Accuracy in depth estimation - Stereo Vision

Question

I am doing a research in stereo vision and I am interested in accuracy of depth estimation in this question. It depends of several factors like:

• Proper stereo calibration (rotation, translation and distortion extraction),
• image resolution,
• camera and lens quality (the less distortion, proper color capturing),
• matching features between two images.

Let's say we have a no low-cost cameras and lenses (no cheap webcams etc).

My question is, what is the accuracy of depth estimation we can achieve in this field? Anyone knows a real stereo vision system that works with some accuracy? Can we achieve 1 mm depth estimation accuracy?

My question also aims in systems implemented in opencv. What accuracy did you manage to achieve?

Answer 1

Q. Anyone knows a real stereo vision system that works with some accuracy? Can we achieve 1 mm depth estimation accuracy?

Yes, you definitely can achieve 1mm (and much better) depth estimation accuracy with a stereo rig (heck, you can do stereo recon with a pair of microscopes). Stereo-based industrial inspection systems with accuracies in the 0.1 mm range are in routine use, and have been since the early 1990's at least. To be clear, by "stereo-based" I mean a 3D reconstruction system using 2 or more geometrically separated sensors, where the 3D location of a point is inferred by triangulating matched images of the 3D point in the sensors. Such a system may use structured light projectors to help with the image matching, however, unlike a proper "structured light-based 3D reconstruction system", it does not rely on a calibrated geometry for the light projector itself.

However, most (likely, all) such stereo systems designed for high accuracy use either some form of structured lighting, or some prior information about the geometry of the reconstructed shapes (or a combination of both), in order to tightly constrain the matching of points to be triangulated. The reason is that, generally speaking, one can triangulate more accurately than they can match, so matching accuracy is the limiting factor for reconstruction accuracy.

One intuitive way to see why this is the case is to look at the simple form of the stereo reconstruction equation: z = f b / d. Here "f" (focal length) and "b" (baseline) summarize the properties of the rig, and they are estimated by calibration, whereas "d" (disparity) expresses the match of the two images of the same 3D point.

Now, crucially, the calibration parameters are "global" ones, and they are estimated based on many measurements taken over the field of view and depth range of interest. Therefore, assuming the calibration procedure is unbiased and that the system is approximately time-invariant, the errors in each of the measurements are averaged out in the parameter estimates. So it is possible, by taking lots of measurements, and by tightly controlling the rig optics, geometry and environment (including vibrations, temperature and humidity changes, etc), to estimate the calibration parameters very accurately, that is, with unbiased estimated values affected by uncertainty of the order of the sensor's resolution, or better, so that the effect of their residual inaccuracies can be neglected within a known volume of space where the rig operates.

However, disparities are point-wise estimates: one states that point p in left image matches (maybe) point q in right image, and any error in the disparity d = (q - p) appears in z scaled by f b. It's a one-shot thing. Worse, the estimation of disparity is, in all nontrivial cases, affected by the (a-priori unknown) geometry and surface properties of the object being analyzed, and by their interaction with the lighting. These conspire - through whatever matching algorithm one uses - to reduce the practical accuracy of reconstruction one can achieve. Structured lighting helps here because it reduces such matching uncertainty: the basic idea is to project sharp, well-focused edges on the object that can be found and matched (often, with subpixel accuracy) in the images. There is a plethora of structured light methods, so I won't go into any details here. But I note that this is an area where using color and carefully choosing the optics of the projector can help a lot.

So, what you can achieve in practice depends, as usual, on how much money you are willing to spend (better optics, lower-noise sensor, rigid materials and design for the rig's mechanics, controlled lighting), and on how well you understand and can constrain your particular reconstruction problem.

Answer 2

I would add that using color is a bad idea even with expensive cameras - just use the gradient of gray intensity. Some producers of high-end stereo cameras (for example Point Grey) used to rely on color and then switched to grey. Also consider a bias and a variance as two components of a stereo matching error. This is important since using a correlation stereo, for example, with a large correlation window would average depth (i.e. model the world as a bunch of fronto-parallel patches) and reduce the bias while increasing the variance and vice versa. So there is always a trade-off.

More than the factors you mentioned above, the accuracy of your stereo will depend on the specifics of the algorithm. It is up to an algorithm to validate depth (important step after stereo estimation) and gracefully patch the holes in textureless areas. For example, consider back-and-forth validation (matching R to L should produce the same candidates as matching L to R), blob noise removal (non Gaussian noise typical for stereo matching removed with connected component algorithm), texture validation (invalidate depth in areas with weak texture), uniqueness validation (having a uni-modal matching score without second and third strong candidates. This is typically a short cut to back-and-forth validation), etc. The accuracy will also depend on sensor noise and sensor's dynamic range.

Finally you have to ask your question about accuracy as a function of depth since d=f*B/z, where B is a baseline between cameras, f is focal length in pixels and z is the distance along optical axis. Thus there is a strong dependence of accuracy on the baseline and distance.

Kinect will provide 1mm accuracy (bias) with quite large variance up to 1m or so. Then it sharply goes down. Kinect would have a dead zone up to 50cm since there is no sufficient overlap of two cameras at a close distance. And yes - Kinect is a stereo camera where one of the cameras is simulated by an IR projector.

I am sure with probabilistic stereo such as Belief Propagation on Markov Random Fields one can achieve a higher accuracy. But those methods assume some strong priors about smoothness of object surfaces or particular surface orientation. See this for example, page 14.