Methods and apparatus for refractive flow measurement with three dimensions and uncertainty
An imaging method and corresponding apparatus according to an embodiment of the present invention enables measurement and visualization of fluid flow. An embodiment method includes obtaining video captured by a video camera with an imaging plane. Representations of motions in the video are correlated. A textured background of the scene can be modeled as stationary, with a refractive field translating between background and video camera. This approach offers multiple advantages over conventional fluid flow visualization, including an ability to use ordinary video equipment outside a laboratory without particle injection. Even natural backgrounds can be used, and fluid motion can be distinguished from refraction changes. Depth and three-dimensional information can be recovered using stereo video, and uncertainty methods can enhance measurement robustness where backgrounds are less textured. Example applications can include avionics and hydrocarbon leak detection.
1. A method comprising:
obtaining videos captured by at least two video cameras having respective imaging planes;
by a processor, determining apparent motions of a refractive field, through which light passes from a textured background to the respective imaging planes, by analyzing changes in intensity or phase in the videos as a function of translations of intensities of elements of the refractive field;
by the processor, determining actual motions of the refractive field by correlating, over time and space, representations of the apparent motions from frame to frame of the videos as a function of translations of refraction gradients of the elements of the refractive field; and
calculating, based on the actual motions determined by correlating the representations of apparent motions over time and space, a depth of the actual motions of the refractive field.
2. The method of claim 1 , further comprising determining, based upon the correlated representations, a three-dimensional velocity of the refractive field.
3. The method of claim 1 , wherein the textured background is out-of-focus at at least one of the camera imaging planes.
4. The method of claim 1 , wherein the imaging planes of the at least two video cameras are parallel to each other.
5. The method of claim 1 , wherein correlating the representations of the apparent motions in the videos includes matching representations of apparent motions in one of the videos to representations of apparent motions in another of the videos.
6. The method of claim 1 , wherein correlating the representations includes assuming that for each given time, and for a given spatial position in the videos, the representations of apparent motions corresponding to the given time and spatial position are the same from video-to-video.
7. The method of claim 1 , further including determining an uncertainty of at least one of the depth of the refractive field and a velocity of the refractive field calculated from the correlated representations.
8. The method of claim 7 , wherein determining the uncertainty includes weighting the representations of the apparent motions as a function of a variance of an optical flow related to the representations of the motions.
9. The method of claim 7 , wherein determining the uncertainty includes defining weighted representations of motions to be a logarithm of a covariance between a representation of the apparent motion in one video and a representation of apparent motion in another video.
10. The method of claim 7 , wherein determining the uncertainty includes weighting the representations of the apparent motions as a function of a degree of texturing of the textured background.
11. The method of claim 1 , wherein correlating the representations of apparent motions includes correlating as a function of the translations of the refractive field through which light passes from a natural textured background to the respective imaging planes.
12. An apparatus comprising:
memory configured to store videos obtained from at least two video cameras with respective imaging planes;
a processor configured to determine apparent motions of a refractive field, through which light passes from a textured background to the respective imaging planes, by analyzing changes in intensity or phase in the videos as a function of translations of intensities of elements of the refractive field;
the processor further configured to determine actual motions of the refractive field by correlating, over time and space, representations of the apparent motions from frame to frame of the videos as a function of translations of refraction gradients of the elements of the refractive field, and
the processor being further configured to calculate, based on the actual motions determined by correlating the representations of apparent motions over time and space, a depth of the actual motions of the refractive field.
13. The apparatus of claim 12 , wherein the processor is further configured to calculate a velocity of the refractive field based upon the correlated representations of the apparent motions.
14. The apparatus of claim 12 , wherein the refractive field is a fluid.
15. The apparatus of claim 12 , wherein the respective imaging planes are parallel to each other.
16. The apparatus of claim 12 , wherein the processor is further configured to match the representations of the apparent motions obtained from one of the video cameras to the representations of the apparent motions obtained from another of the video cameras.
17. The apparatus of claim 12 , wherein the processor is further configured to correlate the representations of the apparent motions using an assumption that for each given time, and for a given spatial position in the videos, the representations of the apparent motion corresponding to the given time and spatial position are the same in the videos.
18. The apparatus of claim 12 , wherein the processor is further configured to determine an uncertainty of at least one of the depth of the refractive field and a velocity of the refractive field calculated from the correlated representations.
19. The apparatus of claim 18 , wherein the processor is further configured to determine the uncertainty using a weighting of the representations of the apparent motions as a function of a variance of an optical flow related to the representations of the apparent motions.
20. The apparatus of claim 18 , wherein the processor is further configured to determine the uncertainty using weighted representations of the apparent motions defined as a logarithm of a covariance between a representation of apparent motion in one video and a representation of apparent motion in another video.
21. The apparatus of claim 18 , wherein the processor is further configured to determine the uncertainty using a weighting of the representations of the apparent motions, the weighting being a function of a degree of texturing of the textured background.
22. The apparatus of claim 12 , wherein the textured background is a natural textured background.
23. The method of claim 1 , wherein the at least two video cameras are microscopy video cameras, and wherein the correlating is done as a function of translations of a microscopic refractive field.
24. The method of claim 1 , further including displaying the actual motions of the refractive field by way of representations in an augmented reality or virtual reality display.