However, both L2 and BL have two deficiencies. First, the noise in the annotation process is not considered in a principled way. L2 and BL make an assumption about per-pixel i.i.d.

The annotation noise in crowd counting is not modeled in traditional crowd counting algorithms based on crowd density maps. In this paper, we first model the annotation noise using a random variable with Gaussian distribution, and derive the pdf of the crowd density value for each spatial location in the image. We then approximate the joint distribution of the density values (i.e., the distribution of density maps) with a full covariance multivariate Gaussian density, and derive a low-rank approximate for tractable implementation. We use our loss function to train a crowd density map estimator and achieve state-of-the-art performance on three large-scale crowd counting datasets, which confirms its effectiveness. Examination of the predictions of the trained model shows that it can correctly predict the locations of people in spite of the noisy training data, which demonstrates the robustness of our loss function to annotation noise.

The annotation noise in crowd counting is not modeled in traditional crowd counting algorithms based on crowd density maps.

Duplicate annotations are rare, and will be corrected by the annotator in the review phase.

The annotation noise in crowd counting is not modeled in traditional crowd counting algorithms based on crowd density maps. In this paper, we first model the annotation noise using a random variable with Gaussian distribution, and derive the pdf of the crowd density value for each spatial location in the image. We then approximate the joint distribution of the density values (i.e., the distribution of density maps) with a full covariance multivariate Gaussian density, and derive a low-rank approximate for tractable implementation. We use our loss function to train a crowd density map estimator and achieve state-of-the-art performance on three large-scale crowd counting datasets, which confirms its effectiveness. Examination of the predictions of the trained model shows that it can correctly predict the locations of people in spite of the noisy training data, which demonstrates the robustness of our loss function to annotation noise.

The annotation noise in crowd counting is not modeled in traditional crowd counting algorithms based on crowd density maps. In this paper, we first model the annotation noise using a random variable with Gaussian distribution, and derive the pdf of the crowd density value for each spatial location in the image. We then approximate the joint distribution of the density values (i.e., the distribution of density maps) with a full covariance multivariate Gaussian density, and derive a low-rank approximate for tractable implementation. We use our loss function to train a crowd density map estimator and achieve state-of-the-art performance on three large-scale crowd counting datasets, which confirms its effectiveness. Examination of the predictions of the trained model shows that it can correctly predict the locations of people in spite of the noisy training data, which demonstrates the robustness of our loss function to annotation noise.

Federated learning (FL) has emerged as a promising paradigm for training segmentation models on decentralized medical data, owing to its privacy-preserving property. However, existing research overlooks the prevalent annotation noise encountered in real-world medical datasets, which limits the performance ceilings of FL. In this paper, we, for the first time, identify and tackle this problem. For problem formulation, we propose a contour evolution for modeling non-independent and identically distributed (Non-IID) noise across pixels within each client and then extend it to the case of multi-source data to form a heterogeneous noise model (i.e., Non-IID annotation noise across clients). For robust learning from annotations with such two-level Non-IID noise, we emphasize the importance of data quality in model aggregation, allowing high-quality clients to have a greater impact on FL. To achieve this, we propose Federated learning with Annotation quAlity-aware AggregatIon, named FedA3I, by introducing a quality factor based on client-wise noise estimation. Specifically, noise estimation at each client is accomplished through the Gaussian mixture model and then incorporated into model aggregation in a layer-wise manner to up-weight high-quality clients. Extensive experiments on two real-world medical image segmentation datasets demonstrate the superior performance of FedA$^3$I against the state-of-the-art approaches in dealing with cross-client annotation noise. The code is available at https://github.com/wnn2000/FedAAAI.

Distantly-Supervised Named Entity Recognition effectively alleviates the burden of time-consuming and expensive annotation in the supervised setting. But the context-free matching process and the limited coverage of knowledge bases introduce inaccurate and incomplete annotation noise respectively. Previous studies either considered only incomplete annotation noise or indiscriminately handle two types of noise with the same strategy. In this paper, we argue that the different causes of two types of noise bring up the requirement of different strategies in model architecture. Therefore, we propose the SANTA to handle these two types of noise separately with (1) Memory-smoothed Focal Loss and Entity-aware KNN to relieve the entity ambiguity problem caused by inaccurate annotation, and (2) Boundary Mixup to alleviate decision boundary shifting problem caused by incomplete annotation and a noise-tolerant loss to improve the robustness. Benefiting from our separate tailored strategies, we confirm in the experiment that the two types of noise are well mitigated. SANTA also achieves a new state-of-the-art on five public datasets.

We develop a Synthetic Fusion Pyramid Network (SPF-Net) with a scale-aware loss function design for accurate crowd counting. Existing crowd-counting methods assume that the training annotation points were accurate and thus ignore the fact that noisy annotations can lead to large model-learning bias and counting error, especially for counting highly dense crowds that appear far away. To the best of our knowledge, this work is the first to properly handle such noise at multiple scales in end-to-end loss design and thus push the crowd counting state-of-the-art. We model the noise of crowd annotation points as a Gaussian and derive the crowd probability density map from the input image. We then approximate the joint distribution of crowd density maps with the full covariance of multiple scales and derive a low-rank approximation for tractability and efficient implementation. The derived scale-aware loss function is used to train the SPF-Net. We show that it outperforms various loss functions on four public datasets: UCF-QNRF, UCF CC 50, NWPU and ShanghaiTech A-B datasets. The proposed SPF-Net can accurately predict the locations of people in the crowd, despite training on noisy training annotations.