Directional 2D Recursive Filters Based on Analog Prototypes and Their Block Filtering Implementation

This work presents a design technique for a type of recursive 2D filter, specifically anisotropic filters, with a frequency response depending on orientation. This design method is based on a 1D analog low-pass prototype filter of a specified approximation type (for instance, elliptical) and imposed order and selectivity. Next, a special frequency transformation is applied to this prototype, leading to a 2D oriented filter in the analog version. Next, applying the well-known bilinear transformation on the two frequency axes, we finally derive the frequency response of the desired 2D directional filter, with a given orientation angle in the frequency plane. The obtained 2D filter is of low complexity, its matrices being of size 5 × 5, and therefore can be efficiently implemented. Moreover, the filter is parametric (tunable), its selectivity and orientation angle being adjustable through independent parameters, which appear explicitly in the filter matrices. Several design examples using the proposed method are given for specified values of parameters (selectivity and orientation angle). The main application of this type of filter is enhancing and extracting straight lines or various oriented features and details from an image, as shown in the provided simulation results. A very efficient system-level implementation is also developed, using the block filtering approach, which ensures a higher degree of parallelism and a lower arithmetic complexity.