Statistical Properties of Bit-Plane Probability Model and Its Application in Supervised Texture Classification

Abstract

The modeling of wavelet subband histograms via the product Bernoulli distributions (PBD) has received a lot of interest and the PBD model has been applied successfully in texture image retrieval. In order to fully understand the usefulness and effectiveness of the PBD model and its associated signature, namely, the bit-plane probability (BP) signature on image processing applications, we discuss and investigate some of their statistical properties. These properties would help to clarify the sufficiency of the BP signature to characterize wavelet subbands, which, in turn, justifies its use in real time applications. We apply the BP signature on supervised texture classification problem and experimental results suggest that the weighted L(1)-norm (rather than the standard L (1)-norm) should be used for the BP signature. Comparative classification experiments show that our method outperforms the current state-of-the-art Generalized Gaussian Density approaches.

Texture Classification by Bit-plane Multifractal Spectrum and Bit-plane Barycentric Coordinates of Wavelet Coefficients Based on SVD

“…We compare both BP-MFS signature and BP-MFS-BCC signature combined with SVD with BP method proposed in [14] and LEH method proposed in [16] on texture images from the Brodatz database and the UMD database. In these experiments, the number of the training samples in each texture image class is set as 8, half of total samples in each class.…”

“…Recently, models based on wavelet subband coefficients have also been used on texture classification. The existing models in literatures contain the Characteristic Generalized Gaussian Density (CGGD) model [12], the Bit-plane Probability (BP) model [13,14], the Refined Histogram [15], the Local Energy Histogram [16], and so on. Particularly, the Bit-plane Probability (BP) signature is a very competitive feature by modeling wavelet high-frequency subband coefficients via the Product Bernoulli Distributions (PBD).…”

“…The Bit-plane Probability (BP) signature is built by the PBD model parameters. More specifically, the BP signature in conjunction with the use of weighted L ଵ -norm distance and the minimum distance classifier is presented concretely in paper [14].…”

Watermark detection on quantized transform coefficients using product bernoulli distributions

“…Assuming statistical independence and denoting the model parameters by pi = P (Xi = 1), the joint distribution of Eq. (3) can be written as a product of Bernoulli distributions (PBD) [16,4] …”

“…In this work we propose we novel watermark detector derived from on a simple model for quantized (integer) DWT or DCT coefficient values based on the bit-plane probability signatures recently introduced for texture retrieval applications [16,4]. The advantages of the proposed watermark detector include the reliable estimation of the model parameters even on heavily quantized data, straightforward integration of the method in multimedia codecs as the computation of the detection statistic can be implemented using integer arithmetic only, thus permitting efficient implementation.…”