Estimating Depth of Monocular Panoramic Image with Teacher-Student Model Fusing Equirectangular and Spherical Representations

Disconnectivity and distortion are the two problems which must be coped with when processing 360 degrees equirectangular images. In this paper, we propose a method of estimating the depth of monocular panoramic image with a teacher-student model fusing equirectangular and spherical representations. In contrast with the existing methods fusing an equirectangular representation with a cube map representation or tangent representation, a spherical representation is a better choice because a sampling on a sphere is more uniform and can also cope with distortion more effectively. In this processing, a novel spherical convolution kernel computing with sampling points on a sphere is developed to extract features from the spherical representation, and then, a Segmentation Feature Fusion(SFF) methodology is utilized to combine the features with ones extracted from the equirectangular representation. In contrast with the existing methods using a teacher-student model to obtain a lighter model of depth estimation, we use a teacher-student model to learn the latent features of depth images. This results in a trained model which estimates the depth map of an equirectangular image using not only the feature maps extracted from an input equirectangular image but also the distilled knowledge learnt from the ground truth of depth map of a training set. In experiments, the proposed method is tested on several well-known 360 monocular depth estimation benchmark datasets, and outperforms the existing methods for the most evaluation indexes.

A Robust Data-driven Process Modeling Applied to Time-series Stochastic Power Flow

In this paper, we propose a robust data-driven process model whose hyperparameters are robustly estimated using the Schweppe-type generalized maximum likelihood estimator. The proposed model is trained on recorded time-series data of voltage phasors and power injections to perform a time-series stochastic power flow calculation. Power system data are often corrupted with outliers caused by large errors, fault conditions, power outages, and extreme weather, to name a few. The proposed model downweights vertical outliers and bad leverage points in the measurements of the training dataset. The weights used to bound the influence of the outliers are calculated using projection statistics, which are a robust version of Mahalanobis distances of the time series data points. The proposed method is demonstrated on the IEEE 33-Bus power distribution system and a real-world unbalanced 240-bus power distribution system heavily integrated with renewable energy sources. Our simulation results show that the proposed robust model can handle up to 25% of outliers in the training data set.