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Jaume Garcia, Debora Gil, Sandra Pujades, & Francesc Carreras. (2008). "A Variational Framework for Assessment of the Left Ventricle Motion " . International Journal Mathematical Modelling of Natural Phenomena, 3(6), 76–100.
Abstract: Impairment of left ventricular contractility due to cardiovascular diseases is reflected in left ventricle (LV) motion patterns. An abnormal change of torsion or long axis shortening LV values can help with the diagnosis and follow-up of LV dysfunction. Tagged Magnetic Resonance (TMR) is a widely spread medical imaging modality that allows estimation of the myocardial tissue local deformation. In this work, we introduce a novel variational framework for extracting the left ventricle dynamics from TMR sequences. A bi-dimensional representation space of TMR images given by Gabor filter banks is defined. Tracking of the phases of the Gabor response is combined using a variational framework which regularizes the deformation field just at areas where the Gabor amplitude drops, while restoring the underlying motion otherwise. The clinical applicability of the proposed method is illustrated by extracting normality models of the ventricular torsion from 19 healthy subjects.
Keywords: Key words: Left Ventricle Dynamics, Ventricular Torsion, Tagged Magnetic Resonance, Motion Tracking, Variational Framework, Gabor Transform.
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Debora Gil, & Petia Radeva. (2004). "Shape Restoration via a Regularized Curvature Flow " . Journal of Mathematical Imaging and Vision, 21(3), 205–223.
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.
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Debora Gil, & Petia Radeva. (2006). "Inhibition of false landmarks " . Pattern Recognition Letters, 27(9), 1022–1030.
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.
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Debora Gil, Aura Hernandez-Sabate, Mireia Brunat, Steven Jansen, & Jordi Martinez-Vilalta. (2011). "Structure-preserving smoothing of biomedical images " . Pattern Recognition, 44(9), 1842–1851.
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.
Keywords: Non-linear smoothing; Differential geometry; Anatomical structures; segmentation; Cardiac magnetic resonance; Computerized tomography
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Debora Gil, Sergio Vera, Agnes Borras, Albert Andaluz, & Miguel Angel Gonzalez Ballester. (2017). "Anatomical Medial Surfaces with Efficient Resolution of Branches Singularities " . Medical Image Analysis, 35, 390–402.
Abstract: Medial surfaces are powerful tools for shape description, but their use has been limited due to the sensibility existing methods to branching artifacts. Medial branching artifacts are associated to perturbations of the object boundary rather than to geometric features. Such instability is a main obstacle for a condent application in shape recognition and description. Medial branches correspond to singularities of the medial surface and, thus, they are problematic for existing morphological and energy-based algorithms. In this paper, we use algebraic geometry concepts in an energy-based approach to compute a medial surface presenting a stable branching topology. We also present an ecient GPU-CPU implementation using standard image processing tools. We show the method computational eciency and quality on a custom made synthetic database. Finally, we present some results on a medical imaging application for localization of abdominal pathologies.
Keywords: Medial Representations; Shape Recognition; Medial Branching Stability ; Singular Points
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Misael Rosales, Petia Radeva, Oriol Rodriguez-Leor, & Debora Gil. (2009). "Modelling of image-catheter motion for 3-D IVUS " . Medical image analysis, 13(1), 91–104.
Abstract: Three-dimensional intravascular ultrasound (IVUS) allows to visualize and obtain volumetric measurements of coronary lesions through an exploration of the cross sections and longitudinal views of arteries. However, the visualization and subsequent morpho-geometric measurements in IVUS longitudinal cuts are subject to distortion caused by periodic image/vessel motion around the IVUS catheter. Usually, to overcome the image motion artifact ECG-gating and image-gated approaches are proposed, leading to slowing the pullback acquisition or disregarding part of IVUS data. In this paper, we argue that the image motion is due to 3-D vessel geometry as well as cardiac dynamics, and propose a dynamic model based on the tracking of an elliptical vessel approximation to recover the rigid transformation and align IVUS images without loosing any IVUS data. We report an extensive validation with synthetic simulated data and in vivo IVUS sequences of 30 patients achieving an average reduction of the image artifact of 97% in synthetic data and 79% in real-data. Our study shows that IVUS alignment improves longitudinal analysis of the IVUS data and is a necessary step towards accurate reconstruction and volumetric measurements of 3-D IVUS.
Keywords: Intravascular ultrasound (IVUS); Motion estimation; Motion decomposition; Fourier
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Debora Gil, Jose Maria-Carazo, & Roberto Marabini. (2006). "On the nature of 2D crystal unbending " . Journal of Structural Biology, 156(3), 546–555.
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.
Keywords: Electron microscopy
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Oriol Pujol, Debora Gil, & Petia Radeva. (2005). "Fundamentals of Stop and Go active models " . Image and Vision Computing, 23(8), 681–691.
Abstract: An efficient snake formulation should conform to the idea of picking the smoothest curve among all the shapes approximating an object of interest. In current geodesic snakes, the regularizing curvature also affects the convergence stage, hindering the latter at concave regions. In the present work, we make use of characteristic functions to define a novel geodesic formulation that decouples regularity and convergence. This term decoupling endows the snake with higher adaptability to non-convex shapes. Convergence is ensured by splitting the definition of the external force into an attractive vector field and a repulsive one. In our paper, we propose to use likelihood maps as approximation of characteristic functions of object appearance. The better efficiency and accuracy of our decoupled scheme are illustrated in the particular case of feature space-based segmentation.
Keywords: Deformable models; Geodesic snakes; Region-based segmentation
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Debora Gil, & Petia Radeva. (2005). "Extending anisotropic operators to recover smooth shapes " . Computer Vision and Image Understanding, 99(1), 110–125.
Abstract: Anisotropic differential operators are widely used in image enhancement processes. Recently, their property of smoothly extending functions to the whole image domain has begun to be exploited. Strong ellipticity of differential operators is a requirement that ensures existence of a unique solution. This condition is too restrictive for operators designed to extend image level sets: their own functionality implies that they should restrict to some vector field. The diffusion tensor that defines the diffusion operator links anisotropic processes with Riemmanian manifolds. In this context, degeneracy implies restricting diffusion to the varieties generated by the vector fields of positive eigenvalues, provided that an integrability condition is satisfied. We will use that any smooth vector field fulfills this integrability requirement to design line connection algorithms for contour completion. As application we present a segmenting strategy that assures convergent snakes whatever the geometry of the object to be modelled is.
Keywords: Contour completion; Functional extension; Differential operators; Riemmanian manifolds; Snake segmentation
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Jorge Bernal, F. Javier Sanchez, Gloria Fernandez Esparrach, Debora Gil, Cristina Rodriguez de Miguel, & Fernando Vilariño. (2015). "WM-DOVA Maps for Accurate Polyp Highlighting in Colonoscopy: Validation vs. Saliency Maps from Physicians " . Computerized Medical Imaging and Graphics, 43, 99–111.
Abstract: We introduce in this paper a novel polyp localization method for colonoscopy videos. Our method is based on a model of appearance for polyps which defines polyp boundaries in terms of valley information. We propose the integration of valley information in a robust way fostering complete, concave and continuous boundaries typically associated to polyps. This integration is done by using a window of radial sectors which accumulate valley information to create WMDOVA1 energy maps related with the likelihood of polyp presence. We perform a double validation of our maps, which include the introduction of two new databases, including the first, up to our knowledge, fully annotated database with clinical metadata associated. First we assess that the highest value corresponds with the location of the polyp in the image. Second, we show that WM-DOVA energy maps can be comparable with saliency maps obtained from physicians' fixations obtained via an eye-tracker. Finally, we prove that our method outperforms state-of-the-art computational saliency results. Our method shows good performance, particularly for small polyps which are reported to be the main sources of polyp miss-rate, which indicates the potential applicability of our method in clinical practice.
Keywords: Polyp localization; Energy Maps; Colonoscopy; Saliency; Valley detection
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