**5.2 Distortion range**

54 Advances in Object Recognition Systems

system, we keep constant the weight connection values which are set to be equal to a

Fig. 7. (Adapted by Kypraios et al., 2008) shows (a) correlation peak-height versus the outof-plane rotation angles of the object over the range of 20° to 70°. We tested the M-HONN system with the true-class object's intermediate car poses over the same range out-of-plane rotated at 10° increments; (b) the non-normalised PCE values of the test images at 10°

Fig. 7 (a) shows the plot of the correlation-peak height for each input image for the M-HONN system. From the plot it is shown that the M-HONN system is invariant to the outof-plane rotation, since it has produced consistent correlation peaks for both the in-class training and non-training images around the fixed-correlation peak-height value of unity. The consistency of the correlation peak values that the M-HONN system has exhibited demonstrate the system's ability to interpolate well between the intermediate car poses at 10 increments. Earlier (Kypraios et al., 2008; Kypraios, 2009; Kypraios, 2010), we have shown the NNET includes information for reference and non-reference images of the trueclass object. Hence, the NNET interpolates non-linearly between the reference and nonreference images to follow the activation function graph. Moreover, the NNET is able to

increments versus the angles of view over the range of 20° to 70°.

generalize between all the reference and non-reference images.

(randomly) chosen image included in the training set, here to be *<sup>o</sup> <sup>60</sup> x m,n* .

The second tests series (Jamal-Aldin et al., 1997; Jamal-Aldin et al., 1998; Kumar & Hassebrook, 1990) was carried out to assess the distortion range (Refregier, 1990; Refregier, 1991, Kypraios et al., 2008) of the M-HONN system. The training set consisted of images for a distortion range over 0 to 90 . We used several smaller test sets, which consisted of two in-class training images at a widely separated angle within the range 10 20 30 40 50 60 70 80 and a third non-training in-class image lying on the bisector angle of the two in-class training images (see Fig. 8 (a)). The intermediate non-training car pose image was 3 <sup>ˆ</sup> 5 ,40 i.e. 3 5 10 15 20 25 30 35 40 . Three randomly chosen training images, out-of-plane rotated at 110 ,130 and 140 , were added in the training set of the M-HONN system which fell inside the false-class. The targets of the trueclass objects and of the false-class objects were found to be best set for the tests series as T 40 true and T 40 false . The M-HONN system has no information built into it on the test images of the intermediate car poses. We constrained the correlation peaks in the constraint matrix to be 1 for the images of the true-class object and 0 for the images of the false-class object.

Fig. 8 (b) shows the correlation-peak height for each input image for the M-HONN system. It is found the system has good performance in recognising all the intermediate car poses of the test set. The correlation-peak height of the in-class input images, intermediate between two training images, lie within a band of greater than 76% of the pre-specified peak-height constant in the constraint matrix *C* for the M-HONN system. From the graph it can be observed that the system tolerated orientation over a range of 3 <sup>ˆ</sup>5 ,40 .
