Kronecker Product of Matrices and Applications to Two-Point Boundary Value Problems Associated With First Order Matrix Difference Systems
Sriram Bhagavathula, P. Sailaja, K.N. Murty
This paper presents a criteria for the existence and uniqueness of solutions to two-point boundary value problems associated with a system of Kronecker product first order differential equation. Some of the natural questions on Kronecker product of matrices about seemingly“simple” cases are still unansweredin spite of their increasing interest and hence some significant results on Kronecker product of matrices are answered in this paper. We mainly explain a set of necessary and sufficient conditions on the decomposition of a matrix into Kronecker product of two matrices.
Region based Feature Fusion of Imperfect Face and Gait cues for human recognition using Median-LBPF and Median-LBPG based PCA followed by LDA
Annbuselvi K, Santhi N, Dr.S. Sivakumar
Abstract— Conventional computer-based multimodal biometric systems for human recognition based on face and gait cues are mainly based on recognition of perfect images of face and gait. There are situations, where perfect face and gait images may not be available which means probe images are imperfect. This paper proposes new methods Median Local Binary Pattern of Face image (Median-LBPF) and Gait image (Median-LBPG) to extract the features of imperfect face and gait images efficiently representing such imperfect images for better recognition. Initially the given imperfect face and gait images are divided into six overlapped regions called top, bottom, left, right, vertical center, horizontally center overlapped half images. The features of these six overlapped regions of imperfect face and gait images in the spatial domain are extracted by using Median-LBPF and Median-LBPG. Subsequently the dimensionality of the feature sets are reduced by a two stage feature reduction algorithms Principal Component Analysis (PCA) followed by Linear Discriminant Analysis (LDA). Next the individual face features and gait features are normalized to have their values lie within similar ranges and are concatenated at feature level. For classification, Euclidean distance measure is used to calculate the minimum of minimum distance between the six overlapped regions of given imperfect face and gait probe images and the corresponding regions of all six overlapped regions in the training sets. The proposed methods are tested by using publically available data sets ORL face and CASIA gait. The experimental results show that features of a region of face and gait images are adequate for recognition and its average recognition performance is same as perfect face and gait images.