A 2D to 3D map includes 3D coordinates of all or a subset of pixels (namely coordinate points) to the 2D image. Implementations choose the interpolation type used, but it is recommended to use a spline based interpolation. See Figure UUU.1.3-1.
Pixels' 3D coordinates could be used for different analyses and computations e.g. measuring the length of a path, and calculating the area of region of interest, 3D computer graphics, registration, shortest distance computation, etc. Some examples of methods using 3D coordinates are listed in the following subsections.
Let the path between points A, and B be represented by set of N following pixels P={pi} and p0=A and pN=B. The length of this path can be computed from the partial lengths between path points by:
and where xi, yi, zi are the 3D coordinates of the point pi which is either available in the 2D to 3D map if pi is a coordinate point or it is computed by interpolation. Here it is assumed that the sequence of path points is known and the path is 4- or 8-connected (i.e., the path points are neighbors with no more than one pixel distance in horizontal, vertical, or diagonal direction). It is recommendable to support sub-pixel processing by using interpolation.
