This chapter provides an overview of the techniques introduced so far when a random sample of landmark configurations is available in two dimensions. In this chapter we make particular use of complex numbers which leads to simple methodology in this important case. Although most of the material for this chapter has been described using general matrix notation in previous chapters, it is often much simpler to use complex vectors in the 2D case. This chapter is designed to be largely self-contained for planar shape analysis using complex notation.

Consider two centred configurations *y* = (*y*_{1}, …, *y _{k}*)

A suitable procedure is to match *w* to *y* using the similarity transformations and the differences between the fitted and observed *y* indicate the magnitude of the difference in shape between *w* and *y*. Consider the complex regression equation

(8.1)

where *A* = (*A*_{1}, *A*_{2})^{T} = (*a* + *ib*, βe^{iθ})^{T} are the 2 × 1 complex parameters with translation *a* + *ib*, scale ...

Start Free Trial

No credit card required