**5.1 Peak sharpness and detectability**

52 Advances in Object Recognition Systems

generalization properties exhibited by a NNET architecture, the number of the training images decreases, in comparison to the typical number of images required for the training

It was proven experimentally that by choosing different values of the classification levels for the true-class ClT and false-class ClF objects, one can control the M-HONN system's behaviour to suit different application requirements, similarly with all the HONN-type

is the absolute distance of the classification levels between the true-class objects

, then the resulting M-HONN system behaves more like a minimum variance

behaves more like a high-pass biased filter, which generally gives sharp correlation peaks and good clutter suppression but is more sensitive to intra-class distortions. Now, when we

synthetic discriminant function (MVSDF) (Kumar, 1986) filter with relatively good intraclass distortion invariance but producing broad correlation peaks. In effect, when Cl

increases, the M-HONN system possesses better discriminatory properties but when Cl

decreases the M-HONN system has better generalising properties. By plotting the isometric

Cl Cl Cl T F (34)

, then the resulting M-HONN system

set of linear combinatorial filters (such as the SDF filter).

Fig. 6. Car park scene used in the training and test sets

and the false-class objects. When we increase Cl

systems. Thus we define:

where Cl 

decrease Cl 

Fig. 5. RX-7 Mazda Efini Police patrol car used in the training and test sets

Here we assessed (Jamal-Aldin et al., 1997; Jamal-Aldin et al., 1998; Kumar & Hassebrook, 1990) M-HONN system's ability to detect non-training in-class images that are oriented at the intermediate angle of view between the training images (Refregier, 1990; Refregier, 1991). The training set consisted of still images out-of-plane rotated between 20 70 degrees at increments of 20 . We tested the M-HONN system with the true-class object's intermediate car poses over the same range at 10 increments. Two randomly chosen intermediate car poses, at 130 and at 140 , were added in the training set of the M-HONN system to create a false-class. We set the target of the false-class object to be T 40 false and of the true-class object to be T 40 true . The M-HONN system had no information on the non-training, intermediate car images in the construction of its composite image. We explicitly constrained the correlation peak in the constraint matrix. Thus, 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. The randomly chosen mask c applied on both the training set and the test set was built from the training set image at 60 , i.e. c= 60 :

 60 *o o o o oo <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> o o o o oo <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> o o <sup>60</sup> <sup>60</sup> o o o o oo <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> <sup>60</sup> x x x x xx 11 12 1n-1 1n 11 1q x x x x xx 21 22 2n-1 2n 21 2q x x x x x x xx m1 m2 mn-1 mn n1 nq w w L w w l Ll w w L w w l Ll W ×L = × w w L w w l Ll* (35)

where *<sup>o</sup> <sup>60</sup> <sup>x</sup> <sup>W</sup>* and *<sup>o</sup> <sup>60</sup> <sup>x</sup> <sup>L</sup>* are the matrices of the input and layer weights. *<sup>o</sup> <sup>60</sup> <sup>x</sup> w m n* are the input weights from the input neuron of the input vector element at row m and column n to the associated hidden layer for the training image *<sup>o</sup> <sup>60</sup> x m,n* at 60 angle of view. *<sup>o</sup> <sup>60</sup> <sup>x</sup> m n l* are the layer weights from the hidden neuron of the layer vector element at row m and column n to the associated output neuron. We set q = 1 since the output layer had only one neuron for a single class of objects. In M-HONN system, instead of multiplying each training image with the corresponding weight connections as done for the constrained- HONN (C-HONN)

Performance Analysis of

**5.2 Distortion range** 

pose image was 3 <sup>ˆ</sup>

false-class object.

**5.3 Discrimination ability** 

of-plane rotated at 40

the Modified-Hybrid Optical Neural Network Object Recognition System Within Cluttered Scenes 55

Fig. 7 (b) shows the non-normalised peak-to-correlation energy (PCE) (Kumar & Hassebrook, 1990) values for the M-HONN system. From the graph, it can be observed that the M-HONN system produced PCE values for the intermediate non-training images close to those produced by the training car images. In effect, the system maintains correlation

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

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

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

The third tests series (Jamal-Aldin et al., 1997; Jamal-Aldin et al., 1998; Kumar & Hassebrook, 1990) was carried out to assess the discrimination ability (Refregier, 1990; Refregier, 1991, Kypraios et al., 2008) of the M-HONN system. In the tests, M-HONN system tried to discriminate between objects of different classes while retaining invariance to inclass distortions. The training set consisted of images of the Jaguar S-type for adistortion range over 20 to 70 at 10 increments. The test set consisted of one training image out-

Police patrol car at the same angle of out-of-plane rotation. Two different training set configuration of still images were experimented with. Firstly, we added two images of the Jaguar S-type at 130 and 140 for the false-class of the system's training set. We constrained the false-class images of the objects to zero correlation peak-height in the synthesis of the M-HONN system's composite image. Secondly, we conducted experiments

5 10 15 20 25 30 35 40 . Three randomly

of the Jaguar S-type and a second image of the out-of-class RX-7

5 ,40 .

peak sharpness for the in-class training and non-training images.

5 ,40 i.e. 3

observed that the system tolerated orientation over a range of 3 <sup>ˆ</sup>

system, we keep constant the weight connection values which are set to be equal to a (randomly) chosen image included in the training set, here to be *<sup>o</sup> <sup>60</sup> x m,n* .

$$\text{(a)}$$

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

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 generalize between all the reference and non-reference images.

Fig. 7 (b) shows the non-normalised peak-to-correlation energy (PCE) (Kumar & Hassebrook, 1990) values for the M-HONN system. From the graph, it can be observed that the M-HONN system produced PCE values for the intermediate non-training images close to those produced by the training car images. In effect, the system maintains correlation peak sharpness for the in-class training and non-training images.
