Multiscale Image Representation Research Articles

An edge detection scheme based on least squares support vector machine in a contourlet HMT domain

In this paper, we have presented a new and effective edge detection scheme based on least squares support vector machine (LS-SVM) classification in a contourlet Hidden Markov Tree Model (contourlet HMT). First, the input noisy image is decomposed into coarser and finer coefficients using a contourlet HMT transform to derive an efficient multiscale and multidirectional image representation. Second, the feature vector is performed through spatial regularity in a contourlet HMT domain, and the coarser coefficients classified using LS-SVM classifier into two classes: noise coefficients and edge coefficients. Next, all noisy contourlet HMT coefficients are well denoised by the BayesShrink method.Finally, the denoised coefficients and edge coefficients are fused using the weighted average rule, and the inverse contourlet HMT is applied to obtain the edge image.Experimental results demonstrate that our scheme can attain improved performance over state-of-the-art edge detection approaches, both qualitatively and quantitatively. Tests were performed on several images from the Berkeley dataset corrupted with Gaussian noise and on other images such as a cameraman, pepper and medical images. The results illustrate that the performance of the proposed scheme is stable.

Fast multiscale directional filter bank-based speckle mitigation in gallstone ultrasound images

Speckle noise is a multiplicative type of noise commonly seen in medical and remote sensing images. It gives a granular appearance that degrades the quality of the recorded images. These speckle noise components need to be mitigated before the image is used for further processing and analysis. This paper presents a novel approach for removing granular speckle noise in gray scale images. We used an efficient multiscale image representation scheme named fast multiscale directional filter bank (FMDFB) along with simple threshold methods such as Vishushrink for image processing. It is a perfect reconstruction framework that can be used for a wide range of image processing applications because of its directionality and reduced computational complexity. The FMDFB-based speckle mitigation is appealing over other traditional multiscale approaches such as wavelets and Contourlets. Our experimental results show that the despeckling performance of the proposed method outperforms the wavelet and Contourlet-based despeckling methods.

A Multiscale Latent Dirichlet Allocation Model for Object-Oriented Clustering of VHR Panchromatic Satellite Images

A novel model is presented to address the problem of semantic clustering of geo-objects in very high resolution panchromatic satellite images. The proposed model combines a probabilistic topic model with a multiscale image representation into an automatic framework by embedding both document and scale selections. The probabilistic topic model is used to characterize the statistical distributions of both intraclass appearance and inter-class coherence of geo-objects within documents, i.e., squared sub-images. Because the bag-of-words assumption involved in the probabilistic topic models does not consider the spatial coherence between topic labels, the multiscale image representation is designed to provide a self-adaptive spatial regularization for various geo-object categories. By introducing scale and document selections, the automatic framework integrates the probabilistic topic model and the multiscale image representation to ensure that words on a site should be allocated the same topic label no matter what documents they reside in. Consequently, unlike the traditional method of applying topic models for analyzing satellite images, the process of explicitly generating a set of documents before modeling and then combining multiple labels for a word on a given site is unnecessary. Gibbs sampling is adopted for parameter estimation and image clustering. Extensive experimental evaluations are designed to first analyze the effect of parameters in the proposed model and then compare the results of our model with those of some state-of-the-art methods for three different types of images. The results indicate that the proposed algorithm consistently outperforms these exiting state-of-the-art methods in all of the experiments.

Directional Multiscale Processing of Images Using Wavelets with Composite Dilations

It is widely recognized that the performance of many image processing algorithms can be significantly improved by applying multiscale image representations with the ability to handle very efficiently directional and other geometric features. Wavelets with composite dilations offer a flexible and especially effective framework for the construction of such representations. Unlike traditional wavelets, this approach enables the construction of waveforms ranging not only over various scales and locations but also over various orientations and other orthogonal transformations. Several useful constructions are derived from this approach, including the well-known shearlet representation and new ones, introduced in this paper. In this work, we introduce and apply a novel multiscale image decomposition algorithm for the efficient digital implementation of wavelets with composite dilations. Due to its ability to handle geometric features efficiently, our new image processing algorithms provide consistent improvements upon competing state-of-the-art methods, as illustrated on a number of image denoising and image enhancement demonstrations.

Texture Image Recognition Algorithm Based on Steerable Pyramid Transform

at present, texture image recognition mostly is identified by using an intelligent algorithm which is based on the feature extraction method in a variety of ways, such as neural network recognization that is based on the wavelet transform or wavelet packet. Steerable pyramid transform is a multidirectional and multi-scale image representation. In this paper, texture recognition algorithm is based on steerable pyramid transform. This method extracts image features which are identified by support vector machine under different methods and resolution, and improves the accuracy of image recognition. Compared with the existing wavelet transform, wavelet packet, ridgelet in the case of noise, the methods' rate of correct identification is superior to other algorithms.

Mixtures of conditional Gaussian scale mixtures applied to multiscale image representations.

We present a probabilistic model for natural images that is based on mixtures of Gaussian scale mixtures and a simple multiscale representation. We show that it is able to generate images with interesting higher-order correlations when trained on natural images or samples from an occlusion-based model. More importantly, our multiscale model allows for a principled evaluation. While it is easy to generate visually appealing images, we demonstrate that our model also yields the best performance reported to date when evaluated with respect to the cross-entropy rate, a measure tightly linked to the average log-likelihood. The ability to quantitatively evaluate our model differentiates it from other multiscale models, for which evaluation of these kinds of measures is usually intractable.

Quasi-random nonlinear scale space

A novel nonlinear scale space framework is proposed for the purpose of multi-scale image representation. The scale space decomposition problem is formulated as a general Bayesian least-squares estimation problem. A quasi-random density estimation approach is introduced for estimating the posterior distribution between consecutive scale space realizations. In addition, the application of the proposed nonlinear scale space framework for edge detection is proposed. Experimental results demonstrate the effectiveness of the proposed scale space framework for constructing scale space representations with significantly better structural localization across all scales when compared to state-of-the-art scale space frameworks such as anisotropic diffusion, regularized nonlinear diffusion, complex nonlinear diffusion, and iterative bilateral scale space methods, especially under scenarios with high noise levels.

Efficient registration of multitemporal and multisensor aerial images based on alignment of nonparametric edge features

The topic of aerial image registration attracts considerable interest within the imaging research community due to its significance for several applications, including change detection, sensor fusion, and topographic mapping. Our interest is focused on finding the optimal transformation between two aerial images that depict the same visual scene in the presence of pronounced spatial, temporal, and sensor variations. We first introduce a stochastic edge estimation process suitable for geometric shape-based registration, which we also compare to intensity-based registration. Furthermore, we propose an objective function that weights the L2 distances of the edge estimates by the feature points' energy, which we denote by sum of normalized squared differences and compare to standard objective functions, such as mutual information and the sum of absolute centered differences. In the optimization stage, we employ a genetic algorithm scheme in a multiscale image representation scheme to enhance the registration accuracy and reduce the computational load. Our experimental tests, measuring registration accuracy, rate of convergence, and statistical properties of registration errors, suggest that the proposed edge-based representation and objective function in conjunction with genetic algorithm optimization are capable of addressing several forms of imaging variations and producing encouraging registration results.

Shape-based Invariant Texture Indexing

This paper introduces a new texture analysis scheme, which is invariant to local geometric and radiometric changes. The proposed methodology relies on the topographic map of images, obtained from the connected components of level sets. This morphological tool, providing a multi-scale and contrast-invariant representation of images, is shown to be well suited to texture analysis. We first make use of invariant moments to extract geometrical information from the topographic map. This yields features that are invariant to local similarities or local affine transformations. These features are invariant to any local contrast change. We then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases. The obtained experimental results outperform the current state of the art in locally invariant texture analysis.

Multiscale image representation using novel integro-differential equations

Motivated by the hierarchical multiscale image representation of Tadmor et. al., (25), we propose a novel integro-differential equation (IDE) for a multiscale image representation. To this end, one integrates in inverse scale space a succession of refined, recursive 'slices' of the image, which are balanced by a typical curvature term at the finer scale. Although the original moti- vation came from a variational approach, the resulting IDE can be extended using standard techniques from PDE-based image processing. We use filtering, edge preserving and tangential smoothing to yield a family of modified IDE models with applications to image denoising and image deblurring problems. The IDE models depend on a user scaling function which is shown to dictate the BV ∗ properties of the residual error. Numerical experiments demonstrate application of the IDE approach to denoising and deblurring.

Image modeling and denoising with orientation-adapted Gaussian scale mixtures.

We develop a statistical model to describe the spatially varying behavior of local neighborhoods of coefficients in a multiscale image representation. Neighborhoods are modeled as samples of a multivariate Gaussian density that are modulated and rotated according to the values of two hidden random variables, thus allowing the model to adapt to the local amplitude and orientation of the signal. A third hidden variable selects between this oriented process and a nonoriented scale mixture of Gaussians process, thus providing adaptability to the local orientedness of the signal. Based on this model, we develop an optimal Bayesian least squares estimator for denoising images and show through simulations that the resulting method exhibits significant improvement over previously published results obtained with Gaussian scale mixtures.

Multiscale deformable registration of noisy medical images

Multiscale image registration techniques are presented for the registration of medical images using deformable registration models. The techniques are particularly effective for registration problems in which one or both of the images to be registered contains significant levels of noise. A brief overview of existing deformable registration techniques is presented, and experiments using B-spline free-form deformation registration models demonstrate that ordinary deformable registration techniques fail to produce accurate results in the presence of significant levels of noise. The hierarchical multiscale image decomposition described in E. Tadmor, S. Nezzar, and L. Vese's, "A multiscale image representation using hierarchical (BV;L2) decompositions" (Multiscale Modeling and Simulations, 2 (2004): 4, pp. 554-579) is reviewed, and multiscale image registration algorithms are developed based on the multiscale decomposition. Accurate registration of noisy images is achieved by obtaining a hierarchical multiscale decomposition of the images and iteratively registering the resulting components. This approach enables a successful regstration of images that contain noise levels well beyond the level at which ordinary deformable registration fails. Numerous image registration experiments demonstrate the accuracy and efficiency of the multiscale registration techniques.

Hybrid multiscale landmark and deformable image registration

An image registration technique is presented for the registration of medical images using a hybrid combination of coarse-scale landmark and B-splines deformable registration techniques. The technique is particularly effective for registration problems in which the images to be registered contain large localized deformations. A brief overview of landmark and deformable registration techniques is presented. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese, A multiscale image representation using hierarchical (BV;L(2)) decompositions, Multiscale Modeling and Simulations, vol. 2, no. 4, pp. 554{579, 2004, is reviewed, and an image registration algorithm is developed based on combining the multiscale decomposition with landmark and deformable techniques. Successful registration of medical images is achieved by first obtaining a hierarchical multiscale decomposition of the images and then using landmark-based registration to register the resulting coarse scales. Corresponding bony structure landmarks are easily identified in the coarse scales, which contain only the large shapes and main features of the image. This registration is then fine tuned by using the resulting transformation as the starting point to deformably register the original images with each other using an iterated multiscale B-splines deformable registration technique. The accuracy and efficiency of the hybrid technique is demonstrated with several image registration case studies in two and three dimensions. Additionally, the hybrid technique is shown to be very robust with respect to the location of landmarks and presence of noise.

A Multiscale Entropy Analysis of Physiological and Malignant Breast Tissues Imaged by an Optical Polarimeter

A Multiscale Entropy Analysis of Physiological and Malignant Breast Tissues Imaged by an Optical Polarimeter There are indications in the literature that polarimetric observations of neoplastic changes in biological tissues may support early diagnosis of cancer. In the present studies, samples of human breast tissue were observed in a polarized light. The images of healthy and malignant tissues were decomposed by a à trous wavelet algorithm. When a multiscale representation of tissue images is determined, their autocorrelation functions are also compared. A comparison of new observables, multiscale entropy and mean entropy vectors are presented. It was found that these observables might be considered as possible indicators of the malignant transformation in tissue.

A rotation-insensitive multiscale image representation based on the wavelet transform: Definition and image recovery algorithm

This paper aims at a multiscale image representation which is rotation- and shift-invariant. The wavelet energy distribution is defined, and an image recovery algorithm is proposed based on the representation. In order to derive the image representation, which is almost rotation-invariant, two or three components in different directions of the discrete binary wavelet transform are integrated into a wavelet energy distribution. The image is recovered from the wavelet energy distribution by iterative operations. It is guaranteed in the proposed iterative operation that the error between the wavelet energy distribution of the recovered image and the given wavelet energy distribution decreases and converges. This paper proposes a coarse-to-fine recovery method which is based on the multiscale property of the wavelet transform, and reduces the danger that the procedure is trapped by a local minimum. The usefulness of the proposed coarse-to-fine recovery method is verified through several image recovery examples. As an application example, the method is applied to contour extraction coding by sampling the wavelet energy distribution along the contour of an image. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(12): 65–78, 1999

A rotation‐insensitive multiscale image representation based on the wavelet transform: Definition and image recovery algorithm

A rotation‐insensitive multiscale image representation based on the wavelet transform: Definition and image recovery algorithm

Unsupervised texture segmentation in a deterministic annealing framework

We present a novel optimization framework for unsupervised texture segmentation that relies on statistical tests as a measure of homogeneity. Texture segmentation is formulated as a data clustering problem based on sparse proximity data. Dissimilarities of pairs of textured regions are computed from a multiscale Gabor filter image representation. We discuss and compare a class of clustering objective functions which is systematically derived from invariance principles. As a general optimization framework, we propose deterministic annealing based on a mean-field approximation. The canonical way to derive clustering algorithms within this framework as well as an efficient implementation of mean-field annealing and the closely related Gibbs sampler are presented. We apply both annealing variants to Brodatz-like microtexture mixtures and real-word images.

Efficient spatial-domain implementation of a multiscale image representation based on Gabor functions

Gabor schemes of multiscale image representation are useful in many computer vision applications. However, the classic Gabor expansion is computationally expensive due to the lack of orthogonality of Gabor functions. Some alternative schemes, based on the application of a bank of Gabor filters, have important advantages such as computational efficiency and robustness, at the cost of redundancy and lack of completeness. In a previous work we proposed a quasicomplete Gabor transform, suitable for fast implementations in either space or frequency domains. Reconstruction was achieved by simply adding together the even Gabor channels. We develop an optimized spatial-domain implementation, using one-dimensional 11-tap filter masks, that is faster and more flexible than Fourier implementations. The reconstruction method is improved by applying fixed and independent weights to the Gabor channels before adding them together. Finally, we analyze and implement, in the spatial domain, two ways to incorporate a high-pass residual, which permits a visually complete representation of the image. © 1998 SPIE and IS&T.

Learning an integral equation approximation to nonlinear anisotropic diffusion in image processing

Multiscale image enhancement and representation is an important part of biological and machine early vision systems. The process of constructing this representation must be both rapid and insensitive to noise, while retaining image structure at all scales. This is a complex task as small scale structure is difficult to distinguish from noise, while larger scale structure requires more computational effort. In both cases, good localization can be problematic. Errors can also arise when conflicting results at different scales require cross-scale arbitration. Structure sensitive multiscale techniques attempt to analyze an image at a variety of scales within a single image. Various techniques are compared. In this paper, we present a technique which obtains an approximate solution to the partial differential equation (PDE) for a specific time, via the solution of an integral equation which is the nonlinear analog of convolution. The kernel function of the integral equation plays the same role that a Green's function does for a linear PDE, allowing the direct solution of the nonlinear PDE for a specific time without requiring integration through intermediate times. We then use a learning technique to approximate the kernel function for arbitrary input images. The result is an improvement in speed and noise-sensitivity, as well as providing a means to parallelize an otherwise serial algorithm.

Representation and detection of multiscale, multiorientation fields using local differentiation filters

AbstractA basic theory is proposed for detecting multiorientation fields from images that have multiple orientations at each point in the field. This theory, representing a multiorientation field by a single set of fundamental constraint equations, differs from conventional methods which use many filters tuned to different orientations. It is also different from the steerable filters proposed by Freeman and Adelson [12]. This theory renders implementation of a selection process of orientation‐tuned filters with high‐magnitude output unnecessary. It also makes it unnecessary to implement a search process for an extreme value output of steerable filters. This theory lets analytical solutions to be derived that explicitly compute multiple orientations. This theory is derived from the operational formalism of the principle of linear superposition. Conventional methods suffer from interference between component signals when multiorientation signal components fall in the tuning range of each filter. As a result, filters with a narrow tuning range are necessary in conventional methods. the algorithms derived from out theory are not negatively influenced by interference. By using these algorithms in multiscale image representation, characteristic image structures such as junctions can be extracted from low‐order image derivatives. This theory is expected to provide a theoretical foundation for the image representation of multiple orientations of the hypercolumn structure in the primary visual cortex of the brain.