Showing papers by "Nicholas Ayache published in 1993"

Non-Rigid Motion Analysis in Medical Images: a Physically Based Approach

Abstract: We present a physically-based deformable model which can be used to track and to analyze non-rigid motion of dynamic structures in time sequences of 2D or 3D medical images. The model considers an object undergoing an elastic deformation as a set of masses linked by springs, where the classical natural lengths of the springs is set equal to zero, and is replaced by a set of constant equilibrium forces, which characterize the shape of the elastic structure in the absence of external forces. This model has the extremely nice property of yielding dynamic equations which are linear and decoupled for each coordinate, whatever the amplitude of the deformation. Compared to the former work of Terzopoulos and his colleagues [12, 27, 26, 15] and Pentland and his colleagues [22, 21, 23, 10], our model can be viewed as a continuation and unification; it provides a reduced algorithmic complexity, and a sound framework for modal analysis, which allows a compact representation of a general deformation by a reduced number of parameters. The power of the approach to segment, track and analyze 2-D and 3-D images is demonstrated by a set of experimental results on various complex medical images (ultrasound and magnetic resonance images).

Evaluating 3D registration of CT-scan images using crest lines

Abstract: We consider the issue of matching 3D objects extracted from medical images. We show that crest lines computed on the object surfaces correspond to meaningful anatomical features, and that they are stable with respect to rigid transformations. We present the current chain of algorithmic modules which automatically extract the major crest lines in 3D CT-Scan images, and then use differential invariants on these lines to register together the 3D images with a high precision. The extraction of the crest lines is done by computing up to third order derivatives of the image intensity function with appropriate 3D filtering of the volumetric images, and by the 'marching lines' algorithm. The recovered lines are then approximated by splines curves, to compute at each point a number of differential invariants. Matching is finally performed by a new geometric hashing method. The whole chain is now completely automatic, and provides extremely robust and accurate results, even in the presence of severe occlusions. In this paper, we briefly describe the whole chain of processes, already presented to evaluate the accuracy of the approach on a couple of CT-scan images of a skull containing external markers.

Device for processing three-dimensional image information, with extraction of significant lines.

Abstract: An image is defined, in correspondence with a predetermined polyhedral meshing of a portion of the space, by a numerical value for each vertex of the meshing. Polygon processing includes receiving a representation of a plane polygon with p vertices, p respective values for these p vertices, and a threshold. In correspondence with the polygon, polygon processing supplies a list of oriented segments linking points of the edges of the polygon which are interpolated as being equal to the threshold, with a predetermined direction convention. Polyhedron processing includes receiving a representation of a polyhedron with the values at its vertices and a threshold. Polyhedron processing then invokes polygon processing for all the faces of the polyhedron, which supplies a list of oriented segments. Polyhedron processing then associates with the polyhedron a list of closed and oriented cycles, constituted by segments from the said list of segments. Main processing includes sequentially presenting a plurality of polyhedrons of the polyhedrons meshing for the polyhedron processing, with the values associated with their vertices and a threshold. The cycles thus obtained belong to an iso-surface of the image for the threshold value.

Large deformable splines, crest lines, and matching

Abstract: We present new deformable spline surfaces for segmentation of 3-D medical images. We explore parametric surfaces of the form x(u, v) with two different topologies, planar and cylindrical, that permit us to segment fine anatomical structures. With respect to earlier approaches that minimize the `energy' of a deformable surface in a potential field, we perform this optimization with successive approximations of dense data, and propose the following key improvements. First, we show that the Euler equation has a closed form solution in a quadratic potential field. Each approximation requires only one iteration. Second, we use tensor products of splines to solve independently the system along parameters u and v. This enables us to work with large meshes of control vertices, e.g., 10,000 vertices and more. Third, with a regularly sampled potential field, each point in the same image voxel is processed in the same way. We use a continuous potential field defined with 3-D volumetric splines to avoid this problem. When the deformation process stops, we end up with a smooth differentiable surface where we measure principle curvatures and directions. We describe next an original algorithm that extracts lines of extremal curvature on the surface. These lines can be matched from different views with an algorithm such as in.GA92. We present experimental evidence with real medical images that illustrate all the previous points. Finally, we outline the spherical topology for spline surfaces. We use Ostrogradsky's formula to compute the exact volume bounded by such a surface.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

New developments on geometric hashing for curve matching

Abstract: The problem of fast rigid matching of 3D curves with subvoxel precision is addressed. More invariant parameters are used, and new hash tables are implemented in order to process larger and more complex sets of data curves. There exists a Bayesian theory of geometric hashing that explains why local minima are not really a problem. The more likely transformation always wins. It is also possible to predict the uncertainty on the match with the help of the Kalman filter, and compare it with real measures. >

An Adaptive Model for 2-D and 3-D dense non rigid motion computation

Abstract: We describe a new method for computing a dense displacement field from a time-sequence of $2D$ or $3D$ images. It consists in minimizing an energy defined on the space of correspondence functions. This energy is divided into two terms, one term which matches contour points and particularly high curvature points, and one regularization term which constrains the continuity of the field. We introduce an adaptive mesh the resolution of which depends on the presence of edges and/or points of high curvature and we show how to use it to reduce the computational time of the method. We present experimental results on medical images which prove the validity of the approach and the accuracy of the computed displacement fields.

Physically based analysis of deformations in 3D images

Abstract: We present a physically based deformable model which can be used to track and to analyze the non-rigid motion of dynamic structures in time sequences of 2-D or 3-D medical images. The model considers an object undergoing an elastic deformation as a set of masses linked by springs, where the natural lengths of the springs is set equal to zero, and is replaced by a set of constant equilibrium forces, which characterize the shape of the elastic structure in the absence of external forces. This model has the extremely nice property of yielding dynamic equations which are linear and decoupled for each coordinate, whatever the amplitude of the deformation. It provides a reduced algorithmic complexity, and a sound framework for modal analysis, which allows a compact representation of a general deformation by a reduced number of parameters. The power of the approach to segment, track, and analyze 2-D and 3-D images is demonstrated by a set of experimental results on various complex medical images.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Reconstruction of digital terrain model with a lake

Abstract: Variational methods have been frequently used for surface reconstruction and contour extraction (snakes). We present a surface reconstruction method where we assume the surface composed of two regions of different types of smoothness. One region of the surface models a `lake' (constant height region with uphill borders). It is surrounded by the other background region which is reconstructed using classic surface regularization. The boundary between the two regions, represented by a closed curve, is determined with the help of an active contour model. Then the surface is reconstructed by minimizing the energy terms in each region. Minimizing a global energy defined on the couple of unknowns -- boundary curve and surface -- permits us to introduce other forces on the curve. The surface reconstruction and contour extraction tasks are then made together. We have applied this model for segmenting a synthetic digital terrain model (DTM) image which represents a noisy mountain and lake.

Device for processing three-dimensional image information with extraction of remarkable lines

Abstract: An image (MI) is defined, in correspondence with a predetermined polyhedral meshing of a portion of space, by a digital value for each vertex of the meshing. A polygon processing (30; 1450; 1650) receives a representation of a plane polygon (F) with p vertices, p respective values for these p vertices, and a threshold (S); it supplies, in correspondence with the polygon F, a list of oriented segments linking points of the edges of the polygon which are interpolated as equal to the threshold, with a predetermined direction convention. A polyhedron processing (20; 1445; 1645) receives a representation of a polyhedron (POLYED) with the values at its vertices and a threshold; then it invokes the polygon processing means (30) for all the faces of the polyhedron, which supplies a list of oriented segments; then it associates with a polyhedron a list of closed and oriented cycles, constituted by segments of the said list of segments. Main processing means (10; 1440; 1640) sequentially present a plurality of polyhedrons of the said meshing to the polyhedron processing means, with the values associated with their vertices and a threshold. The cycles thus obtained belong to an iso-surface of the image for the said threshold value.

Dispositif de traitement d'informations d'images tridimensionnelles, avec extraction de lignes remarquables

Abstract: Une image (MI) est definie, en correspondance d'un maillage polyedrique predetermine d'une portion de l'espace, par une valeur numerique pour chaque sommet du maillage. Un traitement de polygone (30; 1450; 1650), recoit une representation d'un polygone plan (F) a p sommets, p valeurs respectives pour ces p sommets, et un seuil (S); il fournit, en correspondance du polygone F, une liste de segments orientes reliant des points des aretes du polygone interpoles comme egaux au seuil, avec une convention de sens predeterminee. Un traitement de polyedre (20; 1445; 1645) recoit une representation d'un polyedre (POLYED) avec les valeurs en ses sommets et un seuil; puis il sollicite les moyens de traitement de polygone (30) pour toutes les faces du polyedre, ce qui fournit une liste de segments orientes; puis il associe au polyedre une liste de cycles fermes et orientes, constitues de segments de ladite liste de segments. Des moyens de traitement principaux (10; 1440; 1640) presentent sequentiellement une pluralite de polyedres dudit maillage aux moyens de traitement de polyedre, avec les valeurs associees a leurs sommets et un seuil. Les cycles ainsi obtenus appartiennent a une iso-surface de l'image pour ladite valeur de seuil.