On the Spatial Statistics of Optical Flow

S. Roth and M. J. Black, “On the spatial statistics of optical flow,” International Journal of Computer Vision (IJCV), vol. 74, no. 1, pp. 33–50, Aug. 2007. [preprint (opens in new tab)]

Conference version:

S. Roth and M. J. Black, “On the spatial statistics of optical flow,” in Proc. of the IEEE International Conference on Computer Vision (ICCV), vol. 1, Beijing, China, Oct. 2005, pp. 42–49, oral presentation, Honorable Mention for the Marr Prize. [preprint (opens in new tab)]


We present an analysis of the spatial and temporal statistics of “natural” optical flow fields and a novel flow algorithm that exploits their spatial statistics. Training flow fields are constructed using range images of natural scenes and 3D camera motions recovered from hand-held and car-mounted video sequences. A detailed analysis of optical flow statistics in natural scenes is presented and machine learning methods are developed to learn a Markov random field model of optical flow. The prior probability of a flow field is formulated as a Field-of-Experts model that captures the spatial statistics in overlapping patches and is trained using contrastive divergence. This new optical flow prior is compared with previous robust priors and is incorporated into a recent, accurate algorithm for dense optical flow computation. Experiments with natural and synthetic sequences illustrate how the learned optical flow prior quantitatively improves flow accuracy and how it captures the rich spatial structure found in natural scene motion.

Synthetic optical flow database

This data set consists of 800 flow field sequences of 250x200 pixels; each sequence is 2 frames long.

Each data file (available below) contains 100 flow field sequences. Each flow field sequence arises from 3 frames of camera motion, which results in two temporally adjacent flow fields. The viewpoint of the second camera frame coincides with the position of the laser range finder that captured the range images used. Because of that, the second optical flow frame is a better approximation to the optical flow as it would arise if the true 3D geometry of the scene was known. Hence, the second flow frame should be used to study the spatial properties of optical flow.

The data files are in MATLAB V7 format and contain a cell array flow_data. This cell array has two indices, the flow sequence number (1..100), and the frame index (1 or 2). Each cell contains a 250x200x2 flow field.


  • Flow sequences 1 through 100 [mat, ~66MB]
  • Flow sequences 101 through 200 [mat, ~66MB]
  • Flow sequences 201 through 300 [mat, ~66MB]
  • Flow sequences 301 through 400 [mat, ~66MB]
  • Flow sequences 401 through 500 [mat, ~66MB]
  • Flow sequences 501 through 600 [mat, ~66MB]
  • Flow sequences 601 through 700 [mat, ~66MB]
  • Flow sequences 701 through 800 [mat, ~66MB]

Note: The optical flow data available here is provided for research and educational purposes only.

Note 2: This material is based upon work supported by the National Science Foundation under Grant No. 0535075. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.