<title>Modified morphological correlation via binary representation</title>

Abstract

The morphological correlation is the optimal method for searching a reference object in an input scene when the figure of merit is based on the mean absolute error (MAE). In practice, it was found that the morphological correlation exhibits high discrimination ability between similar patterns in recognition systems. It is based on threshold slicing the input image as well as the reference filter into many binary slices, as many as the dynamic range of the input permits. The threshold slices of the input and the reference are then correlated and summed up to obtain the morphological correlation. This operation is characterized by a sharp correlation peak but requires many correlation operations. In this work we propose a novel correlation operation that is characterized by even higher discrimination capabilities than exhibited by the conventional morphological correlation and requires less computational effort. The method is based upon the binary representation of the gray level of each pixel in the image. For example: if the dynamic range allows the definition of 256 levels, i.e., 8 binary bits, then a level of 10 will be represented as 00001010. Unlike the morphological correlation, the proposed modification is based on correlating binary slices that are the bitmap representations. Thus, only 8 slices of the input and the reference are required and only 8 correlations rather than 256 performed. The optical implementation of the new approach is fairly simple and can be utilized via the well-known joint transform correlator architecture. Experimental results demonstrate the advantages of the suggested method.