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Many computer vision methods use consensus maximization to relate measurements containing outliers with the correct transformation model. In the context of rigid shapes, this is typically done using Random Sampling and Consensus (RANSAC) by estimating an analytical model that agrees with the largest number of measurements (inliers). However, small parameter models may not be always available. In this paper, we formulate the model-free consensus maximization as an Integer Program in a graph using ‘rules’ on measurements. We then provide a method to solve it optimally using the Branch and Bound (BnB) paradigm. We focus its application on non-rigid shapes, where we apply the method to remove outlier 3D correspondences and achieve performance superior to the state of the art. Our method works with outlier ratio as high as 80%. We further derive a similar formulation for 3D template to image matching, achieving similar or better performance compared to the state of the art., Lecture Notes in Computer Science, 11208, ISSN:0302-9743, ISSN:1611-3349, Computer Vision – ECCV 2018, ISBN:978-3-030-01224-3, ISBN:978-3-030-01225-0

International audience; We introduce a novel matching algorithm, called DeepMatching, to compute dense correspondences between images. DeepMatching relies on a hierarchical, multi-layer, correlational architecture designed for matching images and was inspired by deep convolutional approaches. The proposed matching algorithm can handle non-rigid deformations and repetitive textures and efficiently determines dense correspondences in the presence of significant changes between images. We evaluate the performance of DeepMatching, in comparison with state-of-the-art matching algorithms, on the Mikolajczyk (Mikolajczyk et al. A comparison of affine region detectors, 2005), the MPI-Sintel (Butler et al. A naturalistic open source movie for optical flow evaluation, 2012) and the Kitti (Geiger et al. Vision meets robotics: The KITTI dataset, 2013) datasets. DeepMatching outperforms the state-of-the-art algorithms and shows excellent results in particular for repetitive textures. We also apply DeepMatching to the computation of optical flow, called DeepFlow, by integrating it in the large displacement optical flow (LDOF) approach of Brox and Malik (Large displacement optical flow: descriptor matching in variational motion estimation, 2011). Additional robustness to large displacements and complex motion is obtained thanks to our matching approach. DeepFlow obtains competitive performance on public benchmarks for optical flow estimation.

International audience; This paper introduces an anisotropic Laplace-Beltrami operator for shape analysis. While keeping useful properties of the standard Laplace-Beltrami operator, it introduces variability in the directions of principal curvature, giving rise to a more intuitive and semantically meaningful diffusion process. Although the benefits of anisotropic diffusion have already been noted in the area of mesh processing (e.g. surface regularization), focusing on the Laplacian itself, rather than on the diffusion process it induces, opens the possibility to effectively replace the omnipresent Laplace-Beltrami operator in many shape analysis methods. After providing a mathematical formulation and analysis of this new operator, we derive a practical implementation on discrete meshes. Further, we demonstrate the effectiveness of our new operator when employed in conjunction with different methods for shape segmentation and matching.

In the context of computer assist surgical techniques, a new elastic registration method of 3D meshes is presented. In our applications, one mesh is a high density mesh (30000 vertexes), the second is a low density one (1000 vertexes). Registration is based upon the minimisation of a symmetric distance between both meshes, defined on the vertexes, in a multi resolution approach. Results on synthetic images are first presented. Then, thanks to this registration method, a statistical model of the skull is build from Computer Tomography exams collected for twelve patients.

Most iconic methods for rigid matching consist in finding and minimizing a registration criterion specifically chosen to solve a given problem. For non-rigid matching, attention has rather focussed on the type of smoothing or physical model of deformation to be used. In this report, we propose to place the non-rigid matching problem into a minimization framework. We have developped our theoretical idea in the case of the least squares criterion, corresponding to the assumption that the intensities of points do not change over time, and we have implemented a first order gradient descent which, along with a multiresolution approach, minimizes this criterion- . We also prove that the «demons» algorithm, thought of until now as an as hoc matching technique, can be seen as an approximation of a second order gradient descent on this criterion. Analysis of the mechanisms of this gradient descent incites us to introduce two different weightings into the filters used to smooth the solution, which we called an a priori weighting improves the solution found for the minimization problem, which is shown by comparing results in a distance-roughness space, while the a posteriori weighting helps tackle the appearance or disappearance of matter and occlusions, both sensitive issues for non-rigid iconic methods.

A major issue in cardiac imaging is the assessment of cardiac function and particularly the identification of ischemic or infarcted tissues. We present in this article a method to reconstruct the displacement field of the left ventricular (LV) motion using 4D planispheric transformations of time and space combined in a first step with B-spline tensor products. Because of the 4D modeling, a) it is possible to include any tag plane direction as input data. b) The use of planispheric coordinates makes the numerical evaluation more stable as compared to prolate spheroidal coordinates, the equivalent focal point being much further from the apical area of the heart. This therefore avoids mathematical instability when the material points of the myocardium are too close to the apical focus. c) In the temporal modeling, a simple adaptation is possible to changing temporal dynamics, such as introduced by ectopic pacing or rapid filling after systole. d) Finally, the strain analysis and displacement parameters that are used for the spatial modeling are computed at any point of the LV volume. Experiments are conducted on a normal and a pathological LV (posterior infarct) in order to assess the tuning of the parameters of the method. The mean RMS-distance error is less than 0.5mm for both LVs. Finally, the motion is analysed as zeroth (displacement) and first order parameters (strain), which estimate are smooth.

Cardiologists assume that analysis of the motion of the heart (especially the left ventricle) can give precise information about the health of the myocardium. A 4D polar transformation is defined to describe the left ventricle (LV) motion and a method is presented to estimate it from sequences of 3D images. The transformation is defined in 3D-planispheric coordinates by a small number of parameters involved in a set of simple linear equations. It is continuous and regular in time and space, periodicity in time can be imposed. The local motion can be easily decomposed into a few canonical motions (centripetal contraction, rotation around the long-axis, elevation). To recover the motion from original data, the 4D polar transformation is calculated using an adaptation of the Iterative Closest Point algorithm. We present the mathematical framework and a demonstration of its feasability on a set of synthetic but realistic datapoints, simulating the motion of the LV and on a gated SPECT sequence.

Single photon emission computed tomography (SPECT) imaging with Thallium 201 or Technetium 99 is used to assess the location or the extent of myocardial infarction or ischemia. A method is proposed to decrease the effect of operator variability and morphologically blind sampling in the quantification of scintigraphic myocardial perfusion studies. To this effect the patient's myocardial images (target cases) are registered automatically over a template image, utilizing non-rigid transformations. The intermediate steps are: 1.~Extraction of feature points in both stress and rest 3D images. We resample the images in a polar geometry to detect edges and we use a priori constraints to filter the points. Those feature points are assumed to be edges of the left ventricle. 2.~Registration of stress and rest images with an affine transformation. The matching method is an adaptation of the Iterative Closest Point algorithm. 3.~Alignment of both stress and rest images on a template using a non-rigid local spline transformation. The matching method is the one used in step 2. 4.~Resampling of both stress and rest images in the geometry of the template. Experiments have been lead on a database including 40 pairs of images selected to obtain a group of image abnormalities and variability. Upon the successful clinical validation of this work, a reliable, operator independent method for the analysis and interpretation of myocardial perfusion scintigraphies will be available.

This paper describes a method to automatically generate the mapping between a completely labeled reference image and the 3D medical image of a patient. To achieve this, we combined three techniques: the extraction of 3D feature lines, their matching using 3D deformable line models, the extension of the deformation to the whole image space using warping techniques. We present experimental results for the segmentation of structures in Magnetic Resonance images of the brain of different patients; the segmentation of the cortical and ventricle structures. We emphasize the advantages of using crest lines deformable models prior to surface based models. This gives a sparser representation of the data, easier to manipulate, and which makes the convergence of the model much less sensitive to initial positionning. In the future, we hope to use this method to generate anatomical atlases, by the automatic interpretation of large sets of 3D medical images.

We present a method to perform the non-rigid matching of two 3D medical images, which is fast and fully automated. We illustrate this method in several applications, such as inter-patient registration, cardiac image sequence analysis, and the automatic registration with anatomical atlases, which we identify as currently important challenges for medical image processing. Several interesting inter-patient matching methods have been proposed recently, showing the interest of such techniques, but whose computation time is still prohibitive for practical clinical applications. The main interest of our methods is to perform a "satisfying" non-rigid matching of large image volumes within only several tens of minutes on a conventional workstation. We describe our method as based on "demons" (in the sense of Maxwell's demons) which locally deform the model to push it into a mold, as opposed to more traditional "attractor" based deformable model techniques. Finally, we present experiments on real data, and discuss two current limitations of our technique: the sensitivity to initial positioning, and to intensity variations between images.

The goal of this paper is to present an efficient framework for non-rigid medical image matching. Previous non-rigid matching often produces unpredictable deformation field and unwanted stretching in the images. The as-rigid-as-possible nature of the Moving-LS technique thus makes it a new candidate by providing transformation that maintains the rigidity of structures for underlying physical reasons, while producing local deformations. In addition, it is very suitable for parallel computation, and the performance can be accelerated by multi-core processors through employment of multiple threads. The results demonstrate that the proposed matching method has good balance between accuracy and speed, and has potential in many medical applications.