Principles of Modern Radar - Volume 2 1891121537

642 CHAPTER 14 Automatic Target RecognitionFIGURE 14-2BMP-2 vehicle atthree aspect angles:a) 0 degrees,b) 45 degrees, andc) 90 degrees.(Reproduced fromMSTAR dataset withpermission.)(a) (b) (c)the position and orientation of the candidate target (see Figure 14-2 for an example ofchanging target features with aspect angle). Pose estimation is useful in that it (1) isrequired for simulating complicated physical mechanisms for developing a set of modelsignatures against which to compare test images, (2) optimizes the search time by reducingthe model database that must be searched, and (3) allows more features to be exploitedin the recognition task [22]. One algorithm for pose estimation translates and rotates atarget-sized rectangular template around the image until the energy within the template ismaximized [1]. A more complex, but robust, scheme is to find closed-contour signaturesof the target through segmentation and then apply four independent, but ranked, criteriafor finding the aspect angle. Three of these criteria are determined from the informationprovided within the smallest rectangle, or bounding box, completely encapsulating thetarget: target-to-background ratio (TBR), perimeter, and edge pixel count. The aspectangle yielding a rectangle with the maximum TBR within the box, minimum perimeter ofthe box itself, and maximizing the number of pixels on the target contour that are in a closeneighborhood to one of the major edges of the box [22]. To counter the limitations of thebounding box criteria caused by box misalignment from anomalies in the segmentationprocess, the Hough transform criteria detects straight lines in the image and the orientationsof the longest three straight lines in the image of the target contour are used to approximatethe target pose [22]. Although these criteria work well, the cardinal points of 0 ◦ and 180 ◦present a generic, round-shaped signature that may require an additional procedure toidentify [22].The Hilbert-Schmidt (minimum mean-squared error) estimator is yet another methodof target aspect estimation [23]. For objects on a flat surface, target orientations exist inthe special orthogonal group of dimension 2 and can be represented by a 2 × 2 matrixwith determinant one [23]. The Hilbert-Schmidt distance between two rotation matrices,A =[ ]cos θ1 − sin θ 1and B =sin θ 1 cos θ 1[ ]cos θ2 − sin θ 2, can then be expressed assin θ 2 cos θ 2d 2 HS (A, B) =‖A − B‖2 HS = tr[(A − B)T (A − B)] = 2n − 2tr[A T B]= 2n − 2tr[B T A] = 4 − 4 cos(θ 1 − θ 2 ) (14.12)where n is the dimension of the rotation matrices (i.e., 2) [23]. In this way, orientation canbe estimated by finding the orientation that minimizes the conditional mean (conditionalon the SAR image and target type) of the squared Hilbert-Schmidt distance (see [23] formore details).