This paper proposes a novel feature detector for selecting local textures that are suitable for accurate multi-camera surface reconstruction, and in particular planar patch fitting techniques. This approach is in contrast to conventional feature detectors, which focus on repeatability under scale and affine transformations rather than suitability for multi-camera reconstruction techniques. The proposed detector selects local textures that are sensitive to affine transformations, which is a fundamental requirement for accurate patch fitting. The proposed detector is evaluated against the SIFT detector on a synthetic dataset and the fitted patches are compared against ground truth. The experiments show that patches originating from the proposed detector are fitted more accurately to the visible surfaces than those originating from SIFT keypoints. In addition, the detector is evaluated on a performance capture studio dataset to show the real-world application of the proposed detector.

MOTIVATION: There is a growing interest in extracting statistical patterns from gene expression time-series data, in which a key challenge is the development of stable and accurate probabilistic models. Currently popular models, however, would be computationally prohibitive unless some independence assumptions are made to describe large-scale data. We propose an unsupervised conditional random fields (CRF) model to overcome this problem by progressively infusing information into the labelling process through a small variable voting pool. RESULTS: An unsupervised CRF model is proposed for efficient analysis of gene expression time series and is successfully applied to gene class discovery and class prediction. The proposed model treats each time series as a random field and assigns an optimal cluster label to each time series, so as to partition the time series into clusters without a priori knowledge about the number of clusters and the initial centroids. Another advantage of the proposed method is the relaxation of independence assumptions.

BACKGROUND: Tight clustering arose recently from a desire to obtain tighter and potentially more informative clusters in gene expression studies. Scattered genes with relatively loose correlations should be excluded from the clusters. However, in the literature there is little work dedicated to this area of research. On the other hand, there has been extensive use of maximum likelihood techniques for model parameter estimation. By contrast, the minimum distance estimator has been largely ignored. RESULTS: In this paper we show the inherent robustness of the minimum distance estimator that makes it a powerful tool for parameter estimation in model-based time-course clustering. To apply minimum distance estimation, a partial mixture model that can naturally incorporate replicate information and allow scattered genes is formulated. We provide experimental results of simulated data fitting, where the minimum distance estimator demonstrates superior performance to the maximum likelihood estimator. Both biological and statistical validations are conducted on a simulated dataset and two real gene expression datasets. Our proposed partial regression clustering algorithm scores top in Gene Ontology driven evaluation, in comparison with four other popular clustering algorithms. CONCLUSION: For the first time partial mixture model is successfully extended to time-course data analysis. The robustness of our partial regression clustering algorithm proves the suitability of the combination of both partial mixture model and minimum distance estimator in this field. We show that tight clustering not only is capable to generate more profound understanding of the dataset under study well in accordance to established biological knowledge, but also presents interesting new hypotheses during interpretation of clustering results. In particular, we provide biological evidences that scattered genes can be relevant and are interesting subjects for study, in contrast to prevailing opinion.

The problem of visible surface estimation for image-based rendering is tackled using a new approach, which combines visual hull and surface estimation techniques. It is shown that the new method combines the best features of both approaches, being more robust than direct surface element estimation and more flexible than the visual hull. The new method uses an estimate of the visual hull as a prior on the ill-posed problem of surface element estimation. To improve the computational preformance of the algorithm, a multiresolution approach to surface patch estimation is used. The patches thus estimated can then be tracked over time, to provide an accurate model of the surface geometry, which is then used for estimation of the scene from arbitrary viewpoints. After a brief description of the algorithm, results are presented to show the improvement in performance which can be obtained using either technique alone. The paper concludes with a discussion of extensions to the work currently under investigation.

Video based rendering algorithms attempt to render videos of a scene from an arbitrary viewpoint, given a set of input video sequences taken from several fixed viewpoints. These algorithms require either a dense camera array or some knowledge of scene structure. By applying sequential Markov Chain Monte Carlo (MCMC) methods, we show it is possible to estimate the surfaces visible within a scene, and track them over time, in an efficient manner. Initially, a particle filter is applied across image scale to estimate the surfaces present in a scene at a fixed point in time. Following this, surfaces are tracked over time using a particle filter which takes advantage of both frame-to-frame dependancies, and a hierarchical surface model derived from a multiresolution Gaussian mixture model analysis of the surface data. This time-varying surface model, and the images, are the input for a rendering algorithm which uses a fuzzy z-buffer and projective texturing to generate reconstructions.

This paper presents a vascular representation and segmentation algorithm based on a multiresolution Hermite model (MHM). A two-dimensional Hermite function intensity model is developed which models blood vessel profiles in a quad-tree structure over a range of spatial resolutions. The use of a multiresolution representation simplifies the image modeling and allows for a robust analysis by combining information across scales. Estimation over scale also reduces the overall computational complexity. As well as using MHM for vessel labelling, the local image modeling can accurately represent vessel directions, widths, amplitudes, and branch points which readily enable the global topology to be inferred. An expectation-maximization (EM) type of optimization scheme is used to estimate local model parameters and an information theoretic test is then applied to select the most appropriate scale/feature model for each region of the image. In the final stage, Bayesian stochastic inference is employed for linking the local features to obtain a description of the global vascular structure. After a detailed description and analysis of MHM, experimental results on two standard retinal databases are given that demonstrate its comparative performance. These show MHM to perform comparably with other retinal vessel labelling methods.

Light fields are known for their potential in generating reconstructions of a scene from novel viewpoints without need for a model of the scene. Reconstruction of novel views, however, often leads to ghosting artefacts, which can be relieved by correcting for the depth of objects within the scene using disparity compensation. Unfortunately, reconstructions from the disparity information suffer from a lack of information on the orientation and smoothness of the underlying surfaces. In this paper, we propose a novel representation of the surfaces present within a scene using a planar patch approach. We discuss the process of estimating patches and introduce a reconstruction algorithm designed to exploit this patch information to produce visually superior reconstructions at higher resolutions. Experimental results demonstrate the effectiveness of this reconstruction technique when compared to traditional reconstruction methods.

A novel image-dependent representation, warplets, based on self-similarity of regions is introduced. The representation is well suited to the description and segmentation of images containing textures and oriented patterns, such as fingerprints. An affine model of an image as a collection of self-similar image blocks is developed and it is shown how textured regions can be represented by a single prototype block together with a set of transformation coefficients. Images regions are aligned to a set of dictionary blocks and their variability captured by PCA analysis. The block-to-block transformations are found by Gaussian mixture modelling of the block spectra and a least-squares estimation. Clustering in the April domain can be used to determine a April dictionary. Experimental results on a variety of images demonstrate the potential of the use of April for segmentation and coding.

This paper introduces a method of image segmentation that partitions an image into regions exhibiting self-similarity. An affine texture de-scription which models an image as a collection of self-similar image blocks is developed. Transformations between prototype and target blocks are estimated by Gaussian Mixture Modelling of block spectra and least-squares estimation. An appropriate set of prototype blocks (codebook) is determined for a given an image by clustering in a fea-ture subspace of discrete samples from an affine symmetry group. The new method is well suited to the description and segmentation of images containing textures, such as fingerprints and medical images and could be used as a basis for indexing and searching in CBIR applications. Ex-perimental results are presented which demonstrate the potential of the method on widely varying images. µ

A volume-based hybrid video coding scheme which combines fractal coding with neighbourhood vector quantisation is reported. The algorithm works as follows: the neighbourhood blocks (the virtual code-book) of a range block r/sub i/ are causally selected from the connected neighbourhood, 9 in the previous time slice, and 4 are within the same time slice. In the implementation, instead of having the neighbourhood blocks collected from the original frames, we compare the range block with the blocks that were actually transmitted, ie., the previously quantised blocks. This prevents quantisation errors from accumulating and gives better rate-distortion performance. The experimental results suggests that the coder's compression performance beats most of the fractal-based video coders.

In this paper, we present a novel algorithm for restoration of noisy video sequences. A video sequence is first transformed into an optimal 3D wavelet domain using basis functions adapted to the contents of the sequence. Assuming that all the major spatiotemporal frequency phenomena present in the sequence produce high amplitude transform coefficients, a modified form of the BayesShrink thresholding method is used to suppress the noise. In order to reduce the effects of Gibbs phenomenon in the restored sequence, translation dependence is removed by averaging the restored instances of the shifted sequence. The algorithm yields promising results in terms of both objective and subjective quality of the restored sequence.

In this paper, a class of Random Field model, defined on a multiresolution array is used in the segmentation of gray level and textured images. The novel feature of one form of the model is that it is able to segment images containing unknown numbers of regions, where there may be significant variation of properties within each region. The estimation algorithms used are stochastic, but because of the multiresolution representation, are fast computationally, requiring only a few iterations per pixel to converge to accurate results, with error rates of 1-2 percent across a range of image structures and textures. The addition of a simple boundary process gives accurate results even at low resolutions, and consequently at very low computational cost.

Image coding methods based on adaptive wavelet transforms and those employing zerotree quantization have been shown to be successful. We present a general zerotree structure for an arbitrary wavelet packet geometry in an image coding framework. A fast basis selection algorithm is developed; it uses a Markov chain based cost estimate of encoding the image using this structure. As a result, our adaptive wavelet zerotree image coder has a relatively low computational complexity, performs comparably to state-of-the-art image coders, and is capable of progressively encoding images.

We describe a method for inferring tree-like vascular structures from 2D imagery. A Markov chain Monte Carlo (MCMC) algorithm is employed to sample from the posterior distribution given local feature estimates, derived from likelihood maximisation for a Gaussian intensity profile. A multiresolution scheme, in which coarse scale estimates are used to initialise the algorithm for finer scales, has been implemented and used to model retinal images. Results are presented to show the effectiveness of the method.

This paper describes an estimation and representation method for object structure in 3D image data. A windowed Fourier transform is used to estimate the parameters of 3D local structures (lines, planes and spheres) across a number of window sizes or scales. We present the estimation method and describe a decision process which aims to find the simplest object description. Results of the method on test data and blood vessels from magnetic resonance imaging are presented. 1

In this paper, work on a new wavelet packet basis selection paradigm is reported which emphasizes the crucial role of the quantization strategy being used. This paradigm is coupled with a new Markov chain based estimation of the cost of zerotree quantization to develop a progressive wavelet packet image coder which gives better results than its wavelet counterpart.

This paper introduces a new generalisation of scale-space and pyramids, which combines statistical modelling with a spatial representation. The representation uses the familiar concept of multiple resolutions, but applied to a Gaussian mixture representation of the image - hence the title MGMM. It is shown that MGMM can approximate any probability density and can adapt to smooth motions. After a presentation of the theory, it is shown how MGMM can be applied to the estimation of visual motion.

A new vector quantizer codebook design for video compression is described. This uses the notion that symmetries in the data, which are seldom captured exactly in any training dataset, are important perceptually and lead to a more robust codebook. The method is illustrated using three-dimensional (3-D) wavelet transformed video sequences.

Introduces a generalisation of scale-space and pyramids, which combines statistical modelling with a spatial representation. The representation uses the familiar concept of multiple resolutions, but applied to a Gaussian mixture representation of the image-hence the title MGMM. It is shown that MGMM can approximate any probability density. Examples show how MGMM can be applied to problems such as segmentation and motion analysis.

A novel wavelet decomposition, based on a set of six oriented bands in each scale, is presented and its use in image data compression described. The new decomposition uses complex wavelets derived from the conventional separable dyadic transform. The new representation is used in a vector quantizer (VQ), which exploits the symmetry relations which exist between the bands in different scales and orientations. The resulting coder performance is competitive with schemes such as embedded zerotrees.

Wavelet packets are an effective representation tool for adaptive waveform analysis of a given signal. We first combine the wavelet packet representation with zerotree quantization for image coding. A general zerotree structure is defined which can adapt itself to any arbitrary wavelet packet basis. We then describe an efficient coding algorithm based on this structure. Finally, the hypothesis for prediction of coefficients from coarser scale to finer scale is tested and its effectiveness is compared with that of zerotree hypothesis for wavelet coefficients.

This paper introduces a new generalisation of the familiar scale-space and wavelet representations, designed specifically to deal with the complexities of representing motions induced in an image sequence by the movement of 3-D objects of which the scene is comprised. It does this by combining an affine representation of local image motions with a local structure model based on Gaussian functions. After a brief review of its symmetry and completeness properties, the representation is applied to the analysis of image motions in a typical video sequence.

A model of natural texture based on a structural component that uses affine coordinate transformations and a stochastic residual component is presented. It is argued that the selection of an appropriate analysis scale can be formulated in terms of a tradeoff between the rate at which parameters are generated and the distortion resulting from the approximation by the structural component. An efficient algorithm for identifying the parameters of the structural model is described and its utility demonstrated on a number of synthetic and natural textures.

In this paper the combination of featureless and feature-based motion analysis is proposed as a way to overcome the limitations that both techniques exhibit when used separately. A multiresolution region-based motion estimator is used to supply affine motion estimates for variable size image regions. These estimates assist the tracking of extracted linear features in the sequence which yield accurate rotational and translational motion estimates for region boundaries. The multiresolution Fourier transform is used as a suitable underlying image representation for both parts of the analysis. The feature extraction and tracking process is described in some detail and results are presented, showing the accuracy of the combined motion estimates.

The purpose of this paper is to explore the relationship between symmetry and locality-properties which are regarded as desirable in any image representation and which are frequently mentioned in connection with wavelet transforms. It is shown how the two conspire to cause uncertainty; a new form of the uncertainty principle is introduced and a novel window design technique presented.

A novel frequency domain approach to the analysis of texture is presented. It consists of two main components: texture synthesis and segmentation. The synthesis method models the relation between pairs of texture patches by an affine transform. Segmentation is accomplished by detecting the texture boundary using a gradient operator. This scheme is implemented in the Fourier domain with varying scales using a generalised wavelet transform, the multiresolution Fourier transform (MFT). The technique has the potential to deal effectively with textures having varying amounts of structural information.>

This paper presents four new feature extraction operators (based on gradient filters), which can be used to extract various edge and corner properties of images. Each of these operators consists of a bilinear combination of 1/sup st/ and 2/sup nd/ order derivatives of the luminance image, and is either invariant or equivariant to rotations of the image. A brief outline of these invariance and equivariance properties is given. The computational requirements of calculating the operators are stated, and some results of their application on clean and noisy images are presented. In these results, an image pyramid is used to show how a multiresolution approach can give robust estimates in the presence of noise.>

Deals with the design of filter kernels having specified radial and angular frequency responses based on combined optimization and frequency sampling. This is used to generate small-radius, low-pass, and edge-detection kernels for multiresolution pyramids. The performance of the new kernels in estimating orientation is shown to be significantly better than that of other commonly used pyramid kernels.>

A wavelet transform specifically designed for Fourier analysis at multiple scales is described and shown to be capable of providing a local representation which is particularly well suited to segmentation problems. It is shown that, by an appropriate choice of analysis window and sampling intervals, it is possible to obtain a Fourier representation which can be computed efficiently and overcomes the limitations of using a fixed scale of window, yet by virtue of its symmetry properties allows simple estimation of such fundamental signal parameters as instantaneous frequency and onset time/position. The transform is applied to the segmentation of both image and audio signals, demonstrating its power to deal with signal events which are localized in either time/space or frequency. Feature extraction and segmentation are performed through the introduction of a class of multiresolution Markov models, whose parameters represent the signal events underlying the segmentation.>

A curve extraction algorithm which is defined within a multiresolution framework is described. An image model based on local features such as lines and edges is assumed, and the parameters of this model are estimated using the multiresolution Fourier transform. The estimated features, which exist at different spatial resolutions, are then combined into curves using an appropriate curvature measure. The scheme is generally applicable and can be implemented in an efficient manner within a hierarchical data structure. Results presented demonstrate that it is capable of identifying curves in natural images.>

The problem of estimating feature orientation from noisy image data is addressed using a multiresolution technique. It is shown that by an appropriate choice of representation of orientation, it is possible to employ simple linear smoothing methods to reduce estimation noise. The smoothing is done using a combination of scale-space recursive filtering and iterative estimation, giving significant improvements in estimated orientations at low computational cost. Applications to enhancement and segmentation are presented.

This paper is an attempt to bring together a number of current ideas in multiresolution image processing into a single framework. The unification is achieved by introducing a two-level image model, comprising a quadtree containing parameters which control the evolution of the image as a sequence of successive refinements through scale-space. Examples of the method's application to image coding and analysis are used to illustrate the principles and show its usefulness.

A class of linear recursive image estimation methods, based on multiresolution image representations, is introduced. Although recursive, the estimators are causal not in the image plane but in a third dimension, that of the scale index. The estimators are efficient computationally and are in general suboptimal for a class of image models based explicitly on the scale-space underlying the multiresolution description. Methods are also presented for adapting the estimates to local image structure across a wide range of scales. The estimates are robust and outperform many of the techniques reported in the literature in terms of computational efficiency, signal-to-noise gain, and subjective appearance. A brief presentation of the theoretical basis of the methods is followed by experimental results and conclusions on the potential of the approach.>

For pt.I see ibid., vol.9, no.6, p.787 (1987). The problem of uncertainty in image feature description is discussed, and it is shown how finite prolate spheroidal sequences can be used in the construction of feature descriptions that combine spatial and frequency-domain locality in an optimal way. Methods of constructing such optimal feature sets, which are suitable for graphical implementation, are described, and some generalizations of the quadtree concept are presented. These methods are illustrated by examples from image processing applications, including feature extraction and texture description. The problem of image segmentation is discussed, and the importance of scale invariance in overcoming the limitations imposed by uncertainty is demonstrated. A novel texture segmentation algorithm that is based on a combination of the new feature description and multiresolution techniques is described and shown to give accurate segmentations on a range of synthetic and natural textures.>

Recent physiological research has indicated that the visual system makes use of units responsive to Gabor signals in the analysis of visual stimuli. Such functions effect a tradeoff between pure spatial- and frequency-domain descriptions. The authors explain the use of such representations in vision, considered as a process in inference from the retinal signals to a symbolic description. The appropriate mathematical structure for the inference is that of the subspaces of the signal vector space, a feature which it shares with quantum mechanics. The theory is derived directly from the fundamental constraints on visual inference. It is then shown to be consistent with many of the known properties of the visual system. In particular, a major feature of the inference system-the occurrence of interference effects-has already been observed in visual system operation.>

The finite prolate spheroidal sequences are those finite sequences which have extremal energy concentrations both in space and spatial frequency. The first part of the paper is devoted to a study of the eigenvalue problem defining the sequences. This reveals those fundamental properties of the sequences which are relevant in image processing applications and shows how they can be generated efficiently. A new version of the sampling theorem is also demonstrated.

Finite forms of the two common eigenvalue problems associated with the uncertainty principle are introduced. The results are extended to two dimensions and it is shown that feature extraction filters produced using these methods are effective in the processing of natural images.

A new class of predictive coding algorithms, based on the quad-tree image representation, is described. Data compression schemes based on these algorithms have been found to produce acceptable images (peak-rms SNR > 30dB) at rates as low as 0.25 bit/pixel.

The uncertainty principle is recognized as one of the fundamental results in signal processing. Its role in inference is, however, less well known outside of quantum mechanics. It is the aim of this paper to provide a unified approach to the problem of uncertainty in image processing. It is shown that uncertainty can be derived from the fundamental constraints on the process of vision-the requirements for class-defining operations which are both shift-invariant and insensitive to changes in illumination. It is thus shown that uncertainty plays a key role in the language of vision, since it affects the choice of both the alphabet, the elementary signals, and the syntax, the inferential structure, of vision. The report is concluded with a number of practical illustrations of these ideas, taken from such image processing tasks as enhancement, data compression, and segmentation.

A new form of image estimator, which takes account of linear features, is derived using a signal equivalent formulation. The estimator is shown to be a nonstationary linear combination of three stationary estimators. The relation of the estimator to human visual physiology is discussed. A method for estimating the nonstationary control information is described and shown to be effective when the estimation is made from noisy data. A suboptimal approach which is computationally less demanding is presented and used in the restoration of a variety of images corrupted by additive white noise. The results show that the method can improve the quality of noisy images even when the signal-to-noise ratio is very low.

A new predictive coder, based on an estimation method which adapts to line and edge features in images, is described. Quantization of the prediction error is performed by a two-level adaptive scheme: an adaptive transform coder, and threshold coding in both transform and spatial domains. Control information, which determines the behavior of the predictor, is quantized using a simple variable rate technique. The results are improved by pre- and postfiltering using a related noncausal form of the estimator. Acceptable images have been produced in this way at bit rates of less than 0.5 bit/pixel.

A non-stationary predictive image coder is described. The predictor is controlled by a compact representation of the image line and edge content. Quantization of the prediction error is performed in both spatial and transform domains. The control information is transmitted using a simple variable-rate scheme. Acceptable results have been obtained with the coder at rates of .5 bit/pixel and below.

A suitable operational definition of the subjective acceptability of an information source to a human user is shown to be the "probability of acceptance in a multiple-choice test." It is shown that acceptance probability relates directly to the user's statistical dependence on a given source. The notion of subjective cost of information is introduced as a concise way of defining such acceptance probabilities and a general statistical model of decision behavior used to establish the relation between expected cost and probability of acceptance. Distortion is then defined as the marginal cost of accepting a replication over that of the original source. It is shown that this leads to a way of determining distortion functions from observation of acceptance decisions. The method is illustrated with an example of image noise evaluation.

Constructions are given of sets of orthogonal multilevel pseudorandom sequences with binomial and uniform amplitude distributions. The sequences are based on binary maximal-length sequences and have similar correlation properties to those sequences. Pseudorandom impulse sequences suitable for nerve impulse simulation are constructed from the uniform-amplitude distribution sequences, and empirical bounds are established on their correlation performance.

General expressions for the probability distribution and density of the sum ofNlow-pass filtered outputs of a multiplier whose inputs are coherent, equal power noisy narrowband signals are derived in a finite series form. Graphs of the density for several values ofNand two signal-noise ratios are presented and discussed.

A class of quadraphase synchronizing sequences, whose lengths may be any power of two, is constructed using codes originally reported by Welti. It is shown that there exist realizations of the codes for both coherent and differentially coherent PSK systems. Like binary maximal length sequences (BMLS) their generation and detection require circuits whose complexity grows as\log_{2}N, whereNis the codelength. Their aperiodic correlation properties, however, are superior to those of any BMLS-their correlation sidelobes are identically zero, giving unambiguous asynchronous detection.