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Personal videos often contain visual distractors, which are objects that are accidentally captured that can distract viewers from focusing on the main subjects. We propose a method to automatically detect and localize these distractors through learning from a manually labeled dataset. To achieve spatially and temporally coherent detection, we propose extracting features at the Temporal-Superpixel (TSP) level using a traditional SVM-based learning framework. We also experiment with end-to-end learning using Convolutional Neural Networks (CNNs), which achieves slightly higher performance than other methods. The classification result is further refined in a post-processing step based on graph-cut optimization. Experimental results show that our method achieves an accuracy of 81% and a recall of 86%. We demonstrate several ways of removing the detected distractors to improve the video quality, including video hole filling; video frame replacement; and camera path re-planning. The user study results show that our method can significantly improve the aesthetic quality of videos.

This paper proposes a neural network approach for efficiently solving general nonlinear convex programs with second-order cone constraints. The proposed neural network model was developed based on a smoothed natural residual merit function involving an unconstrained minimization reformulation of the complementarity problem. We study the existence and convergence of the trajectory of the neural network. Moreover, we show some stability properties for the considered neural network, such as the Lyapunov stability, asymptotic stability, and exponential stability. The examples in this paper provide a further demonstration of the effectiveness of the proposed neural network. This paper can be viewed as a follow-up version of [20], [26] because more stability results are obtained.

Computing the distance among linguistic objects is an essential problem in natural language processing. The word mover’s distance (WMD) has been successfully applied to measure the document distance by synthesizing the low-level word similarity with the framework of optimal transport (OT). However, due to the global transportation nature of OT, the WMD may overestimate the semantic dissimilarity when documents contain unequal semantic details. In this paper, we propose to address this overestimation issue with a novel Wasserstein-Fisher-Rao (WFR) document distance grounded on unbalanced optimal transport theory. Compared to the WMD, the WFR document distance provides a trade-off between global transportation and local truncation, which leads to a better similarity measure for unequal semantic details. Moreover, an efficient prune strategy is particularly designed for the WFR document distance to facilitate the top-k queries among a large number of documents. Extensive experimental results show that the WFR document distance achieves higher accuracy that WMD and even its supervised variation s-WMD.

We study randomly initialized residual networks using mean field theory and the theory of difference equations. Classical feedforward neural networks, such as those with tanh activations, exhibit exponential behavior on the average when propagating inputs forward or gradients backward. The exponential forward dynamics causes rapid collapsing of the input space geometry, while the exponential backward dynamics causes drastic vanishing or exploding gradients. We show, in contrast, that by adding skip connections, the network will, depending on the nonlinearity, adopt subexponential forward and backward dynamics, and in many cases in fact polynomial. The exponents of these polynomials are obtained through analytic methods and proved and verified empirically to be correct. In terms of the" edge of chaos" hypothesis, these subexponential and polynomial laws allow residual networks to" hover over the boundary between stability and chaos," thus preserving the geometry of the input space and the gradient information flow. In our experiments, for each activation function we study here, we initialize residual networks with different hyperparameters and train them on MNIST. Remarkably, our initialization time theory can accurately predict test time performance of these networks, by tracking either the expected amount of gradient explosion or the expected squared distance between the images of two input vectors. Importantly, we show, theoretically as well as empirically, that common initializations such as the Xavier or the He schemes are not optimal for residual networks, because the optimal initialization variances depend on the depth