François G. Meyer

Fast adaptive wavelet packet image compression

Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients, which are often quantized to zero, even at high bit rates. Our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis is placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four times faster than a standard convolution-decimation. An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly out performs one of the best wavelet coder on images such as Barbara and fingerprints, both visually and in term of PSNR.

Wavelet-based estimation of a semiparametric generalized linear model of fMRI time-series

Addresses the problem of detecting significant changes in fMRI time series that are correlated to a stimulus time course. This paper provides a new approach to estimate the parameters of a semiparametric generalized linear model of the fMRI time series. The fMRI signal is described as the sum of two effects: a smooth trend and the response to the stimulus. The trend belongs to a subspace spanned by large scale wavelets. The wavelet transform provides an approximation to the Karhunen-Loeve transform for the long memory noise and we have developed a scale space regression that permits one to carry out the regression in the wavelet domain while omitting the scales that are contaminated by the trend. In order to demonstrate that our approach outperforms the state-of-the art detrending technique, we evaluated our method against a smoothing spline approach. Experiments with simulated data and experimental fMRI data, demonstrate that our approach can infer and remove drifts that cannot be adequately represented with splines.

Comparison of detrending methods for optimal fMRI preprocessing.

Because of the inherently low signal to noise ratio (SNR) of fMRI data, removal of low frequency signal intensity drift is an important preprocessing step, particularly in those brain regions that weakly activate. Two known sources of drift are noise from the MR scanner and aliasing of physiological pulsations. However, the amount and direction of drift is difficult to predict, even between neighboring voxels. Further, there is no concensus on an optimal baseline drift removal algorithm. In this paper, five voxel-based detrending techniques were compared to each other and an auto-detrending algorithm, which automatically selected the optimal method for a given voxel time-series. For a significance level of P < 10(-6), linear and quadratic detrending moderately increased the percentage of activated voxels. Cubic detrending decreased activation, while a wavelet approach increased or decreased activation, depending on the dataset. Spline detrending was the best single algorithm. However, auto-detrending (selecting the best algorithm or none, if detrending is not useful) appears to be the most judicious choice, particularly for analyzing fMRI data with weak activations in the presence of baseline drift.

Tracking myocardial deformation using phase contrast MR velocity fields: a stochastic approach

The authors propose a new approach for tracking the deformation of the left-ventricular (LV) myocardium from two-dimensional (2-D) magnetic resonance (MR) phase contrast velocity fields. The use of phase contrast MR velocity data in cardiac motion problems has been introduced by others (N.J. Pelc et al., 1991) and shown to be potentially useful for tracking discrete tissue elements, and therefore, characterizing LV motion. However, the authors show here that these velocity data: 1) are extremely noisy near the LV borders; and 2) cannot alone be used to estimate the motion and the deformation of the entire myocardium due to noise in the velocity fields. In this new approach, the authors use the natural spatial constraints of the endocardial and epicardial contours, detected semiautomatically in each image frame, to help remove noisy velocity vectors at the LV contours. The information from both the boundaries and the phase contrast velocity data is then integrated into a deforming mesh that is placed over the myocardium at one time frame and then tracked over the entire cardiac cycle. The deformation is guided by a Kalman filter that provides a compromise between 1) believing the dense field velocity and the contour data when it is crisp and coherent in a local spatial and temporal sense and 2) employing a temporally smooth cyclic model of cardiac motion when contour and velocity data are not trustworthy. The Kalman filter is particularly well suited to this task as it produces an optimal estimate of the left ventricles kinematics (in the sense that the error is statistically minimized) given incomplete and noise corrupted data, and given a basic dynamical model of the left ventricle. The method has been evaluated with simulated data; the average error between tracked nodes and theoretical position was 1.8% of the total path length. The algorithm has also been evaluated with phantom data; the average error was 4.4% of the total path length. The authors show that in their initial tests with phantoms that the new approach shows small, but concrete improvements over previous techniques that used primarily phase contrast velocity data alone. They feel that these improvements will be amplified greatly as they move to direct comparisons in in vivo and three-dimensional (3-D) datasets.

Tracking complex primitives in an image sequence

This paper describes a new approach to track complex primitives along image sequences - integrating snake-based contour tracking and region-based motion analysis. First, a snake tracks the region outline and performs segmentation. Then the motion of the extracted region is estimated by a dense analysis of the apparent motion over the region, using spatio-temporal image gradients. Finally, this motion measurement is filtered to predict the region location in the next frame, and thus to guide (i.e. to initialize) the tracking snake in the next frame. Therefore, these two approaches collaborate and exchange information to overcome the limitations of each of them. The method is illustrated by experimental results on real images.

Adaptive wavelet packet basis selection for zerotree image coding

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.

Multilayered image representation: application to image compression

The main contribution of this work is a new paradigm for image representation and image compression. We describe a new multilayered representation technique for images. An image is parsed into a superposition of coherent layers: piecewise smooth regions layer, textures layer, etc. The multilayered decomposition algorithm consists in a cascade of compressions applied successively to the image itself and to the residuals that resulted from the previous compressions. During each iteration of the algorithm, we code the residual part in a lossy way: we only retain the most significant structures of the residual part, which results in a sparse representation. Each layer is encoded independently with a different transform, or basis, at a different bitrate, and the combination of the compressed layers can always be reconstructed in a meaningful way. The strength of the multilayer approach comes from the fact that different sets of basis functions complement each others: some of the basis functions will give reasonable account of the large trend of the data, while others will catch the local transients, or the oscillatory patterns. This multilayered representation has a lot of beautiful applications in image understanding, and image and video coding. We have implemented the algorithm and we have studied its capabilities.

Detection and Segmentation of Concealed Objects in Terahertz Images

Terahertz imaging makes it possible to acquire images of objects concealed underneath clothing by measuring the radiometric temperatures of different objects on a human subject. The goal of this work is to automatically detect and segment concealed objects in broadband 0.1-1 THz images. Due to the inherent physical properties of passive terahertz imaging and associated hardware, images have poor contrast and low signal to noise ratio. Standard segmentation algorithms are unable to segment or detect concealed objects. Our approach relies on two stages. First, we remove the noise from the image using the anisotropic diffusion algorithm. We then detect the boundaries of the concealed objects. We use a mixture of Gaussian densities to model the distribution of the temperature inside the image. We then evolve curves along the isocontours of the image to identify the concealed objects. We have compared our approach with two state-of-the-art segmentation methods. Both methods fail to identify the concealed objects, while our method accurately detected the objects. In addition, our approach was more accurate than a state-of-the-art supervised image segmentation algorithm that required that the concealed objects be already identified. Our approach is completely unsupervised and could work in real-time on dedicated hardware.

Region-Based Tracking in an Image Sequence

This paper addresses the problem of object tracking in a sequence of monocular images. The use of regions as primitives for tracking enables to directly handle consistent object-level entities. A motion-based segmentation process based on normal flows and first order motion models provide instantaneous measurements. Shape, position and motion of each region present in such segmented images are estimated with a recursive algorithm along the sequence. Occlusion situations can be handled. We have carried out experiments on sequences of real images depicting complex outdoor scenes.

Wavelets in Signal and Image Analysis

The intention of this paper is to pro vide an elementary introduction to the subject of discret e-time wavelets. It defines the discret e-t ime wavelet s and reviews t heir properties in a syste mat ic and consiste nt way. Different kinds of ort hogona lity between the wavelets are addressed and the corres pond ing sufficient and necessary condit ions ar e derived . It is shown when discret e-t ime wavelets can be samples of continuous-t ime wavelet s. The condit ions for shift-invari an ce of discrete-time wavelet representations are given in det ail. The appearance of two biorthogonal representation sets of discrete-ti me wavelet s from t he binary subband decomposition /reconstruction of signals is pointed out . When t he numher of different representation scales is finit e, it is shown that in order to obtain the orthogonality betwe en wavelet s, the known requircm cnt for wavelet generating filter can be relaxed .