Color Image Classification via Quaternion Principal Component Analysis Network

The Principal Component Analysis Network (PCANet), which is one of the recently proposed deep learning architectures, achieves the state-of-the-art classification accuracy in various databases. However, the performance of PCANet may be degraded when dealing with color images. In this paper, a Quaternion Principal Component Analysis Network (QPCANet), which is an extension of PCANet, is proposed for color images classification. Compared to PCANet, the proposed QPCANet takes into account the spatial distribution information of color images and ensures larger amount of intra-class invariance of color images. Experiments conducted on different color image datasets such as Caltech-101, UC Merced Land Use, Georgia Tech face and CURet have revealed that the proposed QPCANet achieves higher classification accuracy than PCANet.Comment: 9 figures,5 table

Estimation of fractal dimension and fractal curvatures from digital images

Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several geometric characteristics, namely all the intrinsic volumes (i.e.\ volume, surface area, Euler characteristic etc.) of the parallel sets of a fractal. Motivated by recent results on their limiting behaviour, we use these functionals to estimate the fractal dimension of sets from digital images. Simultaneously, we also obtain estimates of the fractal curvatures of these sets, some fractal counterpart of intrinsic volumes, allowing a finer classification of fractal sets than by means of fractal dimension only. We show the consistency of our estimators and test them on some digital images of self-similar sets.Comment: 30 pages, 8 Figure