If you are not swayed away by this time with the title of this musing, then stay with me for a couple of more minutes – lest you continue to be confused with this very important and primary photogrammetric process.
We by now know that the camera's exterior orientation (EO) is defined by its position XYZ and attitudinal angles -omega phi kappa. These 6 parameters are to be determined accurately so that the measurements we make from the photographs are reliable.
How do we get or deduce these six parameters? In the previous musing, we discussed direct georeferencing technique whereby EO is directly determined by various onboard sensors such as GPS and IMU. This technique came into vogue since last 2 decades. Prior to that the EO used to be computed analytically using only ground control points (GCPs).
For determining EO of a single photograph, we need to have 3 distributed GCPs – to be precise 2 horizontal controls for scaling and 3 vertical points for leveling. We write collinearity condition equation – connecting the ground coordinates of GCPs, camera centre and the corresponding image locations – and solve for EO iteratively. Initial XY of the camera is the mean XY of the GCPs while flying altitude the initial Z.
For determining EO of 2 overlapping photographs, we can still manage with only 3 GCPs – provided they lie in the common area (or the model area) of the photographs.
Let us stretch it further where you are to handle 100s of photos – as seldom, or never, the project area to be mapped is covered by one or two photographs. To give you an idea, a small district of India will have to be covered by about 4000 photos of medium scale. Now to compute EO of these 1000s of photos, how many GCPs are needed? Frighteningly enormous – isn't it?
And GCP acquisition is time consuming and a pretty expensive exercise. Hence, a smart technique was evolved in 1950s to minimize the requirement. It is now being called Bundle Block Adjustment (BBA). Let us interpret each of these words from mapping perspective: Bundle, Block and Adjustment. A block is the set of overlapping photographs covering the project area. A bundle is a bundle of photogrammetric rays (or collinearity constraints) mathematically developed for each point – GCPs, tie points and pass points as well.
We know that pass and tie points are present in multiple models- thanks to the usual 60% overlap and 20% sidelap. Each model computes the ground-space coordinates of tie and pass points. Hence, you have multiple XYZs for the same point – albeit the difference in coordinates is small or negligible. So, the statistical average of these coordinates is the adjusted XYZ that we list and use as derived control/check points.
Remember, least squares theory is widely used in photogrammetric analytics involving huge redundancy; processes are highly iterative; and the computed coordinates go through adjustment.
Let us understand how BBA is done for a large block with optimal control. Visualize you have taken a series of overlapping photos of a beautiful landscape. And you printed them. To reconstruct the scene, you carefully place one over the other so that common area is cut out. You may glue them together to provide a seamless view. Such a mosaic, mathematically, is possible to be made with pass and tie points. Stereo models thus made are parallax free, contiguous and seamless-but the 3D measurements are still in arbitrary space. So let's bring in GCPs to transform the coordinates from arbitrary space to ground space. Moot point is how many GCPs are needed?
Having appreciated that the block of photos is one entity- with strong internal relationship established through glue points of common areas- can we support this entity with 3 control points like we did in single model case? Theoretically yes. However, to contain the sag of the block; to reduce the tensions in the block and to limit the propagation of errors, we introduce a few more points. And of course, a few check points to independently verify the adjustment process.
The output of BBA include EO of all camera stations, XYZ of tie and pass points, camera calibration parameters, error log, check point analysis – besides input data such as GCP data, image coordinates.
Can we reduce the GCP requirement to bare minimum? The EO obtained through direct georeferencing is so good that it just requires one control point at each corner of the block to adjust the whole block however large it may be. Great savings in money and no time overruns.
BBA is a challenging and yet interesting process. In every new block, be ready to expect known unknowns, and of course unknown unknowns besides known knowns. It is a common practice to dichotomise the large blocks into manageable sub-blocks. Adjust the sub-blocks individually and merge the sub-blocks in the final stage. It helps if one gets a bit of hang on the least squares theory, geometry of camera, error analysis and knack of interpreting the long reports and graphs that roll out of every adjustment. Another essential ingredient one should display is patience. A spoonful of it makes the process delicious- I mean- reimbursing and repaying!
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