Varying intrinsic parameters

Can the constant intrinsic parameters hypothesis be relaxed, if more than three views are available? Let's count the unknowns, in the case that n_k parameters are known and n_c parameters are constant. Every view apart from the first one introduces 5 - n_k - n_c unknowns; the first view introduces 5 - n_k unknowns, therefore the unknown intrinsic parameters can be computed provided that

$$5n - 8 \geq (n-1) (5 - n_k - n_c) + 5 - n_k,$$ (55)

which is equivalent to the following equation reported in [36]:

$$n n_k + (n-1) n_c \geq 8 .$$ (56)

Despite the problem for constant intrinsic parameters is far from being completely solved, the more general one in which intrinsic parameters are varying is gaining the attention of researchers. In fact, Bougnoux's method already copes with varying parameters. Heyden and Åström [21] proposed a method that works with varying and unknown focal length and principal point. Later, they proved [22] that it is sufficient to know any of the five intrinsic parameters to make Euclidean reconstruction, even if all other parameters are unknown and varying (this can be obtained as a special case of Eq.56). A similar method that can work with different types of of constraints has been recently presented in [36]. Mendonça and Cipolla algorithm [33] copes with varying parameters as well.