Alignment

Alignment provides a general frame of referencing that can applied to homogeneous (commensurate) as well as heterogeneous (non-commensurate) information.

The information entering a fusion process should be aligned. Let S be the union set of sources. The alignment of the sources defines a common representation (X_S) on the basis of the measurements (z_S)^t, and the representations (X_S)^t at instant t. Differently said, a common co-ordinate system (e.g., geographical space and time) should be found wherein the sources data as well as the global knowledge can be represented. The data are said aligned, and the relevant operations are called alignment operations or alignment processes. This is called alignment, or conditioning.

For example, geocoding airborne or space-borne images is part of the alignment operation. Geocoding aims at providing an assessment of the absolute (or relative) geographical location of a pixel. Similarly mathematical techniques exist, which render two images of the same object superimposable, including a resampling for harmonizing the pixel sizes.

Alignment provides a general frame of referencing that can applied to homogeneous (commensurate) as well as heterogeneous (non-commensurate) data. This is a difficult problem, and there is no general theory. Assume a parallelepiped made of metal, observed by a laser and by X-rays. The common reference space of these two non-commensurate sources has three spatial dimensions. However the depth perception is ill defined because of the depth integration performed by the X-rays sensor and its sensitivity to heterogeneity in the piece of metal. Hence it is not easy to establish the 3-D space under concern. If one adds another source, non-commensurate to the two others, the problem is getting more complicated (e.g., electron microscope).

Alignment may request a conversion / transformation of observations. For example, it may be necessary to convert all data into optical paths in order to combine them. Alternatively, it may request an extraction of attributes, which may be the appropriate quantities to fuse, especially in the case of non-commensurate observations. Models may be necessary for aligning two sets of commensurate observations acquired on different supports, e.g., pin-point measurements integrated over a given period of time and instantaneous measurements of the same entity / phenomenon integrated over a surface or within a volume.

Depending upon the case, corrections of changes in illumination of the object or in attenuation of the signal between the target and the sensor should be performed. This may occur in natural environment: a change in atmospheric constituents induces changes in light propagation, or in industrial environment: dust or paint aerosol may influence the illumination of the object to sense.

The concept of alignment is extended to a wider reference space (representation space). It includes the standardization of units in case of measurements, the calibration of sensors, the corrections of changes in illumination, the standardization in taxonomy if sources are attributes, or in syntax and lexicon if sources are rules, the selection of a common language for verbal or written reports etc.

Indeed alignment is part of the fusion process. It is sometimes considered as a pre-processing, but it should be stressed that this operation is solely performed in order that the information satisfies some constraints imposed by the objectives of the fusion process. That alignment is part of the fusion process may be hidden by the fact that information providers, including instruments makers, may supply data that are already aligned and ready for subsequent processing by customers.

26-08-2001 - Copyright L. Wald, Armines / Ecole des Mines de Paris