Image Alignment

Abstract In this paper we pursue the task of aligning an ensemble of images in an unsupervised manner. This task has been commonly referred to as “congealing” in literature. A form of congealing, using a least-squares criteria, has been recently demonstrated to have desirable properties over conventional congealing. Least-squares congealing can be viewed as an extension of the Lucas & Kanade (LK) image alignment algorithm.

We consider the problem of aligning histological sections for 3D reconstruction and analysis. The method we propose is based on a block-matching strategy that allows us to compute local displacements between the sections. We then collect these local measures to estimate a rigid transformation. Our emphasis is on the necessity to use a robust approach for this estimation step. The process is integrated within a multi-scale scheme to improve both accuracy and computation time.

Lattice-focal camera [15]. We used an idealized analytic formula for the lattice-focal camera [15], ignoring discretization effects; in practice the DOF may not be evenly spanned by an integer square number of lens subsquares. The formula also assumes that the spectrum of a given lens instance matches well its expectation over a random selection of subsquare focal lengths.

Abstract Inverse problems encountered in image processing and computer vision are often ill-posed. Whether set in a Bayesian or energy-based context, such problems require prior assumptions expressed through an a priori probability or a regularization term, respectively. In some cases, the prior term exhibits partial dependence on the observations (eg, images) that is often ignored to simplify modeling and computations.

A comparison paper is presented to evaluate the results from five smoothing filters. The filters are linear, nonlinear isotropic and nonlinear anisotropic designed to smooth homogeneous areas while preserving the higher moments in the data. The methods are outlined and then evaluated on the extent to which edge information is preserved and unwanted noise is suppressed.

Precise image registration is a fundamental task in many computer vision algorithms including superresolution methods. The well known Lucas-Kanade (LK) algorithm is a very popular and efficient method among the various registration techniques. In this paper a modified version of it, based on the Structural Similarity (SSIM) image quality assessment is proposed. The core of the proposed method is contributing the SSIM in the sum of squared difference, which minimized by LK algorithm. Mathematical derivation of the proposed method is based on the unified framework of . Experimental results over 1000 runs on synthesized data validate the better performance of the proposed modification of LK-algorithm, with respect to the original algorithm in terms of the rate and speed of convergence, where the signal-to-noise ratio is low. In addition the result of using the proposed approach in a superresolution application is given.

Multi-sensor information fusion aims at extracting and combining useful information from different sensors. This paper addresses the problem of estimating and visualising motion information from a pair of visible and infrared cameras, using an optical flow technique. Videos from cameras sensitive to visible light are rich in texture and colour information such that a moving target can readily be positioned. On the other hand, videos from infrared cameras provide extra information which cannot be detected in the visible-light spectrum. In this paper we introduce a stochastic rule for combining optical flow computed from two (or more) sources. We also propose a novel motion-contingent selection method for the fusion of the co-registered visible and infrared video sources.

Real world scenes often contain both bright and dark regions, resulting in a high contrast ratio, beyond the capabilities of conventional cameras. For these cases, High Dynamic Range or HDR images can be captured with expensive hardware or by taking multiple exposures of the same scene. However, these methods cost extra resourceseither spatial or temporal resolution is sacrificed, or more than one piece of hardware is needed. In this thesis, a novel technique is presented that is capable of capturing High Dynamic Range images in only one exposure of a conventional camera. We observe that most natural HDR images have only 2-5% pixels that are too bright compared to the rest of the scene to fall inside the dynamic range of a conventional camera. Our method spreads energy from these bright regions into the neighboring unsaturated pixels by defocus blurring. Bright pixels still get clipped in the captured image due to saturation of the sensor; but some information about these clipped pixels gets encoded or multiplexed in the form of superimposed glare patterns in the image. Frequency preservation and decoding of this information can be further improved by using a crossscreen filter instead of using defocus blur. Superimposed glare patterns are recovered with the help of natural image statistics. These glare patterns provide information about how much energy there is in the saturated pixels, which allows a tomography-like reconstruction of the saturated regions. Once the saturated regions are known, the rest of the image can be restored by removing the estimated glare patterns.

The course can be split in two parts. In the implementation part, the kernel estimation process as described in [1] has been studied. The algorithm has been tested against synthetic and real data; and its performance has been discussed. In the reading part, a number of papers have been covered from the list of papers discussed in the graduate level course CPSC 505 "Image Understanding -I: Image Analysis" in Winter Term -I, 2007.

Myocardial motion analysis and quantification is of utmost importance for analyzing contractile heart abnormalities and it can be a symptom of a coronary artery disease. A fundamental problem in processing sequences of images is the computation of the optical flow, which is an approximation to the real image motion. This paper presents a new algorithm for optical flow estimation based on a spatiotemporal-frequency (STF) approach, more specifically on the computation of the Wigner-Ville distribution (WVD) and the Hough Transform (HT) of the motion sequences. The later is a well-known line and shape detection method very robust against incomplete data and noise. The rationale of using the HT in this context is because it provides a value of the displacement field from the STF representation. In addition, a probabilistic approach based on Gaussian mixtures has been implemented in order to improve the accuracy of the motion detection. Experimental results in synthetic sequences are compared with an implementation of the variational technique for local and global motion estimation, where it is shown that the results are accurate and robust to noise degradations. Results obtained in real cardiac magnetic resonance images are presented.

The distribution of digital images with the classic and newest technologies available on Internet has induced a growing interest on systems able to protect the visual content against malicious manipulations performed during their transmission. One of the main problems addressed in this context is the authentication of the image received in a communication. This task is usually performed by localizing the regions of the image which have been tampered. To this aim the received image should be first aligned with the one at the sender by exploiting the information provided by a specific component of the forensic hash associated with the image. In this paper we propose a robust alignment method which makes use of an image hash component based on the Bag of Features paradigm. In order to deal with highly textured and contrasted tampering patterns the spatial distribution of the image features has been encoded in the alignment signature. A block-wise tampering detection based on histograms of oriented gradients representation is also proposed. Specifically, a non-uniform quantization of the histogram of oriented gradient space is used to build the signature of each image block for tampering purposes. Experiments show that the proposed approach obtains good margin in terms of performances with respect to state-of-the art methods.

The distribution of digital images with the classic and newest technologies available on Internet (e.g., emails, social networks, digital repositories) has induced a growing interest on systems able to protect the visual content against malicious manipulations that could be performed during their transmission. One of the main problems addressed in this context is the authentication of the image received in a communication. This task is usually performed by localizing the regions of the image which have been tampered. To this aim the received image should be first registered with the one at the sender by exploiting the information provided by a specific component of the forensic hash associated with the image. In this paper we propose a robust alignment method which makes use of an image signature based on the Bag of Features paradigm. The alignment is based on a voting procedure in the parameter space of the model used to recover the geometric transformation occurred into the manipulated image. Experiments show that the proposed approach obtains good margin in terms of performances with respect to state-of-the art methods.

This thesis explores the use of Parzen windows for modeling image data. The validity of such a model is shown to follow naturally from the elementary Gestalt laws of vicinity, similarity, and continuity of direction. Consistency results are derived for Parzen window estimators, both for continuous-time and discrete-time images. The problem of scale is addressed; A novel plug-in estimator is proposed for the bandwidth (scale) of the window kernels. Asymptotic optimality of the proposed bandwidth is proved. The bandwidth selection scheme is validated for segmentation of real images. The density estimation framework is extended to model more structured images, e.g., those containing structures representable using local or global linear parametric models. Algorithms for robust parameter estimation and segmentation are given. Convergence results are derived for these algorithms. The robust parameter estimation framework is then extended to the problem of registering images of an object undergoing 2-D motion, overall image alignment (camera motion), and partial image alignment (2-D object tracking). For this purpose, novel estimation measures have been proposed. Algorithms have been proposed for the above tasks, and convergence of these algorithms have been proved. All proposed algorithms have been validated on real data.

Although a large variety of image registration methods have been described in the literature, only a few approaches have attempted to address the rigid registration of medical images showing gross dissimilarities (due for instance to lesion evolution) . In the present paper, we develop data driven registration algorithms, relying on robust pixel similarity metrics, that enable an accurate (subvoxel) rigid registration of dissimilar single or multimodal 2D/3D images. In the proposed approach, gross dissimilarities are handled by considering similarity measures related to robust M-estimators. A "soft redescending" estimator (the Geman-McClure p-function) has been adopted to reject gross image dissimilarities during the registration. The registration parameters are estimated using a top down stochatic multigrid relaxation algorithm. Thanks to the stochastic multigrid strategy, the registration is not affected by local minima in the objective function and a manual initialization near the optimal solution is not necessary. The proposed robust similarity metrics compare favourably to the most popular standard similarity metrics, on patient image pairs showing gross dissimilarities. Two case studies are considered : the registration of MR/MR and MR/SPECT image volumes of patients suffering from multiple sclerosis and epilepsy.

Autoradiographic analysis of the functional changes occurring in the rat brain are most often performed on coronal sections that allow a good insight into the events occurring at the structural level but lacks the 3D context which is necessary to fully understand the involvement of the brain structures in specific situations like focal seizures with or without generalization. Therefore a robust, fully-automated algorithm for the registration of serially acquired autoradiographic sections is presented. The method accounts for the main difficulties of autoradiographic alignment: corrupted data (cuts and tears), dissimilarities or discontinuities between slices, non parallel or missing slices. The approach relies on the minimization of a global energy function based on robust statistics. The energy function measures the similarity between a slice and its neighborhood in the 3D volume. No particular direction is privileged in the method, so that global offsets, biases in the estimation or error propagations are avoided. The method is evaluated qualitatively and quantitatively on real autoradiographic data. Rat brain autoradiographic volumes are reconstructed with registration errors less than 1 degree in rotation and less than 1 pixel in translation. #

Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel or point spread function is unknown. Despite of exhaustive research over the last few decades, blind image deconvolution still remains an unsolved problem. In this paper, we present a novel morphology based initial estimation technique of true image for the Iterative Blind Deconvolution (IBD) of linearly degraded images without the explicit knowledge of either the original image or the point spread function. The only constraints imposed are the non-negativity and finite support size of the true image. The restoration process involves Wiener filtering instead of usual inverse filtering in iterative loop. The filter coefficient β that depends on the noise level is also estimated mathematically taking pixel values of blurred image and its median filtered version into consideration. The conventional IBD with these twofold modifications is implemented and experimental results show satisfactory convergence, uniqueness and robustness.

Exposure Fusion and other HDR techniques generate well-exposed images from a bracketed image sequence while reproducing a large dynamic range that far exceeds the dynamic range of a single exposure. Common to all these techniques is the problem that the smallest movements in the captured images generate artefacts (ghosting) that dramatically affect the quality of the final images. This limits the use of HDR and Exposure Fusion techniques because common scenes of interest are usually dynamic. We present a method that adapts Exposure Fusion, as well as standard HDR techniques, to allow for dynamic scene without introducing artefacts. Our method detects clusters of moving pixels within a bracketed exposure sequence with simple binary operations. We show that the proposed technique is able to deal with a large amount of movement in the scene and different movement configurations. The result is a ghost-free and highly detailed exposure fused image at a low computational cost.

The area-based methods, such as that using the Laplacian pyramid and Fourier transform-based phase matching, benefit by highlighting high spatial frequencies to reduce sensitivity to the feature inconsistency problem in the multisensor image registration. The feature extraction and matching methods are more powerful and versatile to process poor quality IR images. We implement multi-scale hierarchical edge detection and edge focusing and introduce a new salience measure for the horizon, for multisensor image registration. The common features extracted from images of two modalities can be still different in detail. Therefore, the transformation space match methods with the Hausdorff distance measure is more suitable than the direct feature matching methods. We have introduced image quadtree partition technique to the Hausdorff distance matching, that dramatically reduces the size of the search space. Image registration of real world visible/IR images of battle fields is shown.

The area-based methods, such as that using the Laplacian pyramid and Fourier transform-based phase matching, benefit by highlighting high spatial frequencies to reduce sensitivity to the feature inconsistency problem in the multisensor image registration. The feature extraction and matching methods are more powerful and versatile to process poor quality IR images. We implement multi-scale hierarchical edge detection and edge focusing and introduce a new salience measure for the horizon, for multisensor image registration. The common features extracted from images of two modalities can be still different in detail. Therefore, the transformation space match methods with the Hausdorff distance measure is more suitable than the direct feature matching methods. We have introduced image quadtree partition technique to the Hausdorff distance matching, that dramatically reduces the size of the search space. Image registration of real world visible/IR images of battle fields is shown.

The model-based face recognition approach is based on constructing a model of the human face, which is able to capture the facial variations. The basic knowledge of human face is highly utilized to create the model. In this paper, we try to address and review the approaches and techniques used in the last ten years for modeling the human face in the 3D domain. Our discussion also shows the pros and cons of each approach used in the 3D face modeling.

The distribution of digital images with the classic and newest technologies available on Internet (e.g., emails, social networks, digital repositories) has induced a growing interest on systems able to protect the visual content against malicious manipulations that could be performed during their transmission. One of the main problems addressed in this context is the authentication of the image received in a communication. This task is usually performed by localizing the regions of the image which have been tampered. To this aim the received image should be first registered with the one at the sender by exploiting the information provided by a specific component of the forensic hash associated with the image. In this paper we propose a robust alignment method which makes use of an image hash component based on the Bag of Visual Words paradigm. The proposed signature is attached to the image before transmission and then analyzed at destination to recover the geometric transformations which have been applied to the received image. The estimator is based on a voting procedure in the parameter space of the geometric model used to recover the transformation occurred to the received image. Experiments show that the proposed approach obtains good margin in terms of performances with respect to state-of-the art methods.

The distribution of digital images with the classic and newest technologies available on Internet has induced a growing interest on systems able to protect the visual content against malicious manipulations performed during their transmission. One of the main problems addressed in this context is the authentication of the image received in a communication. This task is usually performed by localizing the regions of the image which have been tampered. To this aim the received image should be first aligned with the one at the sender by exploiting the information provided by a specific component of the forensic hash associated with the image. In this paper we propose a robust alignment method which makes use of an image hash component based on the Bag of Features paradigm. In order to deal with highly textured and contrasted tampering patterns the spatial distribution of the image features has been encoded in the alignment signature. A block-wise tampering detection based on histograms of oriented gradients representation is also proposed. Specifically, a non-uniform quantization of the histogram of oriented gradient space is used to build the signature of each image block for tampering purposes. Experiments show that the proposed approach obtains good margin in terms of performances with respect to state-of-the art methods.

The distribution of digital images with the classic and newest technologies available on Internet (e.g., emails, social networks, digital repositories) has induced a growing interest on systems able to protect the visual content against malicious manipulations that could be performed during their transmission. One of the main problems addressed in this context is the authentication of the image received in a communication. This task is usually performed by localizing the regions of the image which have been tampered. To this aim the received image should be first registered with the one at the sender by exploiting the information provided by a specific component of the forensic hash associated with the image. In this paper we propose a robust alignment method which makes use of an image signature based on the Bag of Features paradigm. The alignment is based on a voting procedure in the parameter space of the model used to recover the geometric transformation occurred into the manipulated image. Experiments show that the proposed approach obtains good margin in terms of performances with respect to state-of-the art methods.

Digital video stabilisation allows to remove unwanted camera movements producing video sequences without disturbing jerkiness. In this paper we propose a novel fast global motion estimation algorithm for video stabilisation based on block matching of local motion vectors. Some of these vectors are properly filtered out by making use of ad-hoc rules taking into account local similarity, local "activity" and matching effectiveness. Also a temporal analysis of the relative error computed at each frame has been introduced. Reliable information is then used to retrieve inter-frame transformation parameters which are used to remove jerkiness. Experiments on real cases confirm the effectiveness of the proposed approach even in critical conditions.

Automatic alignment (registration) of 3D images of adult fruit fly brains is often influenced by the significant displacement of the relative locations of the two optic lobes (OLs) and the center brain (CB). In one of our ongoing efforts to produce a better image alignment pipeline of adult fruit fly brains, we consider separating CB and OLs and align them independently. This paper reports our automatic method to segregate CB and OLs, in particular under conditions where the signal to noise ratio (SNR) is low, the variation of the image intensity is big, and the relative displacement of OLs and CB is substantial.We design an algorithm to find a minimum-cost 3D surface in a 3D image stack to best separate an OL (of one side, either left or right) from CB. This surface is defined as an aggregation of the respective minimum-cost curves detected in each individual 2D image slice. Each curve is defined by a list of control points that best segregate OL and CB. To obtain the locations of these control points, we derive an energy function that includes an image energy term defined by local pixel intensities and two internal energy terms that constrain the curve’s smoothness and length. Gradient descent method is used to optimize this energy function. To improve both the speed and robustness of the method, for each stack, the locations of optimized control points in a slice are taken as the initialization prior for the next slice. We have tested this approach on simulated and real 3D fly brain image stacks and demonstrated that this method can reasonably segregate OLs from CBs despite the aforementioned difficulties.

The paper describes a back-projection based algorithm, improved by adaptive techniques, able to reconstruct a high-resolution image from multiple low-resolution frames. The proposed approach is mainly based on a specific metric, the uncertainty degree, used in pixel reconstruction and on a local Auto-iterative approach for error correction. Using uncertainty the amount of computation is sensibly reduced. The Auto-iterative technique reduces drastically the number of iterations needed to decrease approximation errors. This method is suitable to be applied when real-time processing is required. Experimental results are presented both in terms of perceived and measured quality.

Photo-based Augmentation is a growing field in particular for Industrial Augmented Reality (IAR) applications. Registration is at the core of every photo-based AR software. This alignment of the image to the 3D model coordinate system is usually achieved with fiducial markers. When a single keyframe is used, the unknown baseline length has to be estimated in order to superimpose virtual models onto the image. In this paper, we develop an automatic algorithm to augment the relative pose, estimated using a single keyframe, into a full pose that will permit superimposition. This is performed by propagating known 2D-3D correspondences to the target image using perspectively corrected template matching and followed by a refinement of the estimated full pose that combines geometric and photometric information. The performance and the stability of the proposed method is extensively demonstrated on synthetic data and its applicability is shown within an industrial AR software for Visual Inspection and Documentation.

We propose a method to accelerate direct volume rendering using programmable graphics hardware (GPU). In the method, texture slices are grouped together to form a texture slab. Rendering non-empty slabs from front to back viewing order generates the resultant image. Considering each pixel of the image as a ray, slab silhouette maps (SSMs) are used to skip empty spaces along the ray direction per pixel basis. Additionally, SSMs contain terminated ray information. The method relies on hardware z-occlusion culling and hardware occlusion queries to accelerate ray traversals. The advantage of this method is that SSMs are created on the fly by the GPU without any preprocessing. The cost of generating the acceleration structure is very small with respect to the total rendering time.

Successful image interpolation requires proper enhancement of high frequency content of image pixels around edges. In this paper, we introduce a simple edge model to estimate high resolution edge profiles from lower resolution values. Pixels around edges are viewed as samples taken from one dimensional (1-D) continuous edge profiles according to 1-D smooth edge contours defining the sampling instants. The image is highpass filtered by wavelets and subpixel edge locations are estimated by minimizing the modeling error in the wavelet domain. Interpolation is carried out by applying the model, wherever applicable, together with a baseline interpolator (here, bilinear) in order to make edges look sharper without introducing artifacts. The results are compared to bilinear interpolation, and significant improvement in terms of SNR, edge sharpness and contour smoothness is observed.

Automated analysis of retinal images usually requires estimating the positions of blood vessels, which contain important features for image alignment and abnormality detection. Matched filtering can produce the best results but is difficult to implement because the vessel orientations and widths are unknown beforehand. Many researchers use Hessian filtering, which provides an estimate for vessel orientation through the use of three orientation templates. We propose a novel filtering approach, called self-matched filtering, which is based on the 180 • rotated version of the noisy vessel signal in the local neighborhood. We show that even though the proposed filter achieves half the signal-to-noise ratio of a matched filter, it does not require the estimation of the vessel scale and orientation, and can outperform Hessian filtering by up to a factor of two in terms of miss detection error.

In this paper different application scenarios are presented for which the merging of unconnected feature point tracks is essential for successful camera motion estimation and 3D reconstruction from video. The first application is drift removal for sequential camera motion estimation of long sequences. The state-of-the-art in drift removal is to apply a RANSAC approach to find unconnected feature point tracks. In this paper an alternative spectral algorithm for pairwise matching of unconnected feature point tracks is used. It is then shown that the algorithms can be combined and applied to novel scenarios where independent camera motion estimations must be registered into a common global coordinate system. In the first scenario multiple moving cameras, which capture the same scene simultaneously, are registered. A second new scenario occurs in situations where the tracking of feature points during sequential camera motion estimation fails completely, e.g., due to large occluding objects in the foreground, and the unconnected tracks of the independent reconstructions must be merged. Three experiments with challenging real video sequences demonstrate that the presented techniques work in practice.

In this paper, a wavelet based method is proposed to estimate the blur in an image using information contained in the image itself. We look at the sharpness of the sharpest edges in the blurred image, which contain information about the blurring. Specifically, a smoothness measure, the Lipschitz exponent, is computed for these sharpest edges. When one assumes that the blur can be described by one parameter (e.g., blur from a gaussian PSF can be described by the variance of the gaussian, defocus blur can be described by the radius of the circular PSF, § § § ). A relation between this parameter and the magnitude of the Lipschitz exponent is shown, which is only dependent on the blur in the image and not on the image contents. This allows us to estimate the blur parameter directly from the image itself.

In this paper, a wavelet based method is proposed to estimate the blur in an image using information contained in the image itself. We look at the sharpness of the sharpest edges in the blurred image, which contain information about the blurring. Specifically, a smoothness measure, the Lipschitz exponent, is computed for these sharpest edges. A relation between the variance of a gaussian point spread function and the magnitude of the Lipschitz exponent is shown, which is only dependent on the blur in the image and not on the image contents. This allows us to estimate the variance of the blur directly from the image itself.

In this paper, we propose a method to recognize faces from a set of consecutive video frames instead of a single image using super-resolution (SR). The SR process uses multiple frames acquired from video and combines information coming from them into a single image in higher resolution. As expected, a single low resolution image would contain less amount of information, than the same image taken from a video sequence with multiple other images with temporal changes from consecutive frames. the proposed method uses SR to generate a super resolved video sequences from a low resolution video sequences and uses frames acquired from the high resolution video sequences to train and test the performance of the principal component analysis based face recognition system. Entropy and MSE were used to check the performance of the system and the results showed the robustness of SR as a preprocessing step for recognition.

We present a new integrated tool, DERMA, which allows to measure and assess the time evolution of chronic wounds. A laser triangulation 3D scanner is used to acquire the wound geometry with high precision and to capture an RGB image aligned to the geometry. DERMA provides a single and uniform interface to: manage patient data, 3D scanning of the lesion region, and to perform different kinds of measurements and comparisons: geometric (on the 3D model) and colorimetric (on the image). All acquired data (3D geometries and images) as well as the measures calculated are stored in a database for monitoring the evolution of the skin lesion over time. The tool, developed in collaboration with dermatologists, is now under field evaluation in two dermatological clinics monitoring the evolution of wounds due to different types of skin diseases.

Flexible macromolecules pose special difficulties for structure determination by crystallography or NMR. Progress can be made by electron microscopy, but electron cryo-microscopy of unstained, hydrated specimens is limited to larger macromolecules because of the inherently low signal-to-noise ratio. For three-dimensional structure determination, the single particles must be invariant in structure. Here, we describe how we have used negative staining and single-particle image processing techniques to explore the structure and flexibility of single molecules of two motor proteins: myosin and dynein. Critical for the success of negative staining is a hydrophilic, thin carbon film, because it produces a low noise background around each molecule, and stabilises the molecule against damage by the stain. The strategy adopted for single-particle image processing exploits the flexibility available within the SPIDER software suite. We illustrate the benefits of successive rounds of image alignment and classification, and the use of whole molecule averages and movies to analyse and display both structure and flexibility within the dynein motor.

Landing is one of the difficult challenges for an unmanned aerial vehicle (UAV). In this paper, we propose a vision-based landing approach for an autonomous UAV using reinforcement learning (RL). The autonomous UAV learns the landing skill from scratch by interacting with the environment. The reinforcement learning algorithm explored and extended in this study is Least-Squares Policy Iteration (LSPI) to gain a fast learning process and a smooth landing trajectory. The proposed approach has been tested with a simulated quadrocopter in an extended version of the USARSim (Unified System for Automation and Robot Simulation) environment. Results showed that LSPI learned the
landing skill very quickly, requiring less than 142 trials.

Myocardial motion analysis and quantification is of utmost importance for analyzing contractile heart abnormalities and it can be a symptom of a coronary artery disease. A fundamental problem in processing sequences of images is the computation of the optical flow, which is an approximation of the real image motion.
This paper presents a new algorithm for optical flow estimation based on a spatiotemporal-frequency (STF) approach. More specifically it relies on the computation of the Wigner–Ville distribution (WVD) and the Hough Transform (HT) of the motion sequences. The latter is a well-known line and shape detection method that is highly robust against incomplete data and noise. The rationale of using the HT
in this context is that it provides a value of the displacement field from the STF representation. In addition, a probabilistic approach based on Gaussian mixtures has been implemented in order to improve the accuracy of the motion detection. Experimental results in the case of synthetic sequences are compared with an implementation of the variational technique for local and global motion estimation, where it is shown that the results are accurate and robust to noise degradations.
Results obtained with real cardiac magnetic resonance images are presented.

Existing parallel magnetic resonance imaging methods are limited by a fundamental trade-off, where suppressing noise introduces aliasing artifacts. Bayesian methods with an appropriately chosen image prior offer a promising alternative; however, previous methods with spatial priors assume that intensities vary smoothly over the entire image, and therefore blur edges. An edge-preserving prior is introduced which instead assumes that intensities are piecewise smooth, and a new approach is proposed to efficiently compute its Bayesian estimate. The estimation task is formulated as an optimization problem, which requires minimizing a non-convex objective function in a space with thousands of dimensions. As a result, traditional continuous minimization methods cannot be applied. This optimization task is closely related to some problems in computer vision for which discrete optimization methods have been developed in the last few years. We adapt these algorithms, which are based on graph cuts, to address our optimization problem. Results of several parallel imaging experiments of brain and torso regions performed under challenging conditions with high acceleration factors are shown and compared with conventional SENSE methods. An empirical analysis indicates visually improved overall quality compared to conventional methods.