**4. Optical correlator classifiers**

Since the pioneering work made by VanderLugt on spatial filtering [26–28], it became possible to construct complex matched filters. Several correlation filters for object recognition have been proposed to improve recognition capability, mostly by modifications of the amplitude or phase of the original matched filter.

### **4.1 Optical correlators categories**

All the optical correlator classifiers can be further categorised based on the computational domain i.e. (a) spatial domain, (b) frequency/Fourier domain, and (c) hybrid domain by a combination of spatial and frequency domains.

For the frequency domain, correlator type of filters are commonly used. The correlator type of filters can be further classified into two main classes, the single type of filters and the cascaded type of filters. From the first class, Jamal-Aldin et al. [29– 31] have presented previously their work on the non-linear difference-of-Gaussians synthetic discriminant function (NL-DOG SDF) filter. Their design of the filter was motivated by the good detectability of the modified difference of Gaussians (DOG) filter [32]. In order to improve the interclass discrimination but still keep an intraclass tolerance for a higher distortion range of the true-class object, a non-linear operation was integrated into the synthesis of the modified synthetic discriminant function filter. The DOG function approximates the second- differential operator on the imageintensity function. In practice, when convolved with the image, the DOG filter results to an edge map of the reduced-resolution image. By properly adjusting the ratio of the standard deviations of the inhibitory and excitatory Gaussians to be equal to 1.6, the DOG filter provides smoother performance for the true-class object distortions, in effect improving the intraclass properties of the filter. The NL-DOG SDF filter is based on integrating the NL-DOG operation into the synthesis of the SDF filter as well as the input test images. Mahalanobis et al. [33], were first to propose the minimum average correlation energy (MACE) filter. The MACE filter belongs to the linear combinatorial type of filters derived from the synthetic discriminant function. It is designed to maximise the training set images peak height and minimise the response of the filter to non-training set input images, with the constraint of keeping the peakamplitude response of the filter to a fixed value for all the true-class objects included in the training set. It can be designed to give a fixed peak-amplitude response to the non-training set images, too. The solution to this resulted optimization problem is found by applying the Langrange multipliers method. The resulting MACE filter produces a sharp peak response with narrow sidelobes and with a fixed peak-height for the true-class object images included in the training set of the filter. Later, Mahalanobis et al. [34] observed that filters may perform better if hard constraints are not imposed on the correlation peaks, and suggested the use of unconstrained correlation filters. Despite the previous work in SDF synthesis that assumed the correlation values at the origin are pre-specified, there is no need for such a constraint. Thus by removing the hard constraints, we increase the number of possible solutions, thus improving the chances of finding a filter with better performance. A statistical approach is used for the design of an unconstrained filter. This method produces sharp peaks, it is computationally simpler and the proposed filters offer improved distortion tolerance. The reason lies in the fact that we do not treat training images as deterministic representations of the objects but as samples of a class whose characteristic

parameters are used in encoding the filter. Three types of metrics [33, 35] are used in the design of the unconstrained filters, namely: the average correlation energy (ACE), the average similarity measure (ASM) and average correlation height (ACH). If a filter is designed to maximise the ACH criterion, it is called the maximum average correlation height (MACH) filter [34, 36]. The MACH filter maximises the relative height of the average correlation peak with respect to the expected distortions. The MACH filter yields a high correlation peak in response to the average of the training image vector. Besides optimising the ACH criterion, in practice some other performance measures, e.g. the ACE and ONV, also need to be balanced to better suit different application scenarios. Thus, based on Refregier's approach on optimal trade-off [36] filters, Mahalanobis et al. designed the optimal-tradeoff [37, 38] maximum average correlation height (OT-MACH) filter, which minimises the average correlation height criterion, holding the others constant. By adjusting the values of the three non-negative parameters of *α*,*β and γ* (0 ≤*α*,*β*,*γ* ≤1), we control the OT-MACH filter's behaviour to match different application requirements. If b = g = 0, the resulting filter behaves much like a minimum variance synthetic discriminant function (MVSDF) [39] filter with relatively good noise tolerance but broad peaks. If *α* ¼ *γ* ¼ 0 then the filter behaves more like a MACE filter, which generally exhibits sharp peaks and good clutter suppression but is very sensitive to distortion of the target object. If *α* ¼ *β* ¼ 0, the filter gives high tolerance for distortion but is less discriminating.

From the second class category of cascaded filters [40], Reed and Coupland [41] have studied a cascade of linear shift invariant processing modules (correlators), each augmented with a non-linear threshold as a means to increase the performance of high speed optical pattern recognition. They propose that their cascaded correlators configuration can be considered as a special case of multilayer feed-forward neural networks. They have proven that their cascaded correlator's non-linear performance can exceed the MACE filter's performance. Mahalanobis et al. [42, 43] have developed the Distance Classifier Correlation Filter (DCCF). Similarly with the work of Reed and Coupland [41], DCCF uses a cascade of shift-invariant linear filters (correlators) to compute the linear distances between the input test image and the trainset images under an optimum transformation. DCCF can be extended to support recognition of multiple object classes. Alkanhal and Kumar [44] have developed the Polynomial Distance Classifier Correlator filter (PDCCF). The underlying theory extends the original linear distance classifier correlation filter to include non-linear functions of the input pattern. PDCCF can optimise jointly all the correlators of the cascaded design, and can support multi-class object recognition.

#### **4.2 Synthetic discriminant function filter**

The main idea behind the Synthetic Discriminant Function (SDF) filter is to include the expected distortions in the filter design such that improved immunity to such distortions is achieved. For example, the inclusion of the out-of-class objects in the filter design achieves multi-class discrimination filter ability. In the conventional SDF filter [28] design the weighted versions of the target object are linearly superimposed, such that when the composite image is cross-correlated with any input training image, the resulting cross-correlation outputs at the origin of these crosscorrelations are the same and are equal to a pre-specified constant.

The basic filter's equation constructed by the weighted combination of the training set images is:

*A Cognitive Digital-Optical Architecture for Object Recognition Applications in Remote… DOI: http://dx.doi.org/10.5772/intechopen.109028*

$$h(\mathbf{x}, \boldsymbol{y}) = \sum\_{i=1}^{N} a\_i \cdot t\_i(\mathbf{x}, \boldsymbol{y}) \tag{9}$$

where

$$\mathfrak{a} = \mathbb{R}^{-1}\mathfrak{c} \tag{10}$$

are the weights, c is an appropriate external vector and

$$R = \iint t\_i(\mathbf{x}, \boldsymbol{\mathcal{y}}) t\_j(\mathbf{x}, \boldsymbol{\mathcal{y}}) \, \text{dxdy} \tag{11}$$

is the correlation matrix of the training image set *ti*.

#### **4.3 Pure SDF correlator classifier for endangered species 1 and 2 speciation**

**Figure 3** shows the block diagram of the Pure SDF Correlator Classifier. The train set consists of images of endangered bird species 1 and 2. Endangered bird species 1's peak value is constrained to be 0.2, and endangered bird species 2's peak value is constrained to be 1.0. By linearly superimposing the constraints weighted training set images, the composite image of the Pure SDF Classifier tool is synthesised. The test set consists of images (snags) of birds captured during an aerial survey. Each test image is then correlated with the composite image of the Pure SDF Correlator Classifier. The center peak of the output correlation plane for each input test image is then used for classifying the object snag as being either an endangered bird species 1 or an endangered bird species 2. A scatter plot of the classified endangered bird species is then drawn. For each input snag the spectral absolute peak (SAP) value Red and SAP value Blue values are used in the scatter plot.
