Design and analysis of various bidirectional 2DPCAs in feature partitioning framework

Abstract

In this paper, we present various of bidirectional 2DPCAs in feature partitioning framework. To capture hybrid variations of images with optimal feature dimensions, we propose bidirectional sub-image PCA (Bi-SIMPCA), bidirectional flexible PCA (Bi-FLPCA), bidirectional extended SIMPCA (Bi-ESIMPCA) and bidirectional extended FLPCA (Bi-EFLPCA). The Bi-SIMPCA operates on a set of partitioned sub-images of original image and extracts the 2DPCA feature by simultaneously considering the row and column directions of sub-images. Bi-SIMPCA neglects the cross-correlation across sub-images. The Bi-FLPCA further improves the Bi-SIMPCA by removing the redundant features using cross-correlation across sub-images. The Bi-ESIMPCA instead operates on the sub-images of an image and the same whole image simultaneously and extracts the 2DPCA features along row and column directions. Bi-ESIMPCA lacks the global cross-correlation across sub-images and whole images. The Bi-EFLPCA further improves the Bi-ESIMPCA by reducing the redundant features using global correlation across sub-images and whole images. The issues, such as summarization of variance, space and time complexities of the proposed methods are investigated as well. The simulation results using YALE and ORL facial datasets with variable image resolutions show the superior performance of Bi-EFLPCA method with respect to feature dimensionality, memory efficiency, recognition accuracy, and speed over the existing variation of bidirectional 2DPCAs.