Accurately measuring the aerosol optical depth (AOD) is essential for our understanding of the climate. Currently, AOD can be measured by (i) satellite instruments, which operate on a global scale but have limited accuracies; and (ii) ground-based instruments, which are more accurate but not widely available. Recent approaches focus on integrating measurements from these two sources to complement each other. In this paper, we further improve the prediction accuracy by using the observation that the AOD varies slowly in the spatial domain. Using a probabilistic approach, we impose this smoothness constraint by a Gaussian random field on the Earth's surface, which can be considered as a two-dimensional manifold. The proposed integration approach is computationally simple, and experimental results on both synthetic and real-world data sets show that it significantly outperforms the state-of-the-art.

We have developed a method for using confidence scores to integrate labels provided by crowdsourcing workers. Although confidence scores can be useful information for estimating the quality of the provided labels, a way to effectively incorporate them into the integration process has not been established. Moreover, some workers are overconfident about the quality of their labels while others are underconfident, and some workers are quite accurate in judging the quality of their labels. This differing reliability of the confidence scores among workers means that the probability distributions for the reported confidence scores differ among workers. To address this problem, we extended the Dawid-Skene model and created two probabilistic models in which the values of unobserved true labels are inferred from the observed provided labels and reported confidence scores by using the expectation-maximization algorithm. Results of experiments using actual crowdsourced data for image labeling and binary question answering tasks showed that incorporating workers' confidence scores can improve the accuracy of integrated crowdsourced labels.