## Spatial Matched Filter Classifiers for SAR (2)

A typical target recognition using SAR is done in multiple stages and is illustrated by the block diagram in Fig. 7 (13). In the first stage, a CFAR detector prescreens by locating potential targets on the basis of radar amplitude. Since a single target may produce multiple detections, the CFAR detections are clustered (grouped together). Then a region of interest (ROI) around the centroid of each cluster is passed to the next stage of the algorithm for further processing.

The second stage takes each ROI as its input and analyzes it. The goal of this discrimination stage is to reject natural-clutter false alarms while accepting real targets. This stage consists of three steps: (1) determining the position and orientation of the detected object, (2) computing simple texture features, and (3) combining the features into a discrimination statistic that measures how “targetlike” the detection object is.

The third stage is classification, where a 2-D pattern-matching algorithm is used to (1) reject clutter false alarms caused by man-made clutter discretes (buildings, bridges, etc.) and (2) classify the remaining detected objects. Those detected objects that pass the second stage are matched against stored reference templates of targets. If none of the matches exceeds a minimum required score, the detected object is classified as clutter; otherwise, the detected object is assigned to the class with the highest match score.

Matched filters are investigated in 2 as pattern-matching classifiers in the target recognition system shown in Fig. 7. They are synthetic discriminant function (SDF), the minimum average correlation energy (MACE) filter, the quadratic distance correlation classifier (QDCC), and the shift-invariant 2-D

r> Fig. 6. Edges refined using IFSAR result. |

pattern-matching classifier. The basic structure of the SDF and MACE filter is characterized in the frequency domain by

where H denotes the DFT of the spatial matched filter. The matrix X is composed of a set of target training vectors obtained by taking the DFT of the target training images. The vector U represents a set of constraints imposed on the values of the correlation peaks obtained when the training vectors are run through the spatial matched filter. The matrix A represents a positive definite weighting matrix. A is an identity matrix for SDF

Fig. 7. Block diagram of a typical baseline target recognition system. [Adapted from Novak et al. (13)]. |

and is the inverse of the following matrix D.

where N is the number of training images and p is the dimension of the training vectors.

In the QDCC, the DFT of the spatial matched filter is expressed by

where m1 and m2 are means of the DFTs of the training images for classes 1 and 2, respectively. S is a diagonal matrix defined by

where M1 and M2 are matrices with elements of m1 and m2 placed on the main diagonal, and Xi and Yi are ith training vectors from classes 1 and 2, respectively.

In the shift-invariant 2-D pattern-matching classifier, the correlation scores are calculated by

where T is the DFT of the dB-normalized test image and Ri is the ith reference template.

Novak et al. (2) did extensive experiment with the high-resolution (1 ft x 1 ft) fully polarimetric SAR data. In the four-class classification experiment using four types of spatial matched filter classifiers, it is reported that all targets are correctly classified (2).

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