Abstract: Crystal unbending, the process that aims to recover a perfect crystal from experimental data, is one of the more important steps in electron crystallography image processing. The unbending process involves three steps: estimation of the unit cell displacements from their ideal positions, extension of the deformation field to the whole image and transformation of the image in order to recover an ideal crystal. In this work, we present a systematic analysis of the second step oriented to address two issues. First, whether the unit cells remain undistorted and only the distance between them should be changed (rigid case) or should be modified with the same deformation suffered by the whole crystal (elastic case). Second, the performance of different extension algorithms (interpolation versus approximation) is explored. Our experiments show that there is no difference between elastic and rigid cases or among the extension algorithms. This implies that the deformation fields are constant over large areas. Furthermore, our results indicate that the main source of error is the transformation of the crystal image.

Abstract: Early diagnosis and accurate treatment of Left Ventricle (LV) dysfunction significantly increases the patient survival. Impairment of LV contractility due to cardiovascular diseases is reflected in its motion patterns. Recent advances in medical imaging, such as Magnetic Resonance (MR), have encouraged research on 3D simulation and modelling of the LV dynamics. Most of the existing 3D models consider just the gross anatomy of the LV and restore a truncated ellipse which deforms along the cardiac cycle. The contraction mechanics of any muscle strongly depends on the spatial orientation of its muscular fibers since the motion that the muscle undergoes mainly takes place along the fibers. It follows that such simplified models do not allow evaluation of the heart electro-mechanical function and coupling, which has recently risen as the key point for understanding the LV functionality . In order to thoroughly understand the LV mechanics it is necessary to consider the complete anatomy of the LV given by the orientation of the myocardial fibres in 3D space as described by Torrent Guasp. We propose developing a 3D patient-sensitive model of the LV integrating, for the first time, the ven- tricular band anatomy (fibers orientation), the LV gross anatomy and its functionality. Such model will represent the LV function as a natural consequence of its own ventricular band anatomy. This might be decisive in restoring a proper LV contraction in patients undergoing pace marker treatment. The LV function is defined as soon as the propagation of the contractile electromechanical pulse has been modelled. In our experiments we have used the wave equation for the propagation of the electric pulse. The electromechanical wave moves on the myocardial surface and should have a conductivity tensor oriented along the muscular fibers. Thus, whatever mathematical model for electric pulse propa- gation [4] we consider, the complete anatomy of the LV should be extracted. The LV gross anatomy is obtained by processing multi slice MR images recorded for each patient. Information about the myocardial fibers distribution can only be extracted by Diffusion Tensor Imag- ing (DTI), which can not provide in vivo information for each patient. As a first approach, we have computed an average model of fibers from several DTI studies of canine hearts. This rough anatomy is the input for our electro-mechanical propagation model simulating LV dynamics. The average fiber orientation is updated until the simulated LV motion agrees with the experimental evidence provided by the LV motion observed in tagged MR (TMR) sequences. Experimental LV motion is recovered by applying image processing, differential geometry and interpolation techniques to 2D TMR slices [5]. The pipeline in figure 1 outlines the interaction between simulations and experimental data leading to our patient-tailored model.

Abstract: Plaque analysis in IVUS planes needs accurate intima and adventitia models. Large variety in adventitia descriptors difficulties its detection and motivates using a classification strategy for selecting points on the structure. Whatever the set of descriptors used, the selection stage suffers from fake responses due to noise and uncompleted true curves. In order to smooth background noise while strengthening responses, we apply a restricted anisotropic filter that homogenizes grey levels along the image significant structures. Candidate points are extracted by means of a simple semi supervised adaptive classification of the filtered image response to edge and calcium detectors. The final model is obtained by interpolating the former line segments with an anisotropic contour closing technique based on functional extension principles.

Abstract: Vessel plaque assessment by analysis of intravascular ultrasound sequences is a useful tool for cardiac disease diagnosis and intervention. Manual detection of luminal (inner) and mediaadventitia (external) vessel borders is the main activity of physicians in the process of lumen narrowing (plaque) quantification. Difficult definition of vessel border descriptors, as well as, shades, artifacts, and blurred signal response due to ultrasound physical properties trouble automated adventitia segmentation. In order to efficiently approach such a complex problem, we propose blending advanced anisotropic filtering operators and statistical classification techniques into a vessel border modelling strategy. Our systematic statistical analysis shows that the reported adventitia detection achieves an accuracy in the range of interobserver variability regardless of plaque nature, vessel geometry, and incomplete vessel borders. Index Terms–-Anisotropic processing, intravascular ultrasound (IVUS), vessel border segmentation, vessel structure classification.

Abstract: Smoothing of biomedical images should preserve gray-level transitions between adjacent tissues, while restoring contours consistent with anatomical structures. Anisotropic diffusion operators are based on image appearance discontinuities (either local or contextual) and might fail at weak inter-tissue transitions. Meanwhile, the output of block-wise and morphological operations is prone to present a block structure due to the shape and size of the considered pixel neighborhood. In this contribution, we use differential geometry concepts to define a diffusion operator that restricts to image consistent level-sets. In this manner, the final state is a non-uniform intensity image presenting homogeneous inter-tissue transitions along anatomical structures, while smoothing intra-structure texture. Experiments on different types of medical images (magnetic resonance, computerized tomography) illustrate its benefit on a further process (such as segmentation) of images.

Abstract: Corners and junctions are landmarks characterized by the lack of differentiability in the unit tangent to the image level curve. Detectors based on differential operators are not, by their own definition, the best posed as they require a higher degree of differentiability to yield a reliable response. We argue that a corner detector should be based on the degree of continuity of the tangent vector to the image level sets, work on the image domain and need no assumptions on neither the image local structure nor the particular geometry of the corner/junction. An operator measuring the degree of differentiability of the projection matrix on the image gradient fulfills the above requirements. Because using smoothing kernels leads to corner misplacement, we suggest an alternative fake response remover based on the receptive field inhibition of spurious details. The combination of both orientation discontinuity detection and noise inhibition produce our inhibition orientation energy (IOE) landmark locator.

Abstract: Any image filtering operator designed for automatic shape restoration should satisfy robustness (whatever the nature and degree of noise is) as well as non-trivial smooth asymptotic behavior. Moreover, a stopping criterion should be determined by characteristics of the evolved image rather than dependent on the number of iterations. Among the several PDE based techniques, curvature flows appear to be highly reliable for strongly noisy images compared to image diffusion processes.
In the present paper, we introduce a regularized curvature flow (RCF) that admits non-trivial steady states. It is based on a measure of the local curve smoothness that takes into account regularity of the curve curvature and serves as stopping term in the mean curvature flow. We prove that this measure decreases over the orbits of RCF, which endows the method with a natural stop criterion in terms of the magnitude of this measure. Further, in its discrete version it produces steady states consisting of piece-wise regular curves. Numerical experiments made on synthetic shapes corrupted with different kinds of noise show the abilities and limitations of each of the current geometric flows and the benefits of RCF. Finally, we present results on real images that illustrate the usefulness of the present approach in practical applications.