We present a simple, fully-convolutional model for real-time (> 30 fps) instance segmentation that achieves competitive results on MS COCO evaluated on a single Titan Xp, which is significantly faster than any previous state-of-the-art approach. Moreover, we obtain this result after training on only one GPU. We accomplish this by breaking instance segmentation into two parallel subtasks: (1) generating a set of prototype masks and (2) predicting per-instance mask coefficients. Then we produce instance masks by linearly combining the prototypes with the mask coefficients. We find that because this process doesn't depend on repooling, this approach produces very high-quality masks and exhibits temporal stability for free. Furthermore, we analyze the emergent behavior of our prototypes and show they learn to localize instances on their own in a translation variant manner, despite being fully-convolutional. We also propose Fast NMS, a drop-in 12 ms faster replacement for standard NMS that only has a marginal performance penalty. Finally, by incorporating deformable convolutions into the backbone network, optimizing the prediction head with better anchor scales and aspect ratios, and adding a novel fast mask re-scoring branch, our YOLACT++ model can achieve 34.1 mAP on MS COCO at 33.5 fps, which is fairly close to the state-of-the-art approaches while still running at real-time.

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We consider in this paper the incompressible laminar flow in a porous channel with expanding or contracting walls. While the head-end is closed by a compliant membrane, the downstream end is left unobstructed. For symmetric injection or suction along the uniformly expanding porous walls, the Navier-Stokes equations are reduced to a single, nonlinear, ordinary differential equation. The latter is obtained via similarity transformations in both time and space. The resulting equation is then solved both numerically and asymptotically, using perturbations in the crossflow Reynolds number R. Two separate approaches are presented for each of the injection and suction cases, respectively. For the large injection case, the governing equation is first integrated and the resulting third-order differential equation is solved using the method of variation of parameters. For the large suction case, the governing equation is first simplified near the wall and then solved using successive approximations. Results are then correlated and compared for variations in R and the dimensionless wall expansion rate α. For injection-induced flow, the asymptotic solution becomes more accurate when R/α is increased. Its deviation from the classic sinusoidal profile arising in nonexpanding channels becomes less significant with successive increases in R. For suction-induced flows, faster wall contractions increase the effective Reynolds number −(α + R), thus leading to more precise approximations. For the same absolute value of R, the suction-flow approximation tends to be the most accurate of the two and the least sensitive to variations in α. As −(α + R) is increased, the suction profile approaches the linear form anticipated in nonexpanding channels. By comparison with the injection-induced flow, suction is characterized by improved accuracy, sharper flow turning, and larger