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

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

Tchebichef Moment Based Hilbert Scan for Image Compression

Image compression is now essential for applications such as transmission and storage in data base, so we need to compress a vast amount of information whereas, the compressed ratio and quality of compressed image must be enhanced, for this reason, this paper develop a new algorithm that used a discrete orthogonal Tchebichef moment based Hilbert curve for image compression. The analyzed image was divided into 8×8 image sub-blocks, the Tchebichef moment has been applied to each one, and then the transformed coefficients 8×8 sub-block shall be reordered in Hilbert scan into a linear array, at this step Huffman coding is implemented. Experimental results show that this algorithm improves the coding efficiency on the one hand; and on the other hand the quality of reconstructed image is also not significantly decreased. Keywords: Huffman Coding, Tchebichef Moment Transforms, Orthogonal Moment Functions, Hilbert, zigzag scan

3D Object Recognition Using Fast Overlapped Block Processing Technique

Three-dimensional (3D) image and medical image processing, which are considered big data analysis, have attracted significant attention during the last few years. To this end, efficient 3D object recognition techniques could be beneficial to such image and medical image processing. However, to date, most of the proposed methods for 3D object recognition experience major challenges in terms of high computational complexity. This is attributed to the fact that the computational complexity and execution time are increased when the dimensions of the object are increased, which is the case in 3D object recognition. Therefore, finding an efficient method for obtaining high recognition accuracy with low computational complexity is essential. To this end, this paper presents an efficient method for 3D object recognition with low computational complexity. Specifically, the proposed method uses a fast overlapped technique, which deals with higher-order polynomials and high-dimensional objects. The fast overlapped block-processing algorithm reduces the computational complexity of feature extraction. This paper also exploits Charlier polynomials and their moments along with support vector machine (SVM). The evaluation of the presented method is carried out using a well-known dataset, the McGill benchmark dataset. Besides, comparisons are performed with existing 3D object recognition methods. The results show that the proposed 3D object recognition approach achieves high recognition rates under different noisy environments. Furthermore, the results show that the presented method has the potential to mitigate noise distortion and outperforms existing methods in terms of computation time under noise-free and different noisy environments

Development of Novel Image Compression Algorithms for Portable Multimedia Applications

Portable multimedia devices such as digital camera, mobile d evices, personal digtal assistants (PDAs), etc. have limited memory, battery life and processing power. Real time processing and transmission using these devices requires image compression algorithms that can compress efficiently with reduced complexity. Due to limited resources, it is not always possible to implement the best algorithms inside these devices. In uncompressed form, both raw and image data occupy an unreasonably large space. However, both raw and image data have a significant amount of statistical and visual redundancy. Consequently, the used storage space can be efficiently reduced by compression. In this thesis, some novel low complexity and embedded image compression algorithms are developed especially suitable for low bit rate image compression using these devices. Despite the rapid progress in the Internet and multimedia technology, demand for data storage and data transmission bandwidth continues to outstrip the capabil- ities of available technology. The browsing of images over In ternet from the image data sets using these devices requires fast encoding and decodin g speed with better rate-distortion performance. With progressive picture build up of the wavelet based coded images, the recent multimedia applications demand goo d quality images at the earlier stages of transmission. This is particularly important if the image is browsed over wireless lines where limited channel capacity, storage and computation are the deciding parameters. Unfortunately, the performance of JPEG codec degrades at low bit rates because of underlying block based DCT transforms. Altho ugh wavelet based codecs provide substantial improvements in progressive picture quality at lower bit rates, these coders do not fully exploit the coding performance at lower bit rates. It is evident from the statistics of transformed images that the number of significant coefficients having magnitude higher than earlier thresholds are very few. These wavelet based codecs code zero to each insignificant subband as it moves from coarsest to finest subbands. It is also demonstrated that there could be six to sev en bit plane passes where wavelet coders encode many zeros as many subbands are likely to be insignificant with respect to early thresholds. Bits indicating insignificance of a coefficient or subband are required, but they don’t code information that reduces distortion of the reconstructed image. This leads to reduction of zero distortion for an increase in non zero bit-rate. Another problem associated with wavelet based coders such as Set partitioning in hierarchical trees (SPIHT), Set partitioning embedded block (SPECK), Wavelet block-tree coding (WBTC) is because of the use of auxiliary lists. The size of list data structures increase exponentially as more and more eleme nts are added, removed or moved in each bitplane pass. This increases the dynamic memory requirement of the codec, which is a less efficient feature for hardware implementations. Later, many listless variants of SPIHT and SPECK, e.g. No list SPIHT (NLS) and Listless SPECK (LSK) respectively are developed. However, these algorithms have similar rate distortion performances, like the list based coders. An improved LSK (ILSK)algorithm proposed in this dissertation that improves the low b it rate performance of LSK by encoding much lesser number of symbols (i.e. zeros) to several insignificant subbands. Further, the ILSK is combined with a block based transform known as discrete Tchebichef transform (DTT). The proposed new coder isnamed as Hierar-chical listless DTT (HLDTT). DTT is chosen over DCT because of it’s similar energy compaction property like discrete cosine transform (DCT). It is demonstrated that the decoded image quality using HLDTT has better visual performance (i.e., Mean Structural Similarity) than the images decoded using DCT based embedded coders in most of the bit rates. The ILSK algorithm is also combined with Lift based wavelet tra nsform to show the superiority over JPEG2000 at lower rates in terms of peak signal-to-noise ratio (PSNR). A full-scalable and random access decodable listless algorithm is also developed which is based on lift based ILSK. The proposed algorithm named as scalable listless embedded block partitioning (S-LEBP) generates bit stream that offer increasing signal-to-noise ratio and spatial resolution. These are very useful features for transmission of images in a heterogeneous network that optimally service each user according to available bandwidth and computing needs. Random access decoding is a very useful feature for extracting/manipulating certain ar ea of an image with minimal decoding work. The idea used in ILSK is also extended to encode and decode color images. The proposed algorithm for coding color images is named as Color listless embedded block partitioning (CLEBP) algorithm. The coding efficiency of CLEBP is compared with Color SPIHT (CSPIHT) and color variant of WBTC algorithm. From the simulation results, it is shown that CLEBP exhibits a significant PSNR performance improvement over the later two algorithms on various types of images. Although many modifications to NLS and LSK have been made, the listless modification to WBTC algorithm has not been reported in the literature. Therefore,a listless variant of WBTC (named as LBTC) algorithm is proposed. LBTC not only reduces the memory requirement by 88-89% but also increases the encoding and decoding speed, while preserving the rate-distortion perform ance at the same time. Further, the combination of DCT with LBTC (named as DCT LBT) and DTT with LBTC (named as Hierarchical listless DTT, HLBTDTT) are compared with some state-of-the-art DCT based embedded coders. It is also shown that the proposed DCT-LBT and HLBT-DTT show significant PSNR improvements over almost all the embedded coders in most of the bit rates. In some multimedia applications e.g., digital camera, camco rders etc., the images always need to have a fixed pre-determined high quality. The extra effort required for quality scalability is wasted. Therefore, non-embedded algo rithms are best suited for these applications. The proposed algorithms can be made non-embedded by encoding a fixed set of bit planes at a time. Instead, a sparse orthogonal transform matrix is proposed, which can be integrated in a JEPG baseline coder. The proposed matrix promises a substantial reduction in hardware complexity with amarginal loss of image quality on a considerable range of bit rates than block based DCT or Integer DCT