The bundle adjustment, or more specifically, the colinearity math model it is based on, is undisputedly the most accurate method to perform 3D scene reconstruction from multiple images. It has been the gold standard since first developed in 1957–1959. The limitations of the method have motivated this investigation into how it could be improved.

The geometry of trilinear bundle adjustment for Multi-Image Measurement. Two lines are projected from image O’’’ (which revolve to a line in object space), and one line is projected from each of the remaining two images.
The Johnson Space Center Image Science and Analysis group (ISAG) started a research project to determine whether it was possible to map the inside of micro-meteoroid impacts on the Orion spacecraft’s thermal protection system tiles. However, the geometry required to look into the tile cavities is oblique to the tile surface, and the stereo models are convergent with one another. It has been found that if camera stations are determined through a bundle adjustment, and the relative orientations decomposed from the camera exterior orientations, then the resulting stereo models often have Y-parallax, and it is difficult to see in 3D. This makes it challenging and tedious to effectively merge measurements from multiple models.

Bundle adjustment, being entirely based on colinearity, requires that there be an object point coordinate calculated for every conjugate image measurement, despite it being well established that geometry that is poor for photogrammetric intersection may in fact be valuable for constraining image orientations. Multiview constraints present an easily automated approach to using the orientation data implied in these tie points that does not involve the object space coordinates. This ability has led to the invention of a new classification of tie points — those that are used only to enforce camera orientation constraints.

The concept of nuisance parameters can be expanded beyond the invention of orientation points. In the time-constrained world of machine vision, a bundle could be tailored to calculate only the necessary object space data. In the case of camera calibration by bundle adjustments, all of the object space coordinates are nuisance parameters. Thus, a free network design that calculates no object point coordinates at all can be used.

Colinearity-based bundle adjustment is generally improved when multiview constraints are included in the math model. In numerous test cases, the enhanced bundle adjustment demonstrated improved reliability and accuracy with reduced total processor time. This constitutes an improvement to the fundamental math model for multi-image measurement. The enhanced bundle adjustment has demonstrated improved reliability and accuracy with reduced total processor time.

This work was done by Orrin Thomas of Geocontrol Systems and Edward Oshel of Jacobs Technology Inc. for Johnson Space Center. MSC-24708-1


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This article first appeared in the September, 2014 issue of Software Tech Briefs Magazine.

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