MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

Tensor transform-based quaternion fourier transform algorithm

Optimal Wiener and homomorphic filtration

In this paper, a general, efficient, split algorithm to compute the two-dimensional quaternion discrete Fourier transform (2-D QDFT), by using the special partitioning in the frequency domain, is introduced. The partition determines an effective transformation, or color image representation in the form of 1-D quaternion signals which allow for splitting the N × M-point 2-D QDFT into a set of 1-D QDFTs. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. In particular, a proposed method of calculating the 2r × 2r -point 2-D QDFT uses 18N2 less multiplications than the well-known column-row method and method of calculation based on the symplectic decomposition. The proposed algorithm is simple to apply and design, which makes it very practical in color image processing in the frequency domain.

Tensor representation of color images and fast 2D quaternion discrete Fourier transform

This paper introduces a novel method of image reconstruction from a finite number of projections by processing the image along parallel rays. The geometry from the image plane is transferred to the Cartesian lattice by means of using the original image's line-integrals to calculate the line-sums of the discrete image to be reconstructed. Such a transformation of geometry allows for the 2D discrete paired transform, whose complete set of functions is defined by directions, to be effectively used in the exact reconstruction of the original image. The model of image reconstruction is described, and both examples and experimental results of implementation of the proposed method are provided for reconstruction on the Cartesian lattice of size 2r×2r, where r ≥ 2.

Image Reconstruction From Finite Number of Projections: Method of Transferring Geometry

Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB® introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan.

The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New concepts include methods of transferring the geometry of rays from the plane to the Cartesian lattice, the point map of projections, the particle and its field function, and the statistical model of averaging. The authors supply numerous examples, MATLAB®-based programs, end-of-chapter problems, and experimental results of implementation.

The main approach for image reconstruction proposed by the authors differs from existing methods of back-projection, iterative reconstruction, and Fourier and Radon filtering. In this book, the authors explain how to process each projection by a system of linear equations, or linear convolutions, to calculate the corresponding part of the 2-D tensor or paired transform of the discrete image. They then describe how to calculate the inverse transform to obtain the reconstruction. The proposed models for image reconstruction from projections are simple and result in more accurate reconstructions.

Introducing a new theory and methods of image reconstruction, this book provides a solid grounding for those interested in further research and in obtaining new results. It encourages readers to develop effective applications of these methods in CT.

Image Processing: Tensor Transform and Discrete Tomography with MATLAB ®

This paper presents a novel approach to compose discrete unitary transforms that are induced by given input signals and applied over other signals. Such transforms are parameterized. Parameters are defined by the signal-generators and the systems of decision equations, of which specified cases are considered. Properties and examples of new transforms, which we call discrete signal-induced heap transforms, are described. The transforms are fast, have simple forms of decomposition, and can be applied for signals of any length.

Nonlinear Approach Of Construction of Fast Unitary Transforms

This paper describes a new class of discrete heap transforms which are unitary energy-preserving transforms and induced by input signals. These transforms have a simple form of composition and fast algorithms for any size of processed signals. We consider the heap transforms, defined by two-dimensional elementary rotations, as satisfying the given decision equations. The main feature of each heap transform is the corresponding system of basis functions, which represent themselves a family of interactive waves which are moving in the field generated by the input signal. Properties and examples of heap transforms, which we also call discrete signal-induced heap transforms, are described in detail.

Discrete unitary transforms generated by moving waves

This paper presents a novel approach to compose nonlinear invertible transforms that can be used effectively in communication systems, as well as in signal and image processing. The transforms have been designed to solve the specific problem of reducing the peak to average power ratio (PAPR) in orthogonal frequency-division multiplexing and other broadband multicarrier systems. The proposed transforms are based on the concept of the sliding norm in spaces of functions or vectors over which the transforms operate. Examples and main properties of these transforms, which we call sliding norm transforms, are described in the continuous-time and discrete-time cases. The transforms are fast and can be simply implemented and used for processing signals of any length.

Merughan M. Grigoryan

Papers

Image Processing: Tensor Transform and Discrete Tomography with MATLAB ®

Nonlinear Approach Of Construction of Fast Unitary Transforms

Discrete unitary transforms generated by moving waves

Method of Sliding Norm Transforms For Peak-to-Average Power Reduction In OFDM Systems