On the use of the discrete Pascal transform in hiding data in images

Abstract

The Discrete Pascal Transform (DPT) has been proved remarkably useful for edge detection, filter design, discrete-time signal interpolation and data hiding. In the present work a new blind fragile data hiding technique for secretly embedding messages into color images, is proposed. The embedding procedure is based on dividing each color image component into even-sized blocks. Information embedding is determined by monitoring the lower-right corner of the DPT coefficient matrix. This particular coefficient suffers the highest change for small pixel modifications. The embedding affects the coefficient's sign. In case that the sign is not the desired one, i.e. negative for a message bit value of '0' and positive for a message bit value of '1', it is changed by repeatedly adding to the block or subtracting from the block the identity matrix. This process is based on the DPT properties and on the sensitivity of the lower-right coefficient in even the smallest pixel changes. The embedding algorithm takes care of the underflows or overflows that may occur during the consecutive additions or subtractions. The method is evaluated in terms of capacity and image distortion. Experiments are conducted using different images and block sizes namely 2x2 / 4x4 / 8x8 / 16x16, and the overall performance of the scheme is quantified. Block size greatly affects capacity and stego-image quality. Comparisons with existing methods prove the superiority of the proposed method.