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Tuesday, December 4, 2012

Single View Metrology

Criminisi, et all, in their work Single View Metrology, describe how 3D affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image. This minimal information is typically the vanishing line of a reference plane, and a vanishing point for a direction not parallel to the plane. Their work shows that affine scene structure may then be determined from the image, without knowledge of the camera’s internal calibration (e.g. focal length), nor of the explicit relation between camera and world (pose).

In particular, they show how to (i) compute the distance between planes parallel to the reference plane (up to a common scale factor); (ii) compute area and length ratios on any plane parallel to the reference plane; (iii) determine the camera’s (viewer’s) location. Simple geometric derivations are given for these results. They also develop an algebraic representation which unifies the three types of measurement and, amongst other advantages, permits a first order error propagation analysis to be performed, associating an uncertainty with each measurement.

They demonstrate the technique for a variety of applications, including height measurements in forensic images and 3D graphical modelling from single images.

Building on this foundation, the Measure 3d tool in Amped FIVE computes real-world distances directly on the image. The Measure 3d Single View Metrology implementation is based on the fact that some image lines, which are parallel in the real-world, join in a point in the image, named the vanishing point, due to the perspective. The vanishing points themselves are obtained by identifying, thanks to the geometric information (two or more lines for each x/y/z direction) provided by the user, sets of 3D points (x,y,z) that belong to the segment lines for each direction of interest. The scene perspective can be reconstructed from vanishing points: transforming the geometric information into a system of linear constraints on the coordinates of the 3D points and using the 2D observations (the known distance) to further constrain the 3D points. As result, 3D measurements may be computed from a single perspective view of a scene given only this minimal geometric information determined from the image.

The validity of the Single View Metrology approach is assessed by the Monte Carlo statistical tests: it determines how the uncertainty propagates from input to output of the computation chain and estimate the measurement accuracy.

But, as powerful as Amped FIVE is, it's only as good as the inputs received from a trained analyst. One of the examples used in my training sessions is a video from a convenience store. I have been to the scene and measured the floor tiles as 12" square. There is a discernible checker board pattern to the tiles, so it's easy to get X and Y segments from an 8' x 8' block of tiles. The store has two entrance/exit doors with security measuring tape affixed to the door frames, giving us the Z. Once this information is put into FIVE, measurements can be taken from within the scene with a high degree of reliability.

The biggest difference between SVM based photogrammetry, and methods like reverse projection photogrammetry, or products like iWitness, is that isn't the need to re-shoot the scene. Measurements are taken of the area that was captured by the video already in hand, like the floor tiles and the door frame - things that don't generally change. These measurements are then used for your calculations, lowering costs and time to completion / results.

Thus, if your are interested in adding Photogrammetry to your offerings, you should consider adding Amped FIVE to your tool kit.

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