Time as an operator/observable in nonrelativistic quantum mechanics

The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated with a quantum state solution to the equation. Under the physical assumption that each spatial, as well as the temporal, component of this current is observable, the position in time becomes an operator and an observable in that the weighted average value of the time of the particle's crossing of a complete hyperplane can be simply defined: ... When the space-time coordinates are (t,x,y,z), the paper analyzes in detail the case that the hyperplane is of the type z=constant. Particles can cross such a hyperplane in either direction, so it proves convenient to introduce an indefinite metric, and correspondingly a sesquilinear inner product with non-Hilbert space structure, for the space of quantum states on such a surface. >... A detailed formalism for computing average crossing times on a z=constant hyperplane, and average dwell times and delay times for a zone of interaction between a pair of z=constant hyperplanes, is presented.Comment: 31 pages, no figures. Differs from published version by minor corrections and additions, and two citation

Two-Stream Action Recognition-Oriented Video Super-Resolution

We study the video super-resolution (SR) problem for facilitating video analytics tasks, e.g. action recognition, instead of for visual quality. The popular action recognition methods based on convolutional networks, exemplified by two-stream networks, are not directly applicable on video of low spatial resolution. This can be remedied by performing video SR prior to recognition, which motivates us to improve the SR procedure for recognition accuracy. Tailored for two-stream action recognition networks, we propose two video SR methods for the spatial and temporal streams respectively. On the one hand, we observe that regions with action are more important to recognition, and we propose an optical-flow guided weighted mean-squared-error loss for our spatial-oriented SR (SoSR) network to emphasize the reconstruction of moving objects. On the other hand, we observe that existing video SR methods incur temporal discontinuity between frames, which also worsens the recognition accuracy, and we propose a siamese network for our temporal-oriented SR (ToSR) training that emphasizes the temporal continuity between consecutive frames. We perform experiments using two state-of-the-art action recognition networks and two well-known datasets--UCF101 and HMDB51. Results demonstrate the effectiveness of our proposed SoSR and ToSR in improving recognition accuracy.Comment: Accepted to ICCV 2019. Code: https://github.com/AlanZhang1995/TwoStreamS

The role of terminators and occlusion cues in motion integration and segmentation: a neural network model

The perceptual interaction of terminators and occlusion cues with the functional processes of motion integration and segmentation is examined using a computational model. Inte-gration is necessary to overcome noise and the inherent ambiguity in locally measured motion direction (the aperture problem). Segmentation is required to detect the presence of motion discontinuities and to prevent spurious integration of motion signals between objects with different trajectories. Terminators are used for motion disambiguation, while occlusion cues are used to suppress motion noise at points where objects intersect. The model illustrates how competitive and cooperative interactions among cells carrying out these functions can account for a number of perceptual effects, including the chopsticks illusion and the occluded diamond illusion. Possible links to the neurophysiology of the middle temporal visual area (MT) are suggested