Alignment is a very useful operation. For example, it can be used for warping, morphing, matching, velocimetry, filter shaping, super-resolution, texture-transfer, and data assimilation. I study field alignment to recover parametric and nonparametric deformations and this is funded through an NSF Grant.A simple image alignment example (play in your browser)
Ravela, Emanuel and McLaughlin have identified the role that field alignment can play in improving assimilation under position errors. Classical formulations of data-assimilation, whether sequential, ensemble-based or variational, are amplitude adjustment methods. Such approaches do not deal well with position errors, which can be seen readily, for example, when a forecast of a localized weather feature is displaced from its observed location. Unless the state is well observed, compensating position errors by adjusting amplitudes can produce unacceptably dìdistorted states, adversely affecting analysis, verication and subsequent forecasts. There are many sources of position error, including errors in initial conditions, observations, model parameters and model structure. It is non-trivial to decompose position error into these constituent sources. But correcting position errors is essential for operationally predicting strong, localized weather events such as tropical cyclones. Indeed, to ameliorate these problems, forecasters currently resort to adhoc procedures, such as bogussing. A technique for field alignment, aligning the current model state with observations is developed by solving an auxiliary variational optimization problem to adjust a continuous field of local displacements. In contrast to other alignment techniques, the preprocessing step does not rely on defining features explicitly, and can coexist easily with feature based methods (when the correspondence problem is solved!). Once alignment has been performed, a standard amplitude-based data assimilation technique may be applied and we have developed both deterministic and ensemble versions of our algorithm (see right).
S. Ravela, K. Emanuel and D. McLaughlin, Data Assimilation
by Field Alignment, [To Appear, Physica (D)]
S. Ravela, K. Emanuel and D. McLaughlin, Multivariate Field Alignment for Data Assimilation, EGU2004