  Images Stacks as Parametric Surfaces (ISPS) is a powerful model that was
originally proposed for image registration. Being closely related to mutual
information (MI) - the most classic similarity measure for image registration,
ISPS works well across different categories of registration problems. The
Signals as Parametric Curves (SPC) model is derived from ISPS extended to
1-dimensional signals. Blind Source Separation (BSS) is a classic problem in
signal processing, where Independent Component Analysis (ICA) based approaches
are popular and effective. Since MI plays an important role in ICA, based on
the close relationship with MI, we apply SPC model to BSS in this paper, and
propose a group of geometrical objective functions that are simple yet
powerful, and serve as replacements of original MI-based objective functions.
Motivated by the geometrical objective functions, we also propose a
second-order-statistics approach, FT-PCA. Both geometrical objective functions
and FT-PCA consider signals as functions instead of stochastic processes, make
use of derivative information of signals, and do not rely on the independence
assumption. In this paper, we discuss the reasonability of the assumptions of
geometrical objective functions and FT-PCA, and show their effectiveness by
synthetic experiments, comparing with other previous classic approaches.
