In this chapter, we start with accuracy analyses with the main emphasis on the specific features of the directional estimates: different LPA orders m and different scales h of the variables. The directionality of the supports and the estimates is specified as corresponding to the anisotropy properties of the object signal y. The directional LPA produces kernels that give accurate reconstruction and estimates for polynomial signals. It follows from the design procedure, which is the moving least-square method, and the polynomials as models of the signal imbedded in the LPA. However, the directional kernels are different from those introduced in Chapter 2 in two important respects. First, the orders m 1 and m 2 of the LPA polynomials are specified for variables x 1 and x 2 independently. Second, these variables enter into the kernels with different scales h 1 and h 2 .