Laurent D. Cohen

Global Minimum for a Finsler Elastica Minimal Path Approach

In this paper, we propose a novel curvature penalized minimal path model via an orientation-lifted Finsler metric and the Euler elastica curve. The original minimal path model computes the globally minimal geodesic by solving an Eikonal partial differential equation (PDE). Essentially, this first-order model is unable to penalize curvature which is related to the path rigidity property in the classical active contour models. To solve this problem, we present an Eikonal PDE-based Finsler elastica minimal path approach to address the curvature-penalized geodesic energy minimization problem. We were successful at adding the curvature penalization to the classical geodesic energy (Caselles et al. in Int J Comput Vis 22(1):61–79, 1997; Cohen and Kimmel in Int J Comput Vis 24(1):57–78, 1997). The basic idea of this work is to interpret the Euler elastica bending energy via a novel Finsler elastica metric that embeds a curvature penalty. This metric is non-Riemannian, anisotropic and asymmetric, and is defined over an orientation-lifted space by adding to the image domain the orientation as an extra space dimension. Based on this orientation lifting, the proposed minimal path model can benefit from both the curvature and orientation of the paths. Thanks to the fast marching method, the global minimum of the curvature-penalized geodesic energy can be computed efficiently. We introduce two anisotropic image data-driven speed functions that are computed by steerable filters. Based on these orientation-dependent speed functions, we can apply the proposed Finsler elastica minimal path model to the applications of closed contour detection, perceptual grouping and tubular structure extraction. Numerical experiments on both synthetic and real images show that these applications of the proposed model indeed obtain promising results.

Vessel tree extraction using radius-lifted keypoints searching scheme and anisotropic fast marching method:

Geodesic methods have been widely applied to image analysis. They are particularly efficient to extract a tubular structure, such as a blood vessel, given its two endpoints in a 2D or 3D medical image. We address here a more difficult problem: the extraction of a full vessel tree structure given a single initial root point, by growing a collection of keypoints or new initial source points, connected by minimal geodesic paths. In this article, those keypoints are iteratively added, using a new detection criteria, which utilize the weighted geodesic distances with respect to a radius-lifted Riemannian metric, the standard Euclidean curve length and a path score. Two main weaknesses of classical keypoints searching approach are that the weighted geodesic distance and the Euclidean path length do not take into account the orientation of the tubular structure or object boundaries, due to the use of an isotropic geodesic Riemannian metric, and suffer from a leakage problem. In contrast, we use an anisotropic geodesic Riemannian metric, and develop new criteria for selecting keypoints based on the path score and automatically stopping the tree growth. Experimental results demonstrate that our method can obtain the expected results, which can extract vessel structures at a finer scale, with increased accuracy.

Ultrasensitive Doppler based neuronavigation system for preclinical brain imaging applications

Ultrasensitive Doppler is a recent medical imaging technique enabling high sensitive acquisition of blood flows which can detect small vascular features without contrast agents. Applied to cerebral imaging of rodents, this method produces very fine vascular maps of the brain at high spatial resolution and leads to functional imaging of brain neuronal activity. These vascular networks contain crucial information about organs structure, and could be used as landmarks to 3D navigate the brain and register external atlas to the data. This study investigates a first step using a 2D correlation-based method to locate in real time young rat, rat, or mouse brain vascular prints in a 3D functional brain atlas.

Color correction in image stitching using histogram specification and global mapping

Color correction is an important problem in image stitching. There is a color inconsistency issue between the images (good quality as a reference image and bad quality as a test image) to be stitched. This paper presents a color correction approach with histogram specification and global mapping. The proposed algorithm can make images share the same color style and obtain color consistency. There are four main steps in this algorithm. Firstly, overlapping regions between a reference image and a test image are obtained. Secondly, an exact histogram specification is conducted for the overlapping region in the test image using the histogram of the overlapping region in the reference image. Thirdly, a global mapping function is obtained by minimizing color differences with an iterative method. Lastly, the global mapping function is applied to the whole test image to produce a color corrected image. Both synthetic dataset and real dataset are tested. The experiments demonstrate that the proposed algorithm outperforms other methods both quantitatively and qualitatively.

3D vessel extraction in the rat brain from Ultrasensitive Doppler images

Ultrasensitive Doppler is a recent medical imaging technique enabling high sensitive acquisition of blood flows which can detect small vascular features without contrast agents. Applied to cerebral tomographic imaging of rodents, this method produces very fine vascular 3D maps of the brain at high spatial resolution of 100 μm. These vascular networks contain characteristic tubular structures that could be used as landmarks to localize the position of the ultrasonic probe and take advantage of the easy-to-use property of ultrasound devices. In this study, we propose a computational method that performs 3D extraction of vascular paths and estimates effective diameters of vessels, from ultrasensitive Doppler 3D reconstructed images of the rat brain. The method is based on the fast marching algorithm to extract curves minimizing length according to a relevant metric.

Fast Asymmetric Fronts Propagation for Image Segmentation

In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic distance maps and the Eikonal partial differential equations. One of the key ingredients for the computation of the geodesic distance map is the geodesic metric, which can govern the action of the geodesic distance level set propagation. We consider a Finsler metric with the Randers form, through which the asymmetry and anisotropy enhancements can be taken into account to prevent the fronts leaking problem during the fronts propagation. These enhancements can be derived from the image edge-dependent vector field such as the gradient vector flow. The numerical implementations are carried out by the Finsler variant of the fast marching method, leading to very efficient interactive segmentation schemes. We apply the proposed Finsler fronts propagation model to image segmentation applications. Specifically, the foreground and background segmentation is implemented by the Voronoi index map. In addition, for the application of tubularity segmentation, we exploit the level set lines of the geodesic distance map associated with the proposed Finsler metric providing that a thresholding value is given.

An Isotropic Minimal Path Based Framework for Segmentation and Quantification of Vascular Networks

Minimal path approaches for image analysis aim to extract curves minimizing an energy functional. The energy of a path corresponds to its weighted curve length according to a relevant metric function. In this study, we design a binary isotropic metric model with the use of a Hessian-based vascular enhancement filter in order to extract geometrical features from vascular networks. We introduce a constrained keypoint search method able to extract subpixel vessel centrelines, diameters and bifurcations. Experiments on retinal images demonstrated that the proposed framework achieves similar even better segmentation performances as compared with methods using more sophisticated metric designs.

PointFlow: A Model for Automatically Tracing Object Boundaries and Inferring Illusory Contours.

In this paper, we propose a novel method for tracing object boundaries automatically based on a method called “PointFlow” in image induced vector fields. The PointFlow method comprises two steps: edge detection and edge integration. Basically, it uses an ordinary differential equation for describing the movement of points under the action of an image-induced vector field and generates induced trajectories. The trajectories of the flows allow to find and integrate edges and determine object boundaries. We also extend the original PointFlow method to make it adaptable to images with complicated scenes. In addition, the PointFlow method can be applied to infer certain illusory contours.

Fast Asymmetric Fronts Propagation for Voronoi Region Partitioning and Image Segmentation

In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic distance maps and the Eikonal partial differential equations. One of the key ingredients for the computation of the geodesic distance map is the geodesic metric, which can govern the action of the geodesic distance level set propagation. We consider a Finsler metric with the Randers form, through which the asymmetry and anisotropy enhancements can be taken into account to prevent the fronts leaking problem during the fronts propagation. These enhancements can be derived from the image edge-dependent vector field such as the gradient vector flow. The numerical implementations are carried out by the Finsler variant of the fast marching method, leading to very efficient interactive segmentation schemes.

Vehicle X-Ray Images Registration

Image registration is definitely one of the most prominent techniques at the heart of computer vision research. Applications range from medical image analysis, remote sensing or robotics to security-related tasks such as surveillance or motion tracking. In our previous work, a solution was provided to address the registration problem involving top-view radiographic images of vehicles. A unidimensional minimization scheme was formulated along with a column-wise constancy constraint on the displacement field.