Steerable Discrete Cosine Transform

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms

Handwritten Arabic character recognition: which feature extraction method?

Recognition of Arabic handwriting characters is a difficult task due to similar appearance of some different characters. However, the selection of the method for feature extraction remains the most important step for achieving high recognition accuracy. The purpose of this paper is to compare the effectiveness of Discrete Cosine Transform and Discrete Wavelet transform to capture discriminative features of Arabic handwritten characters. A new database containing 5600 characters covering all shapes of Arabic handwriting characters has also developed for the purpose of the analysis. The coefficients of both techniques have been used for classification based on a Artificial Neural Network implementation. The results have been analysed and the finding have demonstrated that a Discrete Cosine Transform based feature extraction yields a superior recognition than its counterpart

Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact count is strictly lowered for all N > 4. These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.Comment: 11 page

Evolution of the discrete cosine transform using genetic programming

Compression of 2 dimensional data is important for the efficient transmission, storage and manipulation of Images. The most common technique used for lossy image compression relies on fast application of the Discrete Cosine Transform (DCT). The cosine transform has been heavily researched and many efficient methods have been determined and successfully applied in practice; this paper presents a novel method for evolving a DCT algorithm using genetic programming. We show that it is possible to evolve a very close approximation to a 4 point transform. In theory, an 8 point transform could also be evolved using the same technique

Image Compression using Discrete Cosine Transform & Discrete Wavelet Transform

Image Compression addresses the problem of reducing the amount of data required to represent the digital image. Compression is achieved by the removal of one or more of three basic data redundancies: (1) Coding redundancy, which is present when less than optimal (i.e. the smallest length) code words are used; (2) Interpixel redundancy, which results from correlations between the pixels of an image & (3) psycho visual redundancy which is due to data that is ignored by the human visual system (i.e. visually nonessential information). Huffman codes contain the smallest possible number of code symbols (e.g., bits) per source symbol (e.g., grey level value) subject to the constraint that the source symbols are coded one at a time. So, Huffman coding when combined with technique of reducing the image redundancies using Discrete Cosine Transform (DCT) helps in compressing the image data to a very good extent. The Discrete Cosine Transform (DCT) is an example of transform coding. The current JPEG standard uses the DCT as its basis. The DC relocates the highest energies to the upper left corner of the image. The lesser energy or information is relocated into other areas. The DCT is fast. It can be quickly calculated and is best for images with smooth edges like photos with human subjects. The DCT coefficients are all real numbers unlike the Fourier Transform. The Inverse Discrete Cosine Transform (IDCT) can be used to retrieve the image from its transform representation. The Discrete wavelet transform (DWT) has gained widespread acceptance in signal processing and image compression. Because of their inherent multi-resolution nature, wavelet-coding schemes are especially suitable for applications where scalability and tolerable degradation are important. Recently the JPEG committee has released its new image coding standard, JPEG-2000, which has been based upon DWT