On topology in multidimensional discrete

To study topology in digital binary images, different discrete connectivities have to be used for both the object and the background. We prove equivalences between discrete connectivities, as they are usually defined in a digital space and connectivity in a continuous space. For that purpose, we introduce the notion of regularization of a set of voxels. It will permit us to define continuous sets from discrete ones. We discuss then the choice of a good couple of discrete connectivities for both the object and the background and provide a characterization of such a valid pair. Finally, we use our best choice to demonstrate a separation theorem in dimension n for surfaces made of voxels

A tree-topology preserving pairing for 3D/2D registration

Information Processing in Computer-Assisted Interventions (IPCAI) 2015 Special IssueInternational audiencePurpose: Fusing pre-operative and intra-operative information into a single space aims at taking advantage of two complementary modalities and necessitates a step of registration that must provide good alignment and relevant correspondences. This paper addresses both purposes in the case of 3D/2D vessel tree matching. Method: We propose a registration algorithm endorsing this vascular tree nature by providing a pairing procedure that preserves the tree topology and by integrating this pairing into an iterative algorithm maintaining pairing coherence. In addition, we define two complementary error measures quantifying the resulting alignment error and pairing error. Both are based on manual ground-truth that is independent of the type of transformation to retrieve. Results: Experiments were conducted on a database of 63 clinical cases, evaluating robustness and accuracy of our approach with respect to the iterative closest point algorithm. Conclusion: The proposed method exhibits good results both in term of pairing and alignment as well as low sensitivity to rotations to be compensated (up to 30 degrees)

Assessing the ability of the 2D Fisher-KPP equation to model cell-sheet wound closure

International audienceWe address in this paper the ability of the Fisher-KPP equations to render some of the dynamical features of epithelial cell-sheets during wound closure. Our approach is based on nonlinear parameter identification, in a two-dimensional setting, and using advanced 2D image processing of the video acquired sequences. As original contribution, we lead a detailed study of the profiles of the classically used cost functions, and we address the "wound constant speed" assumption, showing that it should be handled with care. We study five MDCK cell monolayer assays in a reference, activated and inhibited migration conditions. Modulo the inherent variability of biological assays, we show that in the assay where migration is not exogeneously activated or inhibited, the wound velocity is constant. The Fisher-KPP equation is able to accurately predict, until the final closure of the wound, the evolution of the wound area, the mean velocity of the cell front, and the time at which the closure occurred. We also show that for activated as well as for inhibited migration assays, many of the cell-sheet dynamics cannot be well captured by the Fisher-KPP model. Finally, we draw some conclusions related to the identified model parameters, and possible utilization of the model

Systematized calculation of optimal coefficients of 3-D chamfer norms

International audienceChamfer distances are widely used in image analysis, and many ways have been investigated to compute optimal chamfer mask coefficients. Unfortunately, these methods are not systematized: they have to be conducted manually for every mask size or image anisotropy. Since image acquisition (e.g. medical imaging) can lead to anisotropic discrete grids with unpredictable anisotropy value, automated calculation of chamfer mask coefficients becomes mandatory for efficient distance map computation. This article presents a systematized calculation of these coefficients based on the automatic construction of chamfer masks of any size associated with a triangulation that allows to derive analytically the relative error with respect to the Euclidean distance, in any 3-D anisotropic lattice

On optimal chamfer masks and coefficients

This report describes the calculation of local errors in Chamfer masks both in two- and in three-dimensional anisotropic spaces. For these errors, closed forms are given that can be related to the Chamfer mask geometry. Thanks to these calculation, it can be obsrved that the usual Chamfer masks (i.e. 3x3x3 or 5x5x5) have an inhomogeneously distributed error. Moreover, it allows us to design dedicated Chamfer masks by controlling either the complexity of the computation of the distance map (or equivalently the number of vectors in the mask), or the error of the mask in \mathbbZ^2 or in \mathbbZ^3. Last, since Chamfer distances are usually computed with integer weights (and approximate the Euclidean distance up to a multiplicative factor), we demonstrate that the knowledge of the local errors allows a very efficient computation of these weights

Fusion of autoradiographies with an MR volume using 2-D and 3-D linear transformations

In the past years, the development of 3-D medical imaging devices has given access to the 3-D imaging of in vivo tissues, from an anatomical (MR, CT) or even functional point of view (fMRI, PET, SPECT). However, despite huge technological progress, the resolution of these images is still not sufficient to image to anatomical or functional details, that can only be revealed by in vitro imaging (e.g. histology, autoradiography), eventually enhanced by staining. The deep motivation of this work is the comparison of activations detected by fMRI series analysis to the ones that can be observed in autoradiographic images. The aim of the presented work is to fuse the autoradiographic data with the pre-mortem anatomical MR image, to facilitate the above mentioned comparison. First, we reconstruct a 3-D volume, coherent both in geometry and intensity, from the 2-D autoradiographic sections. Second, this volume is fused with the MR image, that allows to geometrically correct the reconstruction to make it comparable to the MR image. We show that this fusion can be achieved by using only simple global transformations (rigid and/or affine, 2-D and 3-D), yielding a very satisfactory result

Automatic calculation of chamfer mask coefficients for large masks and anisotropic images

Chamfer disctances are widely used in image analysis, and many ways have been investigated to compute optimal chamfer mask coefficients. Unfortunately, these methods are not systematized: they have to be conducted manually for every mask size or image anisotropy. Since image acquisistion (e.g. medical imaging) can lead to anisotropic discrete grids with unpredictable anisotropy value, automated calculation of chamfer mask coefficients becomes mandatory for efficient distance map computation. This report presentes a systematized calculation of these coefficients based on the automatic construction of chamfer masks of any size associated with a triangulation that allows to derive analytically the relative error with respect to the Euclidean distance, in any 3-D anisotropic lattice and that also allows to compute norm constraints

Physically Based Rigid Registration of 3-D Free-Form Objects : application to Medical Imaging

The registration of 3-D objects is an important problem in computer vision and especially in medical imaging. It arises when data acquired by different sensors and/or at different times have to be fused. Under the basic assumption that the objects to be registered are rigid, the problem is to recover the six parameters of a rigid transformation. If landmarks or common characteristics % between both objects to register are not available, the problem has to be solved by an iterative method. However such methods are inevitably attracted to local minima. This paper presents a novel iterative method designed for the rigid registration of 3-D objects. Its originality lies in its physical basis: instead of minimizing an energy function with respect to the parameters of the rigid transformation (the classical approach) the minimization is achieved by studying the motion of a rigid object in a potential field. In particular, we consider the kinetic energy of the solid during the registration process, which allows it to «jump over» some local maxima of the potential energy and so avoid some local minima of that energy. We present extensive experimental results on real 3-D medical images. In this particular application, we perform the matching process with the whole segmented volumes

Embryo Cell Membranes Reconstruction by Tensor Voting

International audienceImage-based studies of developing organs or embryos produce a huge quantity of data. To handle such high-throughput experimental protocols, automated computer-assisted methods are highly desirable. This article aims at designing an efficient cell segmentation method from microscopic images. The proposed approach is twofold: first, cell membranes are enhanced or extracted by the means of structure-based filters, and then perceptual grouping (i.e. tensor voting) allows to correct for segmentation gaps. To decrease the computational cost of this last step, we propose different methodologies to reduce the number of voters. Assessment on real data allows us to deduce the most efficient approach

Piecewise Affine Registration of Biological Images for Volume Reconstruction

This manuscript tackles the reconstruction of 3D volumes via mono-modal registration of series of 2D biological images (histological sections, autoradiographs, cryosections, etc.). The process of acquiring these images typically induces composite transformations that we model as a number of rigid or affine local transformations embedded in an elastic one. We propose a registration approach closely derived from this model. Given a pair of input images, we first compute a dense similarity field between them with a block matching algorithm. We use as a similarity measure an extension of the classical correlation coefficient that improves the consistency of the field. A hierarchical clustering algorithm then automatically partitions the field into a number of classes from which we extract independent pairs of sub-images. Our clustering algorithm relies on the Earth mover’s distribution metric and is additionally guided by robust least-square estimation of the transformations associated with each cluster. Finally, the pairs of sub-images are, independently, affinely registered and a hybrid affine/non-linear interpolation scheme is used to compose the output registered image. We investigate the behavior of our approach on several batches of histological data and discuss its sensitivity to parameters and noise