope of the closed set. In fact, counting is decomposable. A dense region can always be divided until the count values of sub-regions are within the previously observed closed set. Inspired by this idea, we propose a simple but effective approach, Spatial Divide-and-Conquer Network (S-DCNet). S-DCNet learns to classify closed-set counts and can generalize to open-set counts via S-DC. S-DCNet is also efficient. To avoid repeatedly computing sub-region convolutional features, S-DC is executed on the feature map instead of on the input image. S-DCNet achieves the state-of-the-art performance on three crowd counting datasets (ShanghaiTech, UCF_CC_50 and UCF-QNRF), a vehicle counting dataset (TRANCOS) and a plant counting dataset (MTC). Compared to the previous best methods, S-DCNet brings a 20.2% relative improvement on the ShanghaiTechPart B, 20.9% on the UCF-QNRF, 22.5% on the TRANCOS and 15.1% on the MTC. Code has been made available at: https://github.com/xhp-hust-2018-2011/S-DCNet.