Directional LPA

The kernel design on the sector is done using a modified version of the Local Polynomial Approximation procedure.

This technique allows to design estimation kernels for smoothing and for differentiation.

Directional LPA kernels have a number of valuable benefits:

1) Unlike many other transforms which start from the continuous domain and then discretized, this technique works directly in the multidimensional discrete domain;
2) The designed kernel are truly multivariable, non-separable and anisotropic with arbitrary orientation, width and length;
3) The desirable smoothness of the kernel along and across the main direction is enabled by the corresponding vanishing moment conditions;
4) The kernel support can be flexibly shaped to any desirable geometry in order to capture geometrical structural and pictorial information. In this way a special design can be done for complex form objects and specific applications;
5) The smoothing and corresponding differentiating directional kernels can be designed;
6) These kernels are by definition asymmetric, allowing efficient edge adaptation. Traditional symmetric or nearly-symmetric supports tend to produce either so-called ringing artifacts or oversmoothing in the vicinity of the edges.

The Directional LPA allows to consider several different problems within a unified framework.