Two-dimensional (2D) recursive digital filters find applications in image processing as in medical X-ray processing. Nonsymmetric half-plane (NSHP) filters have definitely positive magnitude characteristics as opposed to quarter-plane (QP) filters. In this paper, we provide methods for stabilizing the given 2D NSHP polynomial by the planar least squares inverse (PLSI) method. We have proved in this paper that if the given 2D unstable NSHP polynomial and its PLSI are of the same degree, the PLSI polynomial is always stable, irrespective of whether the coefficients of the given polynomial have relationship among its coefficients or not. Examples are given for 2D first-order and second-order cases to prove our results. The generalization is done for the Nth order polynomial

Abstract:The most common reason for blindness among human beings is Glaucoma. The increase of fluid pressure damages the optic nerve which gradually leads to irreversible loss of vision. A technique for automated screening of Glaucoma from the fundal retinal images is presented in this paper. This paper intends to explore the significance of both the approximate and detail coefficients through wavelet packet decomposition (WPD). Decomposition is done with "db3" wavelet function and the images are decomposed up to level-3 producing 84 sub-bands. Two features, the energy and the entropy are calculated for each sub-band producing two feature matrices (158 images × 84 features). The above step is purely a statistical measure based on WPD. To enhance the diagnostic accuracy, the second phase considers the structural (biological) region of interest (ROI) in the image and then extracts the same features. It is worthy to note that direct biological features are not extracted to eliminate the drawbacks of segmentation whereas the biologically significant region is taken as biological-ROI. Interestingly, the detailed coefficient sub-bands (prominent edges) show more significance in the biological-ROI phase. Apart from enhancing the diagnostic accuracy by feature reduction, the paper intends to mark the significance indices, uniqueness and discrimination capability of the significant features (sub-bands) in both the phases. Then, the crisp inputs are fed to the classifier ANN. Finally, from the significant features of the biological-ROI feature matrices, the accuracy is raised to 85% which is notable than the accuracy of 79% achieved without considering the ROI.

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-Glaucoma is one of the most common causes of blindness which is caused by increase of fluid pressure in the eye which damages the optic nerve and eventually causing vision loss. An automated technique to diagnose glaucoma disease can reduce the physicians' effort in screening of Glaucoma in a person through the fundal retinal images. In this paper, optimal hyper analytic wavelet transform for Glaucoma detection technique from fundal retinal images is proposed. The optimal coefficients for transformation process are found out using the hybrid GSO-Cuckoo search algorithm. This technique consists of pre-processing module, optimal transformation module, feature extraction module and classification module. The implementation is carried out with MATLAB and the evaluation metrics employed are accuracy, sensitivity and specificity. Comparative analysis is carried out by comparing the hybrid GSO with the conventional GSO. The results reported in our paper show that the proposed technique has performed well and has achieved good evaluation metric values. Two 10-fold cross validated test runs are performed, yielding an average fitness of 91.13% and 96.2% accuracy with CGD-BPN (Conjugate Gradient Descent-Back Propagation Network) and Support Vector Machines (SVM) respectively. The techniques also gives high sensitivity and specificity values. The attained high evaluation metric values show the efficiency of detecting Glaucoma by the proposed technique.

Two-dimensional digital filters have gained wide acceptance in recent years. For recursive filters, nonsymmetric half-plane versions (also known as semicausal) are more general than quarter-plane versions (also known as causal) in approximating arbitrary magnitude characteristics. The major problem in designing two-dimensional recursive filters is to guarantee their stability with the expected magnitude response. In general, it is very difficult to take stability constraints into account during the stage of approximation. This is the reason why it is useful to develop techniques, by which stability problem can be separated from the approximation problem. In this way, at the end of approximation process, if the filter becomes unstable, there is a need for stabilization procedures that produce a stable filter with similar magnitude response as that of the unstable filter. This paper, demonstrates a stabilization procedure for a two-dimensional nonsymmetric half-plane recursive filters based on planar least squares inverse (PLSI) polynomials. The paper's findings prove that, a new way of form-preserving transformation can be used to obtain stable PLSI polynomials. Therefore obtaining PLSI polynomial is computationally less involved with the proposed formpreserving transformation as compared to existing methods, and the stability of the resulting filters is guaranteed.