Multiscale Edge Research Articles

Faber-Schauder Wavelet Transform, Application to Edge Detection and Image Characterization

The Faber-Schauder wavelet transform is a simple multiscale transformation with many interesting properties in image processing. Some of these properties are: preservation of pixel ranges, arithmetic operations, non requirement of boundary processing, multiscale edge detection, elimination of the constant and the linear correlation, and the use of close neighboring information. In this study we describe this transformation and we propose a mixed scale visualization of the wavelet transform which makes it possible to show the transform result as an image. This visualization is used, with orientation information, to refine edge detection and image characterization by selecting regions with a high density of extrema wavelet coefficients.

Atomic Decomposition by Basis Pursuit

The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries---stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), matching pursuit (MP), and, for special dictionaries, the best orthogonal basis (BOB). Basis pursuit (BP) is a principle for decomposing a signal into an "optimal"' superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution. BP has interesting relations to ideas in areas as diverse as ill-posed problems, abstract harmonic analysis, total variation denoising, and multiscale edge denoising. BP in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked successfully only because of recent advances in linear and quadratic programming by interior-point methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.

Analyzing the Mallat Wavelet Transform to Delineate Contour and Textural Features

Analyzing natural scenes is made difficult when both contour and textural features are present. The problem of building suitable contour models from such images is compounded given texture region segmentation results in poor edge localization and multiscale edge representations cannot always separate salient contour features from irrelevant textural clutter. To overcome these problems, a novel algorithm is presented which first creates a multiscale edge representation using the Mallat wavelet transform and then recombines the edge map at each scale to create a single contour map where textural clutter has been minimized. This algorithm is then applied to natural and synthetic images containing contour features at different spatial scales and texture of varying spatial frequency and orientation. The results show that contour and textural features can be discriminated at each scale and the resulting contour map serves as a more effective representation on which subsequent localization and recognition tasks are based.

Inferring Geological Structures using Wavelet-Based Multiscale Edge Analysis and Forward Models

A set of semi-automatic tools for analysis of potential field data has been developed. These tools use wavelet analysis to automatically detect gradients or edges in potential field data. The tools are normally applied to different levels of upward continuation, providing automatic detection of edges in the potential field data at different scales of resolution. We refer to these edges at different levels of upward continuation as “multiscale edges”.Commonly, sharp contrasts evident in potential field data (edges or gradients) are assumed to result from sharp discontinuities or interfaces between contrasting rock materials such as faults, unconformities, or intrusive contacts. Because of the inherent non-uniqueness of potential field problems, there can be no certain or unambiguous differentiation between different possible source rock geometries without reference to a priori information such as independent geological data. In many cases the a priori information which is most readily available describes a geological “style” which consists of some form of idealised or simplified geometry or expected range/strength of contrasts in rock properties.The common assumption that geological units are sharply bounded by faults and other geological contacts suggests that irregularities in geophysical potential-field images correspond to irregularities in the sub-surface rocks, and this relationship has been the basis for many forward and inverse modelling systems (Jessell, 1999). In order to document the results of the new, semiautomatic edge detection techniques, these techniques have been applied to synthetic datasets (Jessell, 1981; Jessell & Valenta, 1996). Each synthetic dataset investigates an idealised source geometry (e.g. intrusions, faults, dykes) the expected potential field data, and the resulting multiscale edges. The resulting “atlas” of source geometries and multiscale edges aids the interpretation of real-world data. The new analysis techniques and the “atlas” of multiscale edges, have direct application to calculations of depth to source, dip directions, and contact relationships.

A multi-scale morphological approach to SAR image edge detection

This paper introduces a multi-scale morphological edge detection algorithm to extract SAR image edge which suffers seriously from noise. Combining the basic theme of morphology with that of multi-scale analysis, the algorithm presents the outstanding characteristics of accuracy and robustness. Comparative Experiments reveal its fine performance.

BV-type regularization methods for convoluted objectswith edge, flat and grey scales

A variational approach for the robust inversion of linearsmoothing operators is discussed. We employ and generalize theenhancement techniques based on BV- and Perona-Malik-typeregularization methods. The problem is cast as the minimizationof a cost functional consisting of a data fitting and arestoration energy criterion for multiscale objects consistingof edge, flat and grey regions. An iterative algorithm forfinding the restored object that minimizes the cost functionalis developed and analysed. It is based upon a fixed-pointiteration combining a time-marching and successivesubstitution method for finding a solution to a quasi-ellipticpartial differential equation. Global convergence is proved.Numerical examples illustrate the proposed approach.

A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces

We generalize the so-called wavelet transform modulus maxima (WTMM) method to multifractal image analysis. We show that the implementation of this method provides very efficient numerical techniques to characterize statistically the roughness fluctuations of fractal surfaces. We emphasize the wide range of potential applications of this wavelet-based image processing method in fundamental as well as applied sciences. This paper is the first one of a series of three articles. It is mainly devoted to the methodology and to test applications on random self-affine surfaces (e.g., isotropic fractional Brownian surfaces and anisotropic monofractal rough surfaces). Besides its ability to characterize point-wise regularity, the WTMM method is definitely a multiscale edge detection method which can be equally used for pattern recognition, detection of contours and image denoising. Paper II (N. Decoster, S.G. Roux, A. Arneodo, to be published in Eur. Phys. J. B 15 (2000)) will be devoted to some applications of the WTMM method to synthetic multifractal rough surfaces. In paper III (S.G. Roux, A. Arneodo, N. Decoster, to be published in Eur. Phys. J. 15 (2000)), we will report the results of a comparative experimental analysis of high-resolution satellite images of cloudy scenes.

Automatic on-line electronic portal image analysis with a wavelet-based edge detector.

A fully automatic method for on-line electronic portal image analysis is proposed. The method uses multiscale edge detection with wavelets for both the field outline and the anatomical structures. An algorithm to extract and combine the information from different scales has been developed. The edges from the portal image are aligned with the edges from the reference image using chamfer matching. The reference is the first portal image of each treatment. The matching is applied first to the field and subsequently to the anatomy. The setup deviations are quantified as the displacement of the anatomical structures relative to the radiation beam boundaries. The performance of the algorithm was investigated for portal images with different contrast and noise level. The automatic analysis was used first to detect simulated displacements. Then the automatic procedure was tested on anterior-posterior and lateral portal images of a pelvic phantom. In both sets of tests the differences between the measured and the actual shifts were used to quantify the performance. Finally we applied the automatic procedure to clinical images of pelvic and lung regions. The output of the procedure was compared with the results of a manual match performed by a trained operator. The errors for the phantom tests were small: average standard deviation of 0.39 mm and 0.26 degrees and absolute mean error of 0.31 mm and 0.2 degrees were obtained. In the clinical cases average standard deviations of 1.32 mm and 0.6 degrees were found. The average absolute mean errors were 1.09 mm and 0.39 degrees. Failures were registered in 2% of the phantom tests and in 3% of the clinical cases. The algorithm execution is approximately 5 s on a 168 MHz Sun Ultra 2 workstation. The automatic analysis tool is considered to be a very useful tool for on-line setup corrections.

172 REAL TIME EDGES DETECTION USING WAVELET TRANSFORM

One of the way to extract edges uses the fast wavelet transform algorithm. This technique allows the detection of multiscale edges and is used to detect all the details, which are in a picture by modifying the scale. The real time application for edge detection involves the implementation of the algorithm on an integrated circuit like a FPGA and the development of an appropriated board. This article deals about the implementation of a wavelet transform algorithm onto a FPGA and development of an electronic board to detect multiscale edges.

Matching and retrieval based on the vocabulary and grammar of color patterns

We propose a perceptually based system for pattern retrieval and matching. The central idea is that similarity judgment has to be modeled along perceptual dimensions. Hence, we detect basic visual categories that people use in their judgment of similarity, and design a computational model that accepts patterns as input and, depending on the query, produces a set of choices that follow human behavior in pattern matching. There are two major research aspects to our work. The first one addresses the issue of how humans perceive and measure similarity within the domain of color patterns. To understand and describe this mechanism, we performed a subjective experiment which yielded five perceptual criteria used in comparison between color patterns (vocabulary), as well as a set of rules governing the use of these criteria in similarity judgment (grammar). The second research aspect is the implementation of the perceptual criteria and rules in an image retrieval system. Following the processing typical for human vision, we design a system to: (1) extract perceptual features from the vocabulary and (2) perform the comparison between the patterns according to the grammar rules. The modeling of human perception of color patterns is new--starting with a new color codebook design, compact color representation, and texture description through multi-scale edge distribution along different directions. Moreover, we propose new color and texture distance functions that correlate with human performance. The performance of the system is illustrated with numerous examples from image databases from different application domains.

Wavelet Multi-scale Edge Detection for Extraction of Geographic Features to Improve Vector Map Databases

Although numerous at smaller geographic scales, vector databases often do not exist at the more detailed, larger scales. A possible solution is the use of image processing techniques to detect edges in high-resolution satellite imagery. Features such as roads and airports are formed from the edges and matched up with similar features in existing low-resolution vector map databases. By replacing the old features with the new more accurate features, the resolution of the existing map database is improved. To accomplish this, a robust edge detection algorithm is needed that will perform well in noisy conditions. This paper studies and tests one such method, the Wavelet Multi-scale Edge Detector. The wavelet transform breaks down a signal into frequency bands at different levels. Noise present at lower scales smoothes out at higher levels. It is demonstrated that this property can be used to detect edges in noisy satellite imagery. Once edges are located, a new method will be proposed for storing these edges geographically so that features can be formed and paired with existing features in a vector map database.

Artificial neural network visual model for image quality enhancement

An artificial neural network visual model is developed, which extracts multi-scale edge features from the decompressed image and uses these visual features as input to estimate and compensate for the coding distortions. This provides a generic postprocessing technique that can be applied to all the main coding methods. Experimental results involving postprocessing of the JPEG and quadtree coding systems show that the proposed artificial neural network visual model significantly enhances the quality of reconstructed images, both in terms of the objective peak signal-to-noise ratio and subjective visual assessment.

Outlining of the prostate using snakes with shape restrictions based on the wavelet transform (Doctoral Thesis: Dissertation)

This paper considers the problem of deformable contour initialization and modeling for segmentation of the human prostate in medical images. We propose a new technique for elastic deformation restriction to particular object shapes of any closed planar curve using localized multiscale contour parameterization based on the 1D dyadic wavelet transform. For this purpose we define internal curve deformation forces as a result of multiscale parametrical contour analysis. The form restricted contour deformation and its initialization by template matching are performed in a coarse to fine segmentation process based on a multiscale image edge representation containing the important edges of the image at various scales. The method is useful for 3D conformal radiotherapy planning and automatic prostate volume measurements in ultrasonographic diagnosis.

A new hierarchical scheme for approximating the continuous wavelet transform with applications to edge detection

We propose an approximation of a continuous wavelet transform (CWT) that is based on a hierarchical scheme, similar to the fast discrete wavelet transform. This approximation keeps redundancies in time and scale. Furthermore, it preserves properties of the CWT regarding the characterization of singularities and leads to efficient applications in multiscale edge detection.

Analysis of potential field data in the wavelet domain

Various Green’s functions occurring in Poisson potential field theory can be used to construct non-orthogonal, non-compact, continuous wavelets. Such a construction leads to relations between the horizontal derivatives of geophysical field measurements at all heights, and the wavelet transform of the zero height field. The resulting theory lends itself to a number of applications in the processing of potential field data. Some simple, synthetic examples in two dimensions illustrate one inversion approach based upon the maxima of the wavelet transform (multiscale edges). These examples are presented to illustrate, by way of explicit demonstration, the information content of the multiscale edges. We do not suggest that the methods used in these examples be taken literally as a practical algorithm or inversion technique. Rather, we feel that the real thrust of the method is towards physically based, spatially local filtering of geophysical data images using Green’s function wavelets, or compact approximations thereto. To illustrate our first steps in this direction, we present some preliminary results of a 3-D analysis of an aeromagnetic survey.

Adaptive multiscale edge detection based on vision feature of edge and wavelet transform

A new multiscale edge detection method is presented, which is based on an effective edge measure. The effective edge measure, used to adaptively adjust the scales of wavelet transform, is defined using the novel features of image edge obtained from human being vision characteristics. Finally, two experiments show that the proposed algorithm appears to work well.

Bounded diffusion for multiscale edge detection using regularized cubic B-spline fitting

This paper shows that in edge detection the regularization factor alpha is a better scale parameter than the standard deviation (sigma) of the Gaussian pre-filter. The alpha scale space, which exhibits the evolutionary behaviour of an edge in various scales, is the basis for the design of a multiscale edge detector (MRCBS). In MRCBS, the scale is determined adaptively according to the local noise level; the thresholds which control the amount of edge details are adjusted according to the scale; and the anisotropic diffusion is applied in the finest scale to further suppress noise.

Multiscale edge analysis of potential field data

Mapping the three-dimensional distribution of rock properties from potential field data is a difficult and arduous task, with inherent ambiguity remaining a major problem. We apply a combination of automated interpretation procedures, based on multiscale wavelet analysis and three- dimensional visualisation methods, in an attempt to extract geometrical information from potential field datasets, and display this information in an easily understandable and intuitive way. The resulting visualisations are similar to ‘worm’ maps commonly produced by interpretation of aeromagnetic data, but are defined in three dimensions.The techniques are tested on a series of synthetic and observed datasets, of varying complexity and geographical scale. The tests show both the effectiveness of the technique as an aid to the geological interpretation of potential field maps and in its use for providing constraints on the three-dimensional geology.The results of the testing on synthetic datasets show that for certain geometries there is an intuitive relationship between 3D edge location and shape, and subsurface geometries. Such relationships prove particularly robust even under ‘noisy’ conditions where surface features (e.g. the response of laterites in magnetic datasets) mask the coarser scale features that characterise the broader geological picture.Three real datasets at different geographical scales have been analysed. These include the Western Australian gravity dataset (representing the continent-scale), aeromagnetic data covering a 1:100,000 scale map sheet from central Victoria (representing the district-scale), and a prospect- scale aeromagnetic dataset from a mineralised greenstone terrane in Western Australia. The results produce different information at the different scales. At the continent-scale the multiscale edges allow discrimination of different tectonic styles, and comparison of the significance of crustal-scale structures. At the district- to prospect-scale, the edges can be used for geological mapping purposes such as to map subtle changes in sedimentary sequences, map alteration patterns, and constrain pluton geometries at depth.

A multiscale approach to automatic medical image segmentation using self-organizing map

In this paper, a new medical image classification scheme is proposed using self-organizing map (SOM) combined with multiscale technique. It addresses the problem of the handling of edge pixels in the traditional multiscale SOM classifiers. First, to solve the difficulty in manual selection of edge pixels, a multiscale edge detection algorithm based on wavelet transform is proposed. Edge pixels detected are then selected into the training set as a new class and a multiscale SOM classifier is trained using this training set. In this new scheme, the SOM classifier can perform both the classification on the entire image and the edge detection simultaneously. On the other hand, the misclassification of the traditional multiscale SOM classifier in regions near edges is greatly reduced and the correct classification is improved at the same time.

Wavelet-based image enhancement in x-ray imaging and tomography

We consider an application of the wavelet transform to image processing in x-ray imaging and three-dimensional (3-D) tomography aimed at industrial inspection. Our experimental setup works in two operational modes-digital radiography and 3-D cone-beam tomographic data acquisition. Although the x-ray images measured have a large dynamic range and good spatial resolution, their noise properties and contrast are often not optimal. To enhance the images, we suggest applying digital image processing by using wavelet-based algorithms and consider the wavelet-based multiscale edge representation in the framework of the Mallat and Zhong approach [IEEE Trans. Pattern Anal. Mach. Intell. 14, 710 (1992)]. A contrast-enhancement method by use of equalization of the multiscale edges is suggested. Several denoising algorithms based on modifying the modulus and the phase of the multiscale gradients and several contrast-enhancement techniques applying linear and nonlinear multiscale edge stretching are described and compared by use of experimental data. We propose the use of a filter bank of wavelet-based reconstruction filters for the filtered-backprojection reconstruction algorithm. Experimental results show a considerable increase in the performance of the whole x-ray imaging system for both radiographic and tomographic modes in the case of the application of the wavelet-based image-processing algorithms.