Marc Daniel

Geometric modeling of pelvic organs

The pelvic floor can be subjected to different disorders, coming from a physiological change in the spatial configuration of the organs of interest: the bladder, the rectum, the uterus and the vagina. However, resort to surgery to replace them is complicated to achieve. In order to support the decision of the surgeon as to the invasive method to use for the patient, the MoDyPe (Pelvis Dynamics Modeling) project was launched, aiming at building a patient specific pelvic organ behavior. Our approach consists in creating thick surfaces of hollow organs, using periodic B-splines and offsets, then in controlling their discretization and in exporting a hexahedral model to provide input data for the study on the dynamics of the soft bodies of interest. From a segmentation step providing a dataset of 3D points, a function is built to measure the bidirectional distance between the surface and the data. It is minimized with an alternate iterative Hoschek-like method, by updating the parametric map and moving the control points. Several offsets of the base surface are then created to build up the thickness of the organ.

Boundary extraction and simplification of a surface defined by a sparse 3D volume

Reconstructing surfaces with data coming from an automatic acquisition technique always entails the problem of mass of data. It leads to a mandatory data reduction process. Applying the process to the whole set of points induces an important risk of surface shrinking so that the initial boundary extraction is an important step permitting a simplification inside it. The global surface shape will then be better kept. It is nevertheless required to simplify the boundary, which can be done on the extracted boundary. In this paper, we present a new method to extract and simplify the boundary of an elevation surface given as voxels in a large 3D volume having the characteristics to be sparse since many data are missing. We first present our boundary definition based on mathematical relations between a point and its square neighborhoods. Second, we introduce algorithms to extract such a boundary. Third, we simplify this boundary.

Variational geometric modeling with black box constraints and DAGs

CAD modelers enable designers to construct complex 3D shapes with high-level B-Rep operators. This avoids the burden of low level geometric manipulations. However a gap still exists between the shape that the designers have in mind and the way they have to decompose it into a sequence of modeling steps. To bridge this gap, Variational Modeling enables designers to specify constraints the shape must respect. The constraints are converted into an explicit system of mathematical equations (potentially with some inequalities) which the modeler numerically solves. However, most of available programs are 2D sketchers, basically because in higher dimension some constraints may have complex mathematical expressions. This paper introduces a new approach to sketch constrained 3D shapes. The main idea is to replace explicit systems of mathematical equations with (mainly) Computer Graphics routines considered as Black Box Constraints. The obvious difficulty is that the arguments of all routines must have known numerical values. The paper shows how to solve this issue, i.e., ? how to solve and optimize without equations. The feasibility and promises of this approach are illustrated with the developed DECO (Deformation by Constraints) prototype. Extending geometric constraints with black box constraints which have no equation.Solving and optimizing without equation.This approach applies to all history-based or parametric modelers.

Geometric modeling of pelvic organs with thickness

Physiological changes in the spatial configuration of the internal organs in the abdomen can induce different disorders that need surgery. Following the complexity of the surgical procedure, mechanical simulations are necessary but the in vivo factor makes complicate the study of pelvic organs. In order to determine a realistic behavior of these organs, an accurate geometric model associated with a physical modeling is therefore required. Our approach is integrated in the partnership between a geometric and physical module. The Geometric Modeling seeks to build a continuous geometric model: from a dataset of 3D points provided by a Segmentation step, surfaces are created through a B-spline fitting process. An energy function is built to measure the bidirectional distance between surface and data. This energy is minimized with an alternate iterative Hoschek-like method. A thickness is added with an offset formulation, and the geometric model is finally exported in a hexahedral mesh. Afterward, the Physical Modeling tries to calculate the properties of the soft tissues to simulate the organs displacements. The physical parameters attached to the data are determined with a feedback loop between finite-elements deformations and ground-truth acquisition (dynamic MRI).

Multiple reconstruction and dynamic modeling of 3D digital objects using a morphing approach

Organ segmentation and motion simulation of organs can be useful for many clinical purposes such as organ study, diagnostic aid, therapy planning or even tumor destruction. In this paper we present a full workflow starting from a CT-Scan resulting in kidney motion simulation and tumor tracking. Our method is divided into three major steps: kidney segmentation, surface reconstruction and animation. The segmentation is based on a semi-automatic region-growing approach that is refined to improve its results. The reconstruction is performed using the Poisson surface reconstruction and gives a manifold three-dimensional (3D) model of the kidney. Finally, the animation is accomplished using an automatic mesh morphing among the models previously obtained. Thus, the results are purely geometric because they are 3D animated models. Moreover, our method requires only a basic user interaction and is fast enough to be used in a medical environment, which satisfies our constraints. Finally, this method can be easily adapted to magnetic resonance imaging acquisition because only the segmentation part would require minor modifications.

Towards a declarative modeling approach built on top of a CAD modeler

ABSTRACTToday’s CAD modelers are very efficient in processing 3D shapes of CAD models by means of B-Rep modeling operators such as pad, pocket, shaft, groove, hole, fillet and so on. At a lower description level, those modeling operators are based on Euler operators acting directly on the faces, edges and vertices of the B-Rep models. Using such a top-down approach, the designers do not have to work on low-level geometric entities, but rather manipulate so-called structural and detail features to shape directly the CAD models. However, there is still a gap between the shapes the designers have in mind and the way they have to decompose them in a succession of modeling steps. This paper proposes a new declarative modeling approach to design industrial shapes allowing the designers to interact with a CAD software at a more conceptual level. The designers enter a high-level description of the expected shapes that is then transformed through scripts into traditional CAD operators successively called to create...

Triangulation of an elevation surface structured by a sparse 3D grid

This paper proposes a method to triangulate an elevation surface structured in a sparse 3D grid by using a fast search algorithm based on the 2D Delaunay triangulation. After projecting the 3D point clouds onto a natural 2D grid in the x, y plane, we triangulate the surface (actually, we compute a Delaunay triangulation of the 2D point cloud taking advantage of its regular structure). The main novelty of our approach is that the neighboring points of an edge ei are searched in a rectangle supported by the edge ei under consideration. The obtained results show that our method could process very fast, the initial shape of the surface is well preserved, and the topology of the output triangular mesh approximates the input surface of 3D point clouds.

Enhancing the recognition of medication intake using a stereo camera

In this paper, we propose a simple method for estimating the depth of objects with a stereo camera in a medication intake recognition context. A template for each detected object in the left image is matched against the right image, for calculating its horizontal disparity. Then the disparity is used for estimating the distance from camera, so that we can decide whether two objects in occlusion are in genuine contact or not. Experiments show that, the proposed approach is simple and efficient for detecting a true contact between objects in occlusion, a necessary step to further improve a video surveillance system for detection and recognition of medication intake.

Towards a better integration of modelers and black box constraint solvers within the product design process

This paper presents a new way of interaction between modelers and solvers to support the Product Development Process (PDP). The proposed approach extends the functionalities and the power of the solvers by taking into account procedural constraints. A procedural constraint requires calling a procedure or a function of the modeler. This procedure performs a series of actions and geometric computations in a certain order. The modeler calls the solver for solving a main problem, the solver calls the modeler’s procedures, and similarly procedures of the modeler can call the solver for solving sub-problems. The features, specificities, advantages and drawbacks of the proposed approach are presented and discussed. Several examples are also provided to illustrate this approach.

A Review of Two Approaches for Joining 3D Meshes

The construction of smooth surfaces of 3D complex objects is an im- portant problem in many graphical applications. Unfortunately, cracks or holes may appear on their surfaces caused by the limitation of scanners or the differ- ence in resolution levels and subdivision schemes between adjacent faces. In this paper, we introduce two approaches for joining 3D meshes of different resolu- tions to remove the cracks or holes. These approaches use a wavelet transform and a RBF local interpolation or a tangent plane local approximation. They guar- antee that the discrete continuity between meshes is preserved and the connecting mesh can change gradually in resolution between coarse and fine mesh areas.