Probabilistic and sequential computation of optical flow using temporal coherence

KalmanFlow 2.0: Efficient Video Optical Flow Estimation via Context-Aware Kalman Filtering

Recent studies on optical flow typically focus on the estimation of the single flow field in between a pair of images but pay little attention to the multiple consecutive flow fields in a longer video sequence. In this paper, we propose an efficient video optical flow estimation method by exploiting the temporal coherence and context dynamics under a Kalman filtering system. In this system, pixel's motion flow is first formulated as a second-order time-variant state vector and then optimally estimated according to the measurement and system noise levels within the system by maximum a posteriori criteria. Specifically, we evaluate the measurement noise according to the flow's temporal derivative, spatial gradient, and warping error. We determine the system noise based on the similarity of contextual information, which is represented by the compact features learned by pre-trained convolutional neural networks. The context-aware Kalman filtering helps improve the robustness of our method against abrupt change of light and occlusion/dis-occlusion in complicated scenes. The experimental results and analyses on the MPI Sintel, Monkaa, and Driving video datasets demonstrate that the proposed method performs favorably against the state-of-the-art approaches.

Optical flow estimation for a periodic image sequence

We propose a temporal modeling approach for determining image motion from a sequence of images wherein the inherent motion is periodic over time. To exploit the periodic nature of the motion, we use a Fourier harmonic representation to model the temporal evolution of the motion field for the entire sequence. We then determine the motion field simultaneously for the different image frames by estimating the parameters of this representation model, where the model order in the Fourier representation serves as a regularization parameter on the temporal coherence of the motion field. This approach can take advantage of the statistics of all the available data in the image sequence. In our experiments, we tested the proposed approach on several motion types at different noise levels, including translational motion, convergent/divergent motion, and cardiac motion. Our results demonstrate that this approach could lead to more robust estimation of the motion field in the presence of strong imaging noise compared to a frame-by-frame estimation approach.

On Kalman filter solution of space-time interpolation

The approximate Kalman filtering algorithm presented previously (see ibid., vol.3, p.773-88, Nov. 1994) for image sequence processing can introduce unacceptable negative eigenvalues in the information matrix and can have degraded performance in some applications. The improved algorithm presented in this note guarantees a positive definite information matrix, leading to more stable filter performance.

Probabilistic motion estimation based on temporal coherence

We develop a theory for the temporal integration of visual motion motivated by psychophysical experiments. The theory proposes that input data are temporally grouped and used to predict and estimate the motion flows in the image sequence. This temporal grouping can be considered a generalization of the data association techniques that engineers use to study motion sequences. Our temporal grouping theory is expressed in terms of the Bayesian generalization of standard Kalman filtering. To implement the theory, we derive a parallel network that shares some properties of cortical networks. Computer simulations of this network demonstrate that our theory qualitatively accounts for psychophysical experiments on motion occlusion and motion outliers. In deriving our theory, we assumed spatial factorizability of the probability distributions and made the approximation of updating the marginal distributions of velocity at each point. This allowed us to perform local computations and simplified our implementation. We argue that these approximations are suitable for the stimuli we are considering (for which spatial coherence effects are negligible).