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We explore the relationship between Wardrop equilibrium and stationary mean-field games (MFG) on networks with flow-dependent costs. First, we present the notion of Wardrop equilibrium and the first-order MFG model on networks. We then reformulate the MFG problem into a road traffic problem, establishing that the flow distribution of the MFG solution is the correspondingWardrop equilibrium. Next, we prove that the solution of the MFG model can be recovered using the corresponding Wardrop equilibrium. Next, we examine the cost properties and calibrate MFG with respect to travel cost problems on networks. We propose a novel calibration approach for MFGs. Additionally, we demonstrate that non-monotonic MFGs can be generated by even simple travel costs. [ABSTRACT FROM AUTHOR]

The widespread availability of depth sensors like the Kinect camera makes it easy to gather three-dimensional (3D) data. However, accurately and efficiently merging large datasets collected from di¤erent views is still a core problem in computer vision. This question is particularly challenging if the relative positions of the views are not known, if there are few or no overlapping points, or if there are multiple objects. Here, we develop a method to reconstruct the 3D shapes of objects from depth data taken from di¤erent views whose relative positions are not known. Our method does not assume that common points in the views exist nor that the number of objects is known a priori. To reconstruct the shapes, we use partial di¤erential equations (PDE) to compute upper and lower bounds for distance functions, which are solutions of the Eikonal equation constrained by the depth data. To combine various views, we minimize a function that measures the compatibility of relative positions. As we illustrate in several examples, we can reconstruct complex objects, even in the case where multiple views do not overlap, and, therefore, do not have points in common. We present several simulations to illustrate our method including multiple objects, non-convex objects, and complex shapes. Moreover, we present an application of our PDE approach to object classification from depth data. [ABSTRACT FROM AUTHOR]