Karim Makki

Karim Makki, Adrien Bartoli

We show that for a plane imaged by an endoscope the specular isophotes are concentric circles on the scene plane, which appear as nested ellipses in the image. We show that these ellipses can be detected and used to estimate the plane's normal direction, forming a normal reconstruction method, which we validate on simulated data. In practice, the anatomical surfaces visible in endoscopic images are locally planar. We use our method to show that the surface normal can thus be reconstructed for each of the numerous specularities typically visible on moist tissues. We show results on laparoscopic and colonoscopic images.

Karim Makki, Adrien Bartoli

Specularities are numerous in endoscopic images. They occur as many white small elliptic spots, which are generally ruled out as nuisance in image analysis and computer vision methods. Instead, we propose to use specularities as cues for 3D perception. Specifically, we propose a new method to reconstruct, at each specularity, the observed tissue's normal direction (i.e., its orientation) and shape (i.e., its curvature) from a single image. We show results on simulated and real interventional images.

Karim Makki, Jean François Lecomte, Lukas Fuchs et al.

Image-based computational fluid dynamics have long played an important role in leveraging knowledge and understanding of several physical phenomena. In particular, probabilistic computational methods have opened the way to modelling the complex dynamics of systems in purely random turbulent motion. In the field of structural geology, a better understanding of the deformation and stress state both within the salt and the surrounding rocks is of great interest to characterize all kinds of subsurface long-terms energy-storage systems. The objective of this research is to determine the non-linear deformation of the salt boundary over time using a parallelized, stochastic filtering approach from x-ray computed tomography (CT) image time series depicting the evolution of salt structures triggered by gravity and under differential loading. This work represents a first step towards bringing together physical modeling and advanced stochastic image processing methods where model uncertainty is taken into account.

Karim Makki, Amine Bohi, Augustin . C Ogier et al.

Dynamic MRI may capture temporal anatomical changes in soft tissue organs with high contrast but the obtained sequences usually suffer from limited volume coverage which makes the high resolution reconstruction of organ shape trajectories a major challenge in temporal studies. Because of the variability of abdominal organ shapes across time and subjects, the objective of this study is to go towards 3D dense velocity measurements to fully cover the entire surface and to extract meaningful features characterizing the observed organ deformations and enabling clinical action or decision. We present a pipeline for characterization of bladder surface dynamics during deep respiratory movements. For a compact shape representation, the reconstructed temporal volumes were first used to establish subject-specific dynamical 4D mesh sequences using the LDDMM framework. Then, we performed a statistical characterization of organ dynamics from mechanical parameters such as mesh elongations and distortions. Since we refer to organs as non flat surfaces, we have also used the mean curvature changes as metric to quantify surface evolution. However, the numerical computation of curvature is strongly dependant on the surface parameterization. To cope with this dependency, we employed a new method for surface deformation analysis. Independent of parameterization and minimizing the length of the geodesic curves, it stretches smoothly the surface curves towards a sphere by minimizing a Dirichlet energy. An Eulerian PDE approach is used to derive a shape descriptor from the curve-shortening flow. Intercorrelations between individual motion patterns are computed using the Laplace Beltrami operator eigenfunctions for spherical mapping. Application to extracting characterization correlation curves for locally controlled simulated shape trajectories demonstrates the stability of the proposed shape descriptor.

K. Makki, B. Borotikar, M. Garetier et al.

The log Euclidean polyrigid registration framework provides a way to smoothly estimate and interpolate poly-rigid/affine transformations for which the invertibility is guaranteed. This powerful and flexible mathematical framework is currently being used to track the human joint dynamics by first imposing bone rigidity constraints in order to synthetize the spatio-temporal joint deformations later. However, since no closed-form exists, then a computationally expensive integration of ordinary differential equations (ODEs) is required to perform image registration using this framework. To tackle this problem, the exponential map for solving these ODEs is computed using the scaling and squaring method in the literature. In this paper, we propose an algorithm using a matrix diagonalization based method for smooth interpolation of homogeneous polyrigid transformations of human joints during motion. The use of this alternative computational approach to integrate ODEs is well motivated by the fact that bone rigid transformations satisfy the mechanical constraints of human joint motion, which provide conditions that guarantee the diagonalizability of local bone transformations and consequently of the resulting joint transformations. In a comparison with the scaling and squaring method, we discuss the usefulness of the matrix eigendecomposition technique which reduces significantly the computational burden associated with the computation of matrix exponential over a dense regular grid. Finally, we have applied the method to enhance the temporal resolution of dynamic MRI sequences of the ankle joint. To conclude, numerical experiments show that the eigendecomposition method is more capable of balancing the trade-off between accuracy, computation time, and memory requirements.

Karim Makki, Amine Bohi, Augustin C. Ogier et al.

In this paper, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations. As an example, we characterize the behavior of a bladder during a forced respiratory motion with a reduced number of 3D surface points: first, a set of equidistant points representing the vertices of quadrilateral mesh for the surface in the first time frame are tracked throughout a long dynamic MRI sequence using a Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. Second, a novel geometric feature which is invariant to scaling and rotation is proposed for characterizing the temporal organ deformations by employing an Eulerian Partial Differential Equations (PDEs) methodology. We demonstrate the robustness of our feature on both synthetic 3D shapes and realistic dynamic MRI data portraying the bladder deformation during forced respiratory motions. Promising results are obtained, showing that the proposed feature may be useful for several computer vision applications such as medical imaging, aerodynamics and robotics.