Bradley W. Dickinson

Eigenvectors and functions of the discrete Fourier transform

A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be efficiently computed, and possible applications to multiplexing and transform coding are suggested.

Adaptive watermarking in the DCT domain

An adaptive watermarking technique is introduced in this work. A regional perceptual classifier is employed to assign a noise sensitivity index to each region. The watermark is inserted in the original image according to this index by using block DCT. The detection of the watermark is designed to achieve a desired false alarm probability.

The complexity of analog computation

We ask if analog computers can solve NP-complete problems efficiently. Regarding this as unlikely, we formulate a strong version of Churchs Thesis: that any analog computer can be simulated efficiently (in polynomial time) by a digital computer. From this assumption and the assumption that P ≠ NP we can draw conclusions about the operation of physical devices used for computation.

Adaptive model-driven bit allocation for MPEG video coding

We present an adaptive model-driven bit-allocation algorithm for video sequence coding. The algorithm is based on a parametric rate-distortion model, and facilitates both picture-and macroblock-level bit allocation. A region classification scheme is incorporated into the algorithm, which exploits characteristics of human visual perception to efficiently allocate bits according to a regions visual importance. The application of this algorithm to MPEG video coding is discussed in detail. We show that the proposed algorithm is computationally efficient and has many advantages over the MPEG-2 TM5 bit-allocation algorithm.

Temporally adaptive motion interpolation exploiting temporal masking in visual perception

In this paper we present a novel technique to dynamically adapt motion interpolation structures by temporal segmentation. The number of reference frames and the intervals between them are adjusted according to the temporal variation of the input video. Bit-rate control for this dynamic group of pictures (GOP) structure is achieved by taking advantage of temporal masking in human vision. Constant picture quality can be obtained by variable-bit-rate coding using this approach. Further improvement can be made when the intervals between reference frames are chosen by minimizing a measure of the coding difficulty of a GOP. Advantages for low bit-rate coding and implications for variable-bit-rate coding are discussed. Simulations on test video are presented for various GOP structures and temporal segmentation methods, and the results compare favorably with those for conventional fixed GOP structures.

Canonical matrix fraction and state-space descriptions for deterministic and stochastic linear systems

Several results exposing the interrelations between state-space and frequency-domain descriptions of multivariable linear systems are presented. Three canonical forms for constant parameter autoregressive-moving average (ARMA) models for input-output relations are described and shown to corrrespond to three particular canonical forms for the state variable realization of the model. Invariant parameters for the partial realization problem are characterized. For stochastic processes, it is shown how to construct an ARMA model, driven by white noise, whose output has a specified covariance. A two-step procedure is given, based on minimal realization and Cholesky-factorization algorithms. Though the goal is an ARMA model, it proves useful to introduce an artificial state model and to employ the recently developed Chandrasekhar-type equations for state estimation. The important case of autoregressive processes is studied and it is shown how the Chandrasekhar-type equations can be used to obtain and generalize the well known Levinson-Wiggins-Robinson (LWR) recursion for estimation of stationary autoregressive processes.

Phase unwrapping by factorization

An algorithm for the numerical factorization of very high degree but well-conditioned polynomials is developed. This is used to factor the z-transform of finite-length signals, and the zeros are used to calculate the unwrapped phase. The method has been tested on signals up to 512 points in length. A complete Fortran 77 program is given for the case of a real-valued signal. Two related analytical issues are treated. First, the interpretation of phase unwrapping as an interpolation problem is discussed. Second, an explanation is given for the observed numerical difficulties in the method of phase unwrapping using adaptive integration of the phase derivative. The trouble is due to the clustering of the zeros of high degree polynomials near the unit circle.

Information capacity of associative memories

Associative memory networks consisting of highly interconnected binary-valued cells have been used to model neural networks. Tight asymptotic bounds have been found for the information capacity of these networks. The authors derive the asymptotic information capacity of these networks using results from normal approximation theory and theorems about exchangeable random variables. >

Texture Recognition and Image Retrieval Using Gradient Indexing

Abstract Our starting point is gradient indexing, the characterization of texture by a feature vector that comprises a histogram derived from the image gradient field. We investigate the use of gradient indexing for texture recognition and image retrieval. We find that gradient indexing is a robust measure with respect to the number of bins and to the choice of the gradient operator. We also find that the gradient direction and magnitude are equally effective in recognizing different textures. Furthermore, a variant of gradient indexing called local activity spectrum is proposed and shown to have improved performance. Local activity spectrum is employed in an image retrieval system as the texture statistic. The retrieval system is based on a segmentation technique employing a distance measure called Sum of Minimum Distance. This system enables content-based retrieval of database images from templates of arbitrary size.

The use of time-domain selection for improved linear prediction

We show by theoretical argument and by experiment with both synthetic and real data that selection of an undriven segment of voiced speech for analysis by linear predictive coding (LPC) gives more accurate estimates of the poles of the vocal-tract model. In the case of voiced nasal phonemes, this technique provides a simple algorithm for separately determining the poles and the zeros in the model and illustrates the desirability of identifying the portions of the speech wave during which there is a significant driving input. A key problem which remains is the development of a practical algorithm for selecting such segments for analysis.