Fast Computation of Sliding Discrete Tchebichef Moments and Its Application in Duplicated Regions Detection

Abstract

International audienceComputational load remains a major concern when processing signals by means of sliding transforms. In this paper, we present an efficient algorithm for the fast computation of one-dimensional and two-dimensional sliding discrete Tchebichef moments. To do so, we first establish the relationships that exist between the Tchebichef moments of two neighboring windows taking advantage of Tchebichef polynomials’ properties. We then propose an original way to fast compute the moments of one window by utilizing the moment values of its previous window. We further theoretically establish the complexity of our fast algorithm and illustrate its interest within the framework of digital forensics and more precisely the detection of duplicated regions in an audio signal or an image. Our algorithm is used to extract local features of such a signal tampering. Experimental results show that its complexity is independent of the window size, validating the theory. They also exhibit that our algorithm is suitable to digital forensics and beyond to any applications based on sliding Tchebichef moments

Towards an accurate and fast computation of discrete Tchebychev moments for binary and grey‐level images

“…In fact, the proposed method never exceeds 0.3 s in the testing as the Tchebychef Z-transform continues to rise. Table 4 presents different results from existing methods [33] showing the execution time of the DTMs calculation process up to the fifth order. Results are expressed in seconds.…”

“…On the other hand, if NB increases, more blocks are generated; the accuracy of moment's calculation is improved while time execution increases. The complexity proposed in [33] depends only on the moment's order which is good since the moment's order is generally a small number. However, the moment's order is put to the third power when calculating the number of additions and multiplications.…”

“…The proposed method does not depend on the size of the image since normalisation is done (in this case to 128 × 128). However, it depends on the square of the moment's order, which is relatively Table 3 Computation time(s) obtained by the different methods existing in the literature compared with the proposed method Methods Up to order M Direct method Recursive method [27] Recursive method [28] Filter method [30] Tchebychef Ztransform [ [3] NB(M 2 + 5M) NB(2M 2 + 9M) sliding fast method [33] ( small. Additionally, there are no multiplication operations when dealing with binary images.…”

Detection of Tampering by Image Resizing Using Local Tchebichef Moments

“…By the principle analysis of the three image resizing methods, we found that the correlation between adjacent pixels can be destroyed in the process of image resizing. Tchebichef moments have been extensively applied in field of image/vedio such as information security [18], pattern recognition [19] and image quality assessment [20], and so on. Inspired by this, it can be found from experiments that LTM can effectively reflect the correlation changes between adjacent pixels.…”

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

“…The most promising path is to find and compress redundant operations in the for-loop like processing of image patches. In this regard, useful properties of basis functions (such as shift properties in [74,75]) and special data structures (such as complex-valued integral images in [76]) have been explored to improve efficiency.…”