Choroidal neovascularization (CNV), a primary characteristic of wet age-related macular degeneration (wet AMD), represents a leading cause of blindness worldwide. In clinical practice, optical coherence tomography angiography (OCTA) is commonly used for studying CNV-related pathological changes, due to its micron-level resolution and non-invasive nature. Thus, accurate segmentation of CNV regions and vessels in OCTA images is crucial for clinical assessment of wet AMD. However, challenges existed due to irregular CNV shapes and imaging limitations like projection artifacts, noises and boundary blurring. Moreover, the lack of publicly available datasets constraints the CNV analysis. To address these challenges, this paper constructs the first publicly accessible CNV dataset (CNVSeg), and proposes a novel multilateral graph convolutional interaction-enhanced CNV segmentation network (MTG-Net). This network integrates both region and vessel morphological information, exploring semantic and geometric duality constraints within the graph domain. Specifically, MTG-Net consists of a multi-task framework and two graph-based cross-task modules: Multilateral Interaction Graph Reasoning (MIGR) and Multilateral Reinforcement Graph Reasoning (MRGR). The multi-task framework encodes rich geometric features of lesion shapes and surfaces, decoupling the image into three task-specific feature maps. MIGR and MRGR iteratively reason about higher-order relationships across tasks through a graph mechanism, enabling complementary optimization for task-specific objectives. Additionally, an uncertainty-weighted loss is proposed to mitigate the impact of artifacts and noise on segmentation accuracy. Experimental results demonstrate that MTG-Net outperforms existing methods, achieving a Dice socre of 87.21% for region segmentation and 88.12% for vessel segmentation.

Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries. However, such a segmentation strategy cannot take into account the connectivity of the image edge features, increasing the risk of shortcut problem, especially in the case of complicated scenario. In this work, we introduce a new image segmentation model based on the minimal geodesic framework in conjunction with an adaptive cut-based circular optimal path computation scheme and a graph-based boundary proposals grouping scheme. Specifically, the adaptive cut can disconnect the image domain such that the target contours are imposed to pass through this cut only once. The boundary proposals are comprised of precomputed image edge segments, providing the connectivity information for our segmentation model. These boundary proposals are then incorporated into the proposed image segmentation model, such that the target segmentation contours are made up of a set of selected boundary proposals and the corresponding geodesic paths linking them. Experimental results show that the proposed model indeed outperforms state-of-the-art minimal paths-based image segmentation approaches.

The minimal geodesic models established upon the eikonal equation framework are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a planar curve can be mapped to an high-dimensional orientation-dependent space. The convexity shape prior serves as a constraint for the construction of local geodesic metrics encoding a particular curvature constraint. Then the geodesic distances and the corresponding closed geodesic paths in the orientation-lifted space can be efficiently computed through state-of-the-art Hamiltonian fast marching method. In addition, we apply the proposed geodesic models to the active contours, leading to efficient interactive image segmentation algorithms that preserve the advantages of convexity shape prior and curvature penalization.

Tubular structure tracking is a crucial task in the fields of computer vision and medical image analysis. The minimal paths-based approaches have exhibited their strong ability in tracing tubular structures, by which a tubular structure can be naturally modeled as a minimal geodesic path computed with a suitable geodesic metric. However, existing minimal paths-based tracing approaches still suffer from difficulties such as the shortcuts and short branches combination problems, especially when dealing with the images involving complicated tubular tree structures or background. In this paper, we introduce a new minimal paths-based model for minimally interactive tubular structure centerline extraction in conjunction with a perceptual grouping scheme. Basically, we take into account the prescribed tubular trajectories and curvature-penalized geodesic paths to seek suitable shortest paths. The proposed approach can benefit from the local smoothness prior on tubular structures and the global optimality of the used graph-based path searching scheme. Experimental results on both synthetic and real images prove that the proposed model indeed obtains outperformance comparing with the state-of-the-art minimal paths-based tubular structure tracing algorithms.

In this paper, we propose a new minimal path-based framework for minimally interactive tubular structure tracking in conjunction with a perceptual grouping scheme. The minimal path models have shown great advantages in tubular structures tracing. However, they suffer from shortcuts or short branches combination problems especially in the case of tubular network with complicated structures or background. Thus, we utilize the curvature-penalized minimal paths and the prescribed tubular trajectories to seek the desired shortest path. The proposed approach benefits from the local smoothness prior on tubular structures and the global optimality of the graph-based path searching scheme. Experimental results on synthetic and real images prove that the proposed model indeed obtains outperformance to state-of-the-art minimal path-based algorithms.

The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit the image features in conjunction with geometric regularization terms (such as curve length or elastica length) for computing geodesic paths. In this paper, we consider a more complicated problem: finding simple and closed geodesic curves which are imposed a convexity shape prior. The proposed approach relies on an orientation-lifting strategy, by which a planar curve can be mapped to an high-dimensional orientation space. The convexity shape prior serves as a constraint for the construction of local metrics. The geodesic curves in the lifted space then can be efficiently computed through the fast marching method. In addition, we introduce a way to incorporate region-based homogeneity features into the proposed geodesic model so as to solve the region-based segmentation issues with shape prior constraints.

The Voronoi diagram-based dual-front scheme is known as a powerful and efficient technique for addressing the image segmentation and domain partitioning problems. In the basic formulation of existing dual-front approaches, the evolving contour can be considered as the interfaces of adjacent Voronoi regions. Among these dual-front models, a crucial ingredient is regarded as the geodesic metrics by which the geodesic distances and the corresponding Voronoi diagram can be estimated. In this paper, we introduce a new dual-front model based on asymmetric quadratic metrics. These metrics considered are built by the integration of the image features and a vector field derived from the evolving contour. The use of the asymmetry enhancement can reduce the risk for the segmentation contours being stuck at false positions, especially when the initial curves are far away from the target boundaries or the images have complicated intensity distributions. Moreover, the proposed dual-front model can be applied for image segmentation in conjunction with various region-based homogeneity terms. The numerical experiments on both synthetic and real images show that the proposed dual-front model indeed achieves encouraging results.

Minimal paths are regarded as a powerful and efficient tool for boundary detection and image segmentation due to its global optimality and the well-established numerical solutions such as fast marching method. In this paper, we introduce a flexible interactive image segmentation model based on the Eikonal partial differential equation (PDE) framework in conjunction with region-based homogeneity enhancement. A key ingredient in the introduced model is the construction of local geodesic metrics, which are capable of integrating anisotropic and asymmetric edge features, implicit region-based homogeneity features and/or curvature regularization. The incorporation of the region-based homogeneity features into the metrics considered relies on an implicit representation of these features, which is one of the contributions of this work. Moreover, we also introduce a way to build simple closed contours as the concatenation of two disjoint open curves. Experimental results prove that the proposed model indeed outperforms state-of-the-art minimal paths-based image segmentation approaches.

The minimal path method has proven to be particularly useful and efficient in tubular structure segmentation applications. In this paper, we propose a new minimal path model associated with a dynamic Riemannian metric embedded with an appearance feature coherence penalty and an adaptive anisotropy enhancement term. The features that characterize the appearance and anisotropy properties of a tubular structure are extracted through the associated orientation score. The proposed the dynamic Riemannian metric is updated in the course of the geodesic distance computation carried out by the efficient single-pass fast marching method. Compared to the state-of-the-art minimal path models, the proposed minimal path model is able to extract the desired tubular structures from a complicated vessel tree structure. In addition, we propose an efficient prior path-based method to search for vessel radius value at each centerline position of the target. Finally, we perform the numerical experiments on both synthetic and real images. The quantitive validation is carried out on retinal vessel images. The results indicate that the proposed model indeed achieves a promising performance.

We propose a new dynamic Riemannian metric with adaptive anisotropy enhancement and with appearance feature coherence penalization. The appearance features are characterized by the orientation score maps. Unlike the static geodesic metrics which depend on local pointwise information, the dynamic metric can take into account the nonlocal feature coherence penalty in order to extract a desired structure from complicated background or from a vessel tree. We construct the metric using the information from two external reference points which are identified during the geodesic distance computation. Numerical experiments are performed in retinal vessels, including the independent results from the proposed dynamic metric itself and the comparison against existing minimal path models. The results show that the proposed metric indeed gets better performance than state-of-the-art geodesic metrics.

In this paper, we propose a novel algorithm for tracing object boundaries automatically based on a model called “point flow” in image induced vector fields. An ordinary differential equation describes 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 tested our method on real image dataset. Compared with the other classical edge detection and integration models, our point flow method is better at providing precise and continuous curves. The experimental results clearly exhibit the robustness and effectiveness of the proposed method.

In this paper, we propose a new curvature penalized minimal path model for image segmentation via closed contour detection based on the weighted Euler elastica curves, firstly introduced to the field of computer vision in [22]. Our image segmentation method extracts a collection of curvature penalized minimal geodesics, concatenated to form a closed contour, by connecting a set of user-specified points. Globally optimal minimal paths can be computed by solving an Eikonal equation. This first order PDE is traditionally regarded as unable to penalize curvature, which is related to the path acceleration in active contour models. We introduce here a new approach that enables finding a global minimum of the geodesic energy including a curvature term. We achieve this through the use of a novel Finsler metric adding to the image domain the orientation as an extra space dimension. This metric is non-Riemannian and asymmetric, defined on an orientation lifted space, incorporating the curvature penalty in the geodesic energy. Experiments show that the proposed Finsler minimal path model indeed outperforms state-of-the-art minimal path models in both synthetic and real images.

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Segmentation methods based on energy minimization techniques like geodesic active contour model generally needs manual intervention to provide initial points to calculate minimal paths. In this paper, we propose complete automation of segmentation. Seeds and Tips are automatically detected, and geodesics are calculated using Anisotropic Fast Marching algorithm. Fast Marching algorithm computes in a single pass, the evolution of the front, at a speed locally given by its position. Anisotropic Fast Marching (AFM) is a variant of Fast Marching, in which the the measure of path length (and the front speed) depends not only on the path position, but also on path direction and orientation. In this work, a gradient based metric has been defined and AFM is evaluated iteratively over a set of points which are automatically detected on the object boundary. Geodesic voting is then applied to get the segmented structure.

Geodesic methods have been widely applied to image analysis [1]. 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 [2]. We address here a more difficult problem: the extraction of a full vessel tree structure given a single initial root, by growing a collection of keypoints, connected by geodesic minimal paths as in [3]. Keypoints are iteratively added, using selection criteria which compare geodesic distances with the standard euclidean curve length and a path score. A weakness of existing approaches is that the geodesic length and the euclidean path length are locally proportional, due to the use of an isotropic geodesic potential P(x). In contrast, we use an anisotropic geodesic potential P(x, v), and develop new criteria for selecting keypoints and stopping the tree growth. Experimental results demonstrate that our method can extract vessel structures at a finer scale, with increased accuracy.

Active contours and minimal paths have been extensively studied theoretical tools for image segmentation. The recent geodesically linked active contour model, which basically consists in a set of vertices connected by paths of minimal cost, blend the bene ts of both concepts. This makes up a closed piecewise-smooth curve, over which an edge or region energy functional can be formulated. As an important shortcoming, the geodesically linked active contour model in its initial formulation does not guarantee the curve to be simple, consistent with respect to the purpose of segmentation. In this paper, we propose to extract a relevant contour from a set of possible paths, such that the resulting structure ts the image data and is simple. Toward this goal, we introduce a novel term to favor the simplicity of the generated contour, as well as a local search method to choose the best combination among possible paths.

This article introduces a novel class of active contour models for image segmentation. It makes use of nonlocal comparisons between pairs of patches within each region to be segmented. The corresponding variational segmentation problem is implemented using a level set formulation that can handle an arbitrary number of regions. The pairwise interaction of features constrains only the local homogeneity of image features, which is crucial in capturing regions with smoothly spatially varying features. This segmentation method is generic and can be adapted to various segmentation problems by designing an appropriate metric between patches. We instantiate this framework using several classes of features and metrics. Piecewise smooth grayscale and color images are handled using $L^2$ distance between image patches. We show examples of efficient segmentation of natural color images. Locally oriented textures are segmented using the $L^2$ distance between patches of Gabor coefficients. We use a Wasserstein distance between local empirical distributions for locally homogeneous random textures. A correlation metric between local motion signatures is able to segment piecewise smooth optical flows.

This article introduces a new variational image segmentation method that makes use of non-local comparisons between pairs of patches in the image and is robust to missing data (e.g. damaged pixels or large missing regions). The resulting segmentation is at the heart of a novel inpainting algorithm that also uses a non-local regularization. This segmentation and inpainting approach only requires a local homogeneity of the features inside and outside the region to be segmented. In contrast to existing region-based segmentation methods, it allows us to segment regions with smoothly varying intensity as well as multiple objects with different intensities. This comparison principle is also less sensitive to initialization than edge-based approaches.

In this paper, we present a new approach for segmentation of tubular structures in 2D images providing minimal interaction. The main objective is to extract centerlines and boundaries of the vessels at the same time. The first step is to represent the trajectory of the vessel not as a 2D curve but to go up a dimension and represent the entire vessel as a 3D curve, where each point represents a 2D disc (two coordinates for the center point and one for the radius). The 2D vessel structure is then obtained as the envelope of the family of discs traversed along this 3D curve. Since this 2D shape is defined simply from a 3D curve, we are able to fully exploit minimal path techniques to obtain globally minimizing trajectories between two or more user supplied points using front propagation. The main contribution of our approach consists on building a multi-resolution metric that guides the propagation in this 3D space. We have chosen to exploit the tubular structure of the vessels one wants to extract to built an anisotropic metric giving higher speed on the center of the vessels and also when the minimal path tangent is coherent with the vessel's direction. This measure is required to be robust against the disturbance introduced by noise or adjacent structures with intensity similar to the target vessel. Indeed, if we examine the flux of the projected image gradient along a given direction on a circle of a given radius (or scale), one can prove that this flux is maximal at the center of the vessel, in its direction and with its exact radius. This approach is called optimally oriented flux. Combining anisotropic minimal paths techniques and optimally oriented flux we obtain promising results on noisy synthetic and real data.

We propose a new image compression method based on geodesic Delaunay triangulations. Triangulations are generated by a progressive geodesic meshing algorithm which exploits the anisotropy of images through a farthest point sampling strategy. This seeding is performed according to anisotropic geodesic distances which force the anisotropic Delaunay triangles to follow the geometry of the image. Geodesic computations are performed using a Riemannian Fast Marching, which recursively updates the geodesic distance to the seed points. A linear spline approximation on this triangulation allows to approximate faithfully sharp edges and directional features in images. The compression is achieved by coding both the coefficients of the spline approximation and the deviation of the geodesic triangulation from an Euclidean Delaunay triangulation. Numerical results show that taking into account the anisotropy improves the approximation by isotropic triangulations of complex images. The resulting encoder competes well with wavelet-based encoder such as JPEG-2000 on geometric images.

This paper proposes new hash functions for indexing local image descriptors. These functions are first applied and evaluated as a range neighbor algorithm. We show that it obtains similar results as several state of the art algorithms. In the context of near duplicate image retrieval, we integrated the proposed hash functions within a bag of words approach. Because most of the other methods use a kmeans-based vocabulary, they require an off-line learning stage and highest performance is obtained when the vocabulary is learned on the searched database. For application where images are often added or removed from the searched dataset, the learning stage must be repeated regularly in order to keep high recalls. We show that our hash functions in a bag of words approach has similar recalls as bag of words with kmeans vocabulary learned on the searched dataset, but our method does not require any learning stage. It is thus very well adapted to near duplicate image retrieval applications where the dataset evolves regularly as there is no need to update the vocabulary to guarantee the best performance.

In this paper, we address the problem of constrained segmentation of natural images, in which a human user places one seed point inside each object of interest in the image and the task is to determine the object boundaries. For this purpose, we study the connection between seed-based and hierarchical segmentation. We consider an Ultrametric Contour Map (UCM), the representation of a hierarchy of segmentations as a real-valued boundary image. Starting from a set of seed points, we propose an algorithm for constructing Voronoi tessellations with respect to a distance defined by the UCM. As a result, the main contribution of the paper is a method that allows exploiting the information of any hierarchical scheme for constrained segmentation. Our algorithm is parameter-free, computationally efficient and robust. We prove the interest of the approach proposed by evaluating quantitatively the results with respect to ground-truth data.

This paper proposes a novel algorithm to reconstruct a 3D surface from a calibrated set of images. In a first pass, it uses Scale Invariant Features Transform (SIFT) descriptor correspondences to drive the deformation of a mesh toward the true object surface. We introduce a method to handle the fact that these local descriptors are computed at positions that are not projections of mesh vertices in the images. In order to avoid projective deformations due to the large windows of interest of this descriptor, correspondences are only computed between images from the same viewpoint. This is used in a first pass to recover large concavities of the object. In a second pass, a one dimensional Lucas-Kanade tracker is used to recover small scale details. Using publicly available benchmarks, our algorithm obtains high accuracy while being among the fastest ones.

This paper presents a new method to segment thin tree structures, such as extensions of microglia and cardiac or cerebral blood vessels. The Fast Marching method allows the segmentation of tree structures from a single point chosen by the user when a priori information is available about the length of the tree. In our case, no a priori information about the length of the tree structure to extract is available. We propose here to compute geodesics from a set of points scattered in the image. The targeted structure corresponds to image points with a high geodesic density. To compute the geodesic density we propose two methods. The first method defines the geodesic density of pixels in the image as the number of geodesics that cross this pixel. The second method consists in solving the transport equation with a velocity computed from the gradient of the distance map. In this method, the geodesic density is computed by integrating in short time the solution of the transport equation. To our knowledge this is the first time that geodesic voting is introduced. Numerical results from confocal microscope images are presented and show the interest of our approach.

In this paper, we present a new method for segmenting closed contours and surfaces. Our work builds on a variant of the Fast Marching algorithm. First, an initial point on the desired contour is chosen by the user. Next, new keypoints are detected automatically using a front propagation approach. We assume that the desired object has a closed boundary. This a-priori knowledge on the topology is used to devise a relevant criterion for stopping the keypoint detection and front propagation. The final domain visited by the front will yield a band surrounding the object of interest. Linking pairs of neighboring keypoints with minimal paths allows us to extract a closed contour from a 2D image. Detection of a variety of objects on real images is demonstrated. Using a similar same idea, we can extract networks of minimal paths from a 3D image called Geodesic Meshing. The proposed method is applied to 3D data with promising results.

This paper presents a new method to quickly extract geodesic paths on images and 3D meshes. We use a heuristic to drive the front propagation procedure of the classical Fast Marching. This results in a modification of the Fast Marching algorithm that is similar to the A algorithm used in artificial intelligence. In order to find very quickly geodesic paths between any given couples of points, we advocate for the initial computation of distance maps to a set of landmark points and make use of these distance maps through a relevant heuristic. We show that our method brings a large speed up for large scale applications that require the extraction of geodesics on images and 3D meshes. We introduce two distortion metrics in order to find an optimal seeding of landmark points for the targeted applications. We also propose a compression scheme to reduce the memory requirement without impacting the quality of the extracted paths.

This video presents an application of geodesic computation on 3D meshes to surface remeshing. The connectivity of the resulting mesh is computed using a geodesic Delaunay triangulation of the sampling points. The user can provide a speed function to conform the remeshing to various contraints such as curvature variation or texture gradient. This remeshing method is fast thanks to the use of the fast marching algorithm. It is simple to implement, robust and can serve as a basis building block for further processing of the surface such as segmentation or flattening.

In this paper we introduce a novel edge-based, implicit approach for single object segmentation in 3D images. From a couple of curves, traced by the user on the object to be segmented, we implicitly generate a surface that contains the set of minimal paths joining them. These paths are minimal with respect to a cost function that takes lower values on the object to be extracted, hence they are within a small distance from it. Unlike other variational approaches, our method is not concerned with local minima traps. Our algorithm has been successfully applied to 3D medical images and synthetic images.

Semiconductor quantum dots (QDs) are new fluorescent probes with great promise for ultrasensitive biological imaging. When detected at the single-molecule level, QD-tagged molecules can be observed and tracked in the membrane of live cells over unprecedented durations. The motion of these individual molecules, recorded in sequences of fluorescence images, can reveal aspects of the dynamics of cellular processes that remain hidden in conventional ensemble imaging. Due to QD complex optical properties, such as fluorescence intermittency, the quantitative analysis of these sequences is, however, challenging and requires advanced algorithms. We present here a novel approach, which, instead of a frame by frame analysis, is based on perceptual grouping in a spatiotemporal volume. By applying a detection process based on an image fluorescence model, we first obtain an unstructured set of points. Individual molecular trajectories are then considered as minimal paths in a Riemannian metric derived from the fluorescence image stack. These paths are computed with a variant of the fast marching method and few parameters are required. We demonstrate the ability of our algorithm to track intermittent objects both in sequences of synthetic data and in experimental measurements obtained with individual QD-tagged receptors in the membrane of live neurons. While developed for tracking QDs, this method can, however, be used with any fluorescent probes.

This paper presents a new method for extraction of buildings in aerial images. We first present a method based on rectangular buildings, which are the most common constructions. We then extend this method to more complex shapes by decomposition in a set of rectangles. These rectangles are used to enhance a 3D reconstruction of the digital elevation model (DEM). Based on stereo data, we use the DEM and the orthoimage for a first segmentation of all areas at elevation above ground. We estimate the rectangle parameters over any given blob and define a criterion for checking the similarity between shape and model. We introduce a new approach for automatic reconstruction of buildings of complex shapes using an iterative splitting of the region until it is covered by a set of rectangles. This automatic process is successfully illustrated on synthetic and real examples. In order to refine location and size of the model, we present a deformable rectangle template. The final rectangle and complex shape models are used together with elevation to obtain a 3D realistic reconstruction of the scene including building models.

We address the problem of finding a set of contour curves in a 2D or 3D image. We consider the problem of perceptual grouping and contour completion, where the data is an unstructured set of regions in the image. A new method to find complete curves from a set of edge points is presented. Contours, are found as minimal paths between connected components, using the fast marching algorithm. We find the minimal paths between each of these components, until the complete set of these "regions" is connected. The paths are obtained using backpropagation from the saddle points to both components. We then extend this technique to 3D. The data is a set of connected components in a 3D image. We find 3D minimal paths that link together these components. Using a potential based on vessel detection, we illustrate the capability of our approach to reconstruct tree structures in a 3D medical image dataset.

Segmentation of bright blobs in an image is an important problem in computer vision and particularly in biomedical imaging. In retinal angiography, segmentation of drusen, a yellowish deposit located on the retina, is a serious challenge in proper diagnosis and prevention of further complications. Drusen extraction using classic segmentation methods does not lead to good results. We present a new segmentation method based on new transformations we introduced in mathematical morphology. It is based on the search for a new class of regional maxima components of the image. These maxima correspond to the regions inside the drusen. We present experimental results for drusen extraction using images containing examples having different types and shapes of drusen. We also apply our segmentation technique to two important cases of dynamic sequences of drusen images. The first case is for tracking the average gray level of a particular drusen in a sequence of angiographic images during a fluorescein exam. The second case is for registration and matching of two angiographic images from widely spaced exams in order to characterize the evolution of drusen.

A common approach in fingerprint matching algorithms consists of minimizing a similarity measure between feature vectors of both images, over a set of linear transformations of one image to the other. In this work we propose the thin-plate spline as a more accurate model for the geometric transformations that arise in fingerprint images. In addition we show how such a model can be integrated into a matching algorithm by means of a two-step iterative minimization with auxiliary variables. Such a method allows to correct many of the false pairings of minutiae commonly found by matching algorithms based on linear transforms.

We address the problem of convergence of a motion estimation algorithm for signal matching and image registration. We introduce a new multiresolution algorithm, based on the Fourier pyramid. In the case of a global translation, we prove mean quadratic convergence of our algorithm under some reasonable assumptions. The algorithm starts at the finest resolution for which the assumption is satisfied, and then refines until the highest resolution is reached. We illustrate the method by showing results on simple 1D signals and a 3D functional MR image.

The goal of this article is the segmentation of angiographic eye fundus images in order to extract "drusen", yellowish deposits at the retina level. Since classical segmentation methods are not efficient for the automatic extraction of drusen, we introduce a new adaptive approach. We give an adaptive algorithm based on mathematical morphology transforms. For the "maxima h-/spl infin/" transform, we propose an automatic definition of the contrast parameter h. We also introduce an approach with a non-constant function, h(x). The result highlights the bright blobs over an uniform background. Our method gives very satisfying results on typical images.

A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model's energy between two points. Initialization is made easier and the curve cannot be trapped at a local minimum by spurious edges. We modify the "snake" energy by including the internal regularization term in the external potential term. Our method is based on the interpretation of the snake as a path of minimal length in a Riemannian metric, or as a path of minimal cost. We then make use of a new efficient numerical method to find the shortest path which is the global minimum of the energy among all paths joining the two end points. The method is extended to closed contours, given only one point on the objects boundary by using a topology-based saddle search routine. We show examples of our method applied to real aerial and medical images.

A new approach of edge integration for shape modeling is presented. It is used to find the global minimum of an active contour model's energy between two points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the "snake" energy by including the internal regularization term in the external potential term. Our method is based on the interpretation of the snake as a path of minimal length in a Riemannian metric, or as a path of minimal weighted distance. We then make use of a new numerical method to find the shortest path which is the global minimum of the energy among all paths joining the two endpoints. We show examples of our method applied to real aerial and medical images.

Doppler tissue imaging (DTI) is a new technique that provides image information on values of intramyocardial wall velocity. This specific capability makes easier the automatic myocardial boundary extraction and tracking task. We apply a variation on active contour models to an M-mode ultrasound image. This is in fact an image made from a time sequence of digitized 1D images. To the feature energy term derived from the grey scale conventional ultrasound image, is added a velocity term that makes the time displacement in the image close to the DTI data velocity. This permits data fusion of the two images obtained from conventional and DTI techniques. We illustrate the efficiency of the method that is now used by clinicians.

This paper studies the problem of face identification for the particular application of an automatic cash machine withdrawal: the problem is to decide if a person identifying himself by a secret code is the same person registered in the database. The identification process consists of three main stages. The localization of salient features is obtained by using morphological operators and spatio-temporal information. The location of these features are used to achieve a normalization of the face image with regard to the corresponding face in the database. Facial features, such as eyes, mouth and nose, are extracted by an active contour model which is able to incorporate information about the global shape of each object. Finally, the identification is achieved by face warping including a deformation measure.

We present a mathematical formulation for curve and surface reconstruction algorithms by introduction of auxiliary variables. For deformable models and templates, two step iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the potential data attraction and then globally smoothed. We show how these approaches can be interpreted as the introduction of auxiliary variables and the minimization of a two variables energy. This permits us to transform an implicit data constraint defined by a non convex potential into an explicit convex reconstruction problem. We show some mathematical properties and results on this new auxiliary problem, in particular when the potential is a function of the distance to the closest feature point. We then illustrate our approach for some deformable models and templates and image restoration.>

Recovery of 3D data with simple parametric models has been the subject of many studies over the last ten years. Many have used the notion of superquadrics, introduced for graphics in Barr (1994). It appears however that whilst superquadrics could describe a wide variety of forms, they are too simple to recover and describe complex shapes. This paper describes a two-step method to fit a parametric deformable surface to 3D points. We suppose that a 3D image has been segmented to get a set of 3D points. The first step consists in our version of a superquadric fit with global tapering. We then make use of the technique of free-form deformations, as in computer graphics. We present experimental results with synthetic and real 3D medical images where the original points are laid on an iso-surface.

We present in this paper some improvements to the hyperquadric model allowing an efficient representation of the shape through a numerical parameterization and an energy minimization approach for data fitting. This last feature gives an accurate location of the image edge points independently of the implicit description of the shape. The advantage of our model is that it describes global shape properties through a unique implicit equation yielding a representation of the shape by means of its parameters, independently of the chosen numerical resolution.

The use of energy-minimizing curves, known as "snakes" to extract features of interest in images has been introduced by Kass, Witkin and Terzopoulos (1987). A balloon model was introduced by Cohen (1991) as a way to generalize and solve some of the problems encountered with the original method. A 3-D generalization of the balloon model as a 3-D deformable surface, which evolves in 3-D images, is presented. It is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential. We also show properties of energy-minimizing surfaces concerning their relationship with 3-D edge points. To solve the minimization problem for a surface, two simplified approaches are shown first, defining a 3-D surface as a series of 2-D planar curves. Then, after comparing finite-element method and finite-difference method in the 2-D problem, we solve the 3-D model using the finite-element method yielding greater stability and faster convergence. This model is applied for segmenting magnetic resonance images.>

A 3-D generalization of the balloon model as a 3-D deformable surface, which evolves in 3-D images, is presented. It is deformed under the action of internal and external forces attracting the surface toward detected edge elements by means of an attraction potential. To solve the minimization problem for a surface, two simplified approaches are shown, defining a 3-D surface as a series of 2-D planar curves. Then the 3-D model is solved using the finite-element method, yielding greater stability and faster convergence. This model has been used to segment magnetic resonance images.>

A 3D deformable model is introduced which evolves in true 3D images, under the action of internal forces (describing some elasticity properties of the surface), and external forces attracting the surface toward some detected edges. The formalism leads to the minimization of an energy which is expressed as a functional. The authors use a variational approach and a finite-element method to express the surface in a discrete basis of continuous functions. This leads to a reduced computational complexity and a better numerical stability. The power of the approach to segment 3D images is demonstrated by a set of experimental results on various complex medical 3D images.>

The authors present a model of deformation which solves some of the problems encountered with the original method such as instability and initial data while reducing the computational complexity. This model makes the curve, behave like a balloon which is inflated by an additional force. The initial curve need no longer be close to the solution to converge. The external forces that push the curve to the edges are modified to give more stable results. The system is solved using a conform finite element method in the minimization process. The evolution to the equilibrium presents less oscillations, convergence is obtained faster, and the final results are more accurate. This model is applied for segmenting ultrasound and magnetic resonance images. The authors have also made a first stage to 3-D object reconstruction. by tracking the extracted contour on a series of successive cross sections.>

A method of image data compression based on vector quantization (VQ) is described. Instead of quantizing blocks of the image by the vectors, the vectors are first rescaled to be the closest to the block. The most representative patterns of the image are sought, with two blocks having the same pattern if they are similar after a scaling. A method of VQ is introduced using a smaller image which captures all the useful information instead of separated quanta. This can be applied to picture encoding and texture detection.>