Due to their heavy reliance on server infrastructure, the current computation-intensive SaaS suffer from scalability issues compared to the existing data-intensive commercial SaaS. Offloading certain computations to the client browser can resolve these scalability issues but the current Browser APIs are complex to use and integrate in a single software. We propose in this paper four high level APIs that harness existing browser-based paradigms and proven software architectures to reduce the complexity of parallel computing and device-agnostic interactive rendering in the web browser. To allow experimental results, we have developed a proof-of-concept browser-based and interactive diffusion MRI where we have particularly deployed a parallel Diffusion Tensor Estimation. Our platform provides us easy APIs achieving up to 4 times speedup in parallel computation and real-time interactive rendering performances across different Browsers and Devices in comparison to other existing solutions in the Diffusion MRI Community.

In this work, we present a novel computational framework for analytically generating a complete set of algebraically independent Rotation Invariant Features (RIF) given the Laplace-series expansion of a spherical function. Our computational framework provides a closed-form solution for these new invariants, which are the natural expansion of the well known spherical mean, power-spectrum and bispectrum invariants. We highlight the maximal number of algebraically independent invariants which can be obtained from a truncated Spherical Harmonic (SH) representation of a spherical function and show that most of these new invariants can be linked to statistical and geometrical measures of spherical functions, such as the mean, the variance and the volume of the spherical signal. Moreover, we demonstrate their application to dMRI signal modeling including the Apparent Diffusion Coefficient (ADC), the diffusion signal and the fiber Orientation Distribution Function (fODF). In addition, using both synthetic and real data, we test the ability of our invariants to estimate brain tissue microstructure in healthy subjects and show that our framework provides more flexibility and open up new opportunities for innovative development in the domain of microstructure recovery from diffusion MRI.

In this letter, we propose a supervised method for the classification of fully polarimetric synthetic aperture radar (PolSAR) images based on active contour models. We use an “a priori” estimation, obtained from training data, of the complex Wishart distributions of the different types of regions in the image (for instance, water, crops, grass, forest or urban). The information of the Wishart distributions is included in the active contour models to guide the level set evolution. We study the case of two classes and the case of three or more classes separately. We present some experimental results on the synthetic data and real PolSAR images to show the performance of the proposed model. The results are compared with other well-known supervised classification methods, and, for actual PolSAR data, our method shows an overall precision of 94.31% and a $\kappa $ coefficient of 0.937.

The Fast Marching method is widely employed in several fields of image processing. Some years ago a Multi-Stencil version (MSFM) was introduced to improve its accuracy by solving the equation for a set of stencils and choosing the best solution at each considered node. The following work proposes a modified numerical scheme for MSFM to take into account the variation of the local cost, which has proven to be second order. The influence of the stencil set choice on the algorithm outcome with respect to stencil orthogonality and axis swapping is also explored, where stencils are taken from neighborhoods of varying radius. The experimental results show that the proposed schemes improve the accuracy of their original counterparts, and that the use of permutation-invariant stencil sets provides robustness against shifted vector coordinates in the stencil set.

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

We introduce an original approach for the cerebral white matter connectivity mapping from diffusion tensor imaging (DTI). Our method relies on a global modeling of the acquired magnetic resonance imaging volume as a Riemannian manifold whose metric directly derives from the diffusion tensor. These tensors will be used to measure physical three-dimensional distances between different locations of a brain diffusion tensor image. The key concept is the notion of geodesic distance that will allow us to find optimal paths in the white matter. We claim that such optimal paths are reasonable approximations of neural fiber bundles. The geodesic distance function can be seen as the solution of two theoretically equivalent but, in practice, significantly different problems in the partial differential equation framework: an initial value problem which is intrinsically dynamic, and a boundary value problem which is, on the contrary, intrinsically stationary. The two approaches have very different properties which make them more or less adequate for our problem and more or less computationally efficient. The dynamic formulation is quite easy to implement but has several practical drawbacks. On the contrary, the stationary formulation is much more tedious to implement; we will show, however, that it has many virtues which make it more suitable for our connectivity mapping problem. Finally, we will present different possible measures of connectivity, reflecting the degree of connectivity between different regions of the brain. We will illustrate these notions on synthetic and real DTI datasets.

We propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function (ODF) estimated from high angular resolution diffusion imaging (HARDI). We show that in order to perform accurate probabilistic tractography, one needs to use a fibre ODF estimation and not the diffusion ODF. We use a new fibre ODF estimation obtained from a sharpening deconvolution transform (SDT) of the diffusion ODF reconstructed from q-ball imaging (QBI). This SDT provides new insight into the relationship between the HARDI signal, the diffusion ODF, and the fibre ODF. We demonstrate that the SDT agrees with classical spherical deconvolution and improves the angular resolution of QBI. Another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre ODF. An extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions. Finally, as an application of our new probabilistic tracking, we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects. Most current diffusion tensor imaging (DTI)-based methods neglect these fibres, which might lead to incorrect interpretations of brain functions.

We present a Diffusion Maps clustering method applied to diffusion MRI in order to segment complex white matter fiber bundles. It is well-known that diffusion tensor imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent High Angular Resolution Diffusion Imaging (HARDI) such has Q-Ball Imaging (QBI) have been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maximum(a) agreeing with the underlying fiber population. In this paper, we use the ODF representation in a small set of spherical harmonic coefficients as input to the Diffusion Maps clustering method. We first show the advantage of using Diffusion Maps clustering over classical methods such as N-Cuts and Laplacian Eigenmaps. In particular, our ODF Diffusion Maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in the segmentation and automatically exhibits the number of clusters segmenting the Q-Ball image by using an adaptative scale-space parameter. We also show that our ODF Diffusion Maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our method succeeds to separate fiber bundles and crossing regions whereas the DT- based methods generate artifacts and exhibit wrong number of clusters. Finally, we show results on a real brain dataset where we successfully segment the fiber bundles.

We propose a novel, fast and robust technique for the computation of anatomical connectivity in the brain. Our approach exploits the information provided by Diffusion Tensor Magnetic Resonance Imaging (or DTI) and models the white matter by using Riemannian geometry and control theory. We show that it is possible, from a region of interest, to compute the geodesic distance to any other point and the associated optimal vector field. The latter can be used to trace shortest paths coinciding with neural fiber bundles. We also demonstrate that no explicit computation of those 3D curves is necessary to assess the degree of connectivity of the region of interest with the rest of the brain. We finally introduce a general local connectivity measure whose statistics along the optimal paths may be used to evaluate the degree of connectivity of any pair of voxels. All those quantities can be computed simultaneously in a Fast Marching framework, directly yielding the connectivity maps. Apart from being extremely fast, this method has other advantages such as the strict respect of the convoluted geometry of white matter, the fact that it is parameter-free, and its robustness to noise. We illustrate our technique by showing results on real and synthetic datasets. OurGCM(Geodesic Connectivity Mapping) algorithm is implemented in C++ and will be soon available on the web.

We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images (DTI). A DTI produces, from a set of diffusion-weighted MR images, tensor-valued images where each voxel is assigned with a 3 x 3 symmetric, positive-definite matrix. This second order tensor is simply the covariance matrix of a local Gaussian process, with zero-mean, modeling the average motion of water molecules. As we will show in this paper, the definition of a dissimilarity measure and statistics between such quantities is a nontrivial task which must be tackled carefully. We claim and demonstrate that, by using the theoretically well-founded differential geometrical properties of the manifold of multivariate normal distributions, it is possible to improve the quality of the segmentation results obtained with other dissimilarity measures such as the Euclidean distance or the Kullback-Leibler divergence. The main goal of this paper is to prove that the choice of the probability metric, i.e., the dissimilarity measure, has a deep impact on the tensor statistics and, hence, on the achieved results. We introduce a variational formulation, in the level-set framework, to estimate the optimal segmentation of a DTI according to the following hypothesis: Diffusion tensors exhibit a Gaussian distribution in the different partitions. We must also respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the DTI. We show how to express all the statistical quantities for the different probability metrics. We validate and compare the results obtained on various synthetic data-sets, a biological rat spinal cord phantom and human brain DTIs.

In this paper, we focus on techniques for vector-valued image regularization, based on variational methods and PDEs. Starting from the study of PDE-based formalisms previously proposed in the literature for the regularization of scalar and vector-valued data, we propose a unifying expression that gathers the majority of these previous frameworks into a single generic anisotropic diffusion equation. On one hand, the resulting expression provides a simple interpretation of the regularization process in terms of local filtering with spatially adaptive Gaussian kernels. On the other hand, it naturally disassembles any regularization scheme into the smoothing process itself and the underlying geometry that drives the smoothing. Thus, we can easily specialize our generic expression into different regularization PDEs that fulfill desired smoothing behaviors, depending on the considered application: image restoration, inpainting, magnification, flow visualization, etc. Specific numerical schemes are also proposed, allowing us to implement our regularization framework with accuracy by taking the local filtering properties of the proposed equations into account. Finally, we illustrate the wide range of applications handled by our selected anisotropic diffusion equations with application results on color images.

We propose a novel and efficient approach for active unsupervised texture segmentation. First, we show how we can extract a small set of good features for texture segmentation based on the structure tensor and nonlinear diffusion. Then, we propose a variational framework that incorporates these features in a level set based unsupervised segmentation process that adaptively takes into account their estimated statistical information inside and outside the region to segment. The approach has been tested on various textured images, and its performance is favorably compared to recent studies.

We address the problem of vector-valued image regularization with variational methods and PDEs. From the study of existing formalisms, we propose a unifying framework based on a very local interpretation of the regularization processes. The resulting equations are then specialized into new regularization PDEs and corresponding numerical schemes that respect the local geometry of vector-valued images. They are finally applied on a wide variety of image processing problems, including color image restoration, in-painting, magnification and flow visualization.

We consider the reconstruction of MRI images by minimizing regularized cost-functions. To accelerate the computation of the estimate, two forms of half-quadratic regularization, multiplicative and additive, are often used. In Nikolova and Ng (2002), we have compared both theoretically and experimentally the efficiency of these two forms using one-dimensional signals. The goal of this paper is to compare experimentally the efficiency of these two forms using MRI image reconstruction. We find that using the additive form is more computationally effective than using the multiplicative form.

In many medical computer vision tasks the relevant data is attached to a specific tissue such as the colon or the cortex. This situation calls for regularization techniques which are defined over surfaces. We introduce in this paper the Beltrami flow over implicit manifolds. This new regularization technique overcomes the over-smoothing of the L/sub 2/ flow and the staircasing effects of the L/sub 1/ flow, that were recently suggested via the harmonic map methods. The key of our approach is first to clarify the link between the intrinsic Polyakov action and the implicit harmonic energy functional and then use the geometrical understanding of the Beltrami flow to generalize it to images on implicitly defined non flat surfaces. It is shown that once again the Beltrami flow interpolates between the L/sub 2/ and L/sub 1/ flows on non flat surfaces. The implementation scheme of this flow is presented and various experimental results obtained on a set of various real images illustrate the performances of the approach as well as the differences with the harmonic map flows. This extension of the Beltrami flow to the case of non flat surfaces opens new perspectives in the regularization of noisy data defined on manifolds.

We address three crucial issues encountered in DT-MRI (diffusion tensor magnetic resonance imaging): diffusion tensor estimation, regularization and fiber bundle visualization. We first review related algorithms existing in the literature and propose then alternative variational formalisms that lead to new and improved schemes, thanks to the preservation of important tensor constraints (positivity, symmetry). We illustrate how our complete DT-MRI processing pipeline can be successfully used to construct and draw fiber bundles in the white matter of the brain, from a set of noisy raw MRl images.

In this paper, we study, in this paper, the problem of denoising images/data which are defined are nonflat surfaces. This problem arises often in many medical imaging tasks. The Beltrami flow which was defined in an explicit-intrinsic manner is generalized here to nonflat surfaces and is defined in an implicit way. We formulate the flow in a variational way which is generalized to a scalar field defined over an n-dimensional manifold. The implementation scheme of this flow is presented and various experimental results obtained on a set of real images illustrate the performances of the approach as well as the differences between various flows of interests.

In this paper, we present a general framework for multiscale segmentation of range images in planar facets. We propose a formulation of the problem as the minimization of a multiscale separable energy, which involves two terms: a goodness-of-fit term and a regularization term, the scale parameter being the relative weight between the two terms. We then recall a general parameter-free method to build a hierarchy of regions in which segmentation is expressed as a cut. Afterwards, we explicit the energy derived for a simple-shaped planar facet model and based on a formulation that confronts the complexity of the model and the goodness of fit of the data. We then extend this model to integrate gradients information from images, which leads us to a formulation of a simple-shaped planar and homogeneous facet model. Some results on digital elevation models (DEM) obtained from aerial images with and without image constraints are provided.

The paper deals with the problem of regularizing noisy fields of diffusion tensors, considered as symmetric and semi-positive definite n /spl times/ n matrices (such as for instance 2D structure tensors or DT-MRI medical images). We first propose a simple anisotropic, PDE-based scheme that acts directly on the matrix coefficients and preserves the semi-positive constraint thanks to a specific reprojection step. The limitations of this algorithm lead us to introduce a more effective approach based on constrained spectral regularizations acting on the tensor orientations (eigenvectors) and diffusivities (eigenvalues), while explicitly taking the tensor constraints into account. The regularization of the orientation part uses orthogonal matrix diffusion PDE's and local vector alignment procedures. For the interesting 3D case, a special implementation scheme designed to numerically fit the tensor constraints is also proposed. Experimental results on synthetic and real DT-MRI data sets finally illustrates the proposed tensor regularization framework.

Recursive filtering structures reduce drastically the computational effort required for different tasks in image processing. These operations are done with a fixed number of operations per output point independently of the size of the neighbourhood considered. In this paper we show that implicit numerical implementations of some partial differential equations (PDEs) provide algorithms that can be interpreted in terms of recursive filters. We show, in particular, that the classical second order recursive filter introduced by Deriche (1987, 1990) is in fact a particular implementation of the heat equation. Using the well-known Neumann boundary condition for the heat equation, we propose some new implementation of the filter. We extend this linear filter to a nonlinear recursive smoothing filter, following the general idea of anisotropic diffusion. We present some comparison results with the classical Perona-Malik model.

This paper presents a new variational framework for detecting and tracking multiple moving objects in image sequences. Motion detection is performed using a statistical framework for which the observed interframe difference density function is approximated using a mixture model. This model is composed of two components, namely, the static (background) and the mobile (moving objects) one. Both components are zero-mean and obey Laplacian or Gaussian law. This statistical framework is used to provide the motion detection boundaries. Additionally, the original frame is used to provide the moving object boundaries. Then, the detection and the tracking problem are addressed in a common framework that employs a geodesic active contour objective function. This function is minimized using a gradient descent method. A new approach named Hermes is proposed, which exploits aspects from the well-known front propagation algorithms and compares favorably to them. Very promising experimental results are provided using real video sequences.

This paper addresses the problem of tracking several non-rigid objects over a sequence of frames acquired from a static observer using boundary and region-based information under a coupled geodesic active contour framework. Given the current frame, a statistical analysis is performed on the observed difference frame which provides a measurement that distinguishes between the static and mobile regions in terms of conditional probabilities. An objective function is defined that integrates boundary-based and region-based module by seeking curves that attract the object boundaries and maximize the a posteriori segmentation probability on the interior curve regions with respect to intensity and motion properties. This function is minimized using a gradient descent method. The associated Euler-Lagrange PDE is implemented using a Level-Set approach, where a very fast front propagation algorithm evolves the initial curve towards the final tracking result. Very promising experimental results are provided using real video sequences.

This paper presents a variational method for supervised texture segmentation which is based on ideas coming from the curve propagation theory. We assume that a preferable texture pattern is known (e.g., the pattern that we want to distinguish from the rest of the image). The textured feature space is generated by filtering the input and the preferable pattern image using Gabor filters, and analyzing their responses as multi-component conditional probability density functions. The texture segmentation is obtained by minimizing a Geodesic Active Contour Model objective function where the boundary-based information is expressed via discontinuities on the statistical space associated with the multi-modal textured feature space. This function is minimized using a gradient descent method where the obtained PDE is implemented using a level set approach, that handles naturally the topological changes. Finally a fast method is used for the level set implementation. The performance of our method is demonstrated on a variety of synthetic and real textured images.

The paper presents a novel variational method for supervised texture segmentation. The textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters, and analyzing their responses as multi-component conditional probability density functions. The texture segmentation is obtained by unifying region and boundary based information as an improved Geodesic Active Contour Model. The defined objective function is minimized using a gradient-descent method where a level set approach is used to implement the obtained PDE. According to this PDE, the curve propagation towards the final solution is guided by boundary and region based segmentation forces, and is constrained by a regularity force. The level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled. The performance of our method is demonstrated on a variety of synthetic and real textured frames.

This paper presents a framework for detecting and tracking moving objects in a sequence of images. Using a statistical approach, where the inter-frame difference is modeled by a mixture of two Laplacian or Gaussian distributions, and an energy minimization based approach, we reformulate the motion detection and tracking problem as a front propagation problem. The Euler-Lagrange equation of the designed energy functional is first derived and the flow minimizing the energy is then obtained. Following the work by Caselles et al. (1995) and Malladi et al. (1995), the contours to be detected and tracked are modeled as geodesic active contours evolving toward the minimum of the designed energy, under the influence of internal and external image dependent forces. Using the level set formulation scheme of Osher and Sethian (1988), complex curves can be detected and tracked and topological changes for the evolving curves are naturally managed. To reduce the computational cost required by a direct implementation, of the formulation scheme of Osher and Sethian (1988), a new approach exploiting aspects from the classical narrow band and fast marching methods is proposed and favorably compared to them. In order to further reduce the CPU time, a multi-scale approach has also been considered. Very promising experimental results are provided using real video sequences.

We present a new method for matching points in stereoscopic, uncalibrated color images. Our approach consists of characterizing points of interest using differential invariants. We define additional invariants of first order, exploiting color information. We show that this contribution makes the characterization sufficient for first order. In addition, we make our description robust to usual transformations of image. We present a robust generalization of a gray level corner detector to the case of color images. We also propose a simple and efficient scheme for matching these points, using our characterization. Finally, we present matching results and the epipolar geometry obtained on complex scenes, which clearly show the pertinence of our approach. We are able to match points robustly and rapidly, using only first order derivatives.

We present a variational approach such that during image restoration, edges detected in the original image are being preserved. We compare the mathematical foundation of this method with respect to some of the well known methods recently proposed in the literature within the class of PDE based algorithms (anisotropic diffusion, mean curvature motion, min/max flow technique). The performance of our approach is carefully examined and compared to the classical methods. Experimental results on synthetic and real images illustrate the capabilities of all the studied approaches.

The main problem for building a mosaic is the computation of the warping functions (homographies). In fact two cases are to be distinguished. The first is when the homography is mainly a translation (i.e. The rotation around the optical axis and the zooming factor are small). The second is the general case (when the rotation around the optical axis and zooming are arbitrary). Some efficient methods have been developed to solve the first case. But the second case is more difficult, in particular, when the rotation around the optical axis is very large (90 degrees or more). Often in this case human interaction is needed to provide a first approximation of the transformation that will bring one back to the first case. The authors present a method to solve this problem without human interaction for any rotation around the optical axis and fairly large zooming factors.

We present a new approach based on partial differential equations (PDE) to restore noisy blurred images. After studying the methods to denoise images, staying as close as possible to the input image and methods to restore discontinuities, we propose a new scheme which combines all this schemes. A quantified numerical test on a synthetic image demonstrates the efficiency of our scheme and the role of varying the parameters for denoising, enhancement and coupling. A result on a real image is also presented.

This paper presents a framework for detecting multiple moving moving objects in a sequence of images. Using a statistical approach, where the inter-frame difference is modeled by a mixture of two Laplacian distributions and a deformable contour-based energy minimization approach, we reformulate the motion detection problem as a front propagation problem. Following the work of geodesic active contours, we transform the moving objects detection problem into an equivalent problem of geodesic computation, which is solved using a level set formulation scheme. To reduce the computational cost required by a direct implementation of the formulation scheme the narrow band technique is used. In order to further reduce the CPU time, a multi-scale approach has also been considered. Very promising experimental results are provided using real video sequences.

A terrain-based underwater navigation using sonar bathymetric profiles is presented. It deals with matching high resolution local depth maps against a large, on-board, low resolution reference map. The matching algorithm locates the local depth map within the a priori larger map to determine absolute position and heading of the vehicle. It uses cliff maps which are steep gradient contours extracted from both local and reference maps. This segmentation provides us with a means to extract critical points, which are defined as high curvature values. The problem is reduced to a singular point-based matching algorithm: given two point sets, find correspondences and estimate transformation between the two sets. In order to register maps at different scales, a part of this study concentrates on partial differential equations based scale-space techniques. This approach is tested using real terrain data of the Var underwater canyon (France).

The paper describes an approach to the tracking of complex shapes through image sequences, that combines deformable region models and deformable contours. A deformable region model is presented: its optimisation is based on texture correlation and is constrained by the use of a motion model, such as rigid, affine or homographic. The use of texture information (versus edge information) noticeably improves the tracking performances of deformable models in the presence of texture. Then the region contour is refined using an edge based deformable model in order to better deal with specularities, non planar objects and occlusions. The method is illustrated and validated by experimental results on real images.>

Recently, we have shown that the differential properties of the surfaces represented by 3D volumic images can be recovered using their partial derivatives. For instance, the crest lines can be characterized by the first, second and third partial derivatives of the grey level function I(x, y, z). In this paper, we show that: the computation of the partial derivatives of an image can be improved using recursive filters which approximate the Gaussian filter; a multi-scale approach solves many of the instability problems arising from the computation of the partial derivatives; and we illustrate the previous point for the crest line extraction (a crest point is a zero-crossing of the derivative of the maximum curvature along the maximum curvature direction). We present experimental results of crest point extraction on real 3-D medical data.>

This paper describes a new approach to track complex primitives along image sequences - integrating snake-based contour tracking and region-based motion analysis. First, a snake tracks the region outline and performs segmentation. Then the motion of the extracted region is estimated by a dense analysis of the apparent motion over the region, using spatio-temporal image gradients. Finally, this motion measurement is filtered to predict the region location in the next frame, and thus to guide (i.e. to initialize) the tracking snake in the next frame. Therefore, these two approaches collaborate and exchange information to overcome the limitations of each of them. The method is illustrated by experimental results on real images.

Presents a multi-scale approach to extract crest lines in volume 3D image. The key point of the authors' approach is to characterize crest points using the first, second and third order partial derivatives of the grey level image function I(x, y, z). These partial derivatives are computed using a recursive filter approximating the Gaussian and its derivatives. Then the width of the filters defines the scale. The authors present experimental results obtained on real data.

The development of an efficient model-based approach to detect and characterize precisely important features such as edges, corners and vertices is discussed. The key is to propose some efficient models associated to each of these features directly from the image by searching the parameters of the model that best approximate the observed grey level image intensities. Due to the large amount of time required by a first approach that assumes the blur of the imaging acquisition system to be describable by a 2-D Gaussian filter, different solutions that drastically reduce this computational time are considered and developed. The problem of the initialization phase in the minimization process is considered, and an original and efficient solution is proposed. A large number of experiments involving real images are conducted in order to test and compare the reliability, the robustness, and the efficiency of the proposed approaches.>

The authors propose to replace a set of connected 3-D points or line segments with a 3-D formable curve, using weighted least-squares approximation. The parameters of the 3-D energy-minimizing curve are updated so that its 2-D projections on two or three stereoscopic images converge toward the corresponding image edges. Thus, a more realistic representation of the real non-polygonal world is obtained. The case where no initial 3-D information is provided is also considered. A novel approach is proposed to match a given 2-D curve in the first image to its corresponding position in the second image. The curve is tracked between the two images by a deformable curve constrained by a 2-D motion model. The position of the 2-D curve in the second image is then refined by relaxing the motion constraint. As a result, the correspondences between the curves of both images are known. An initial estimate of the 3-D curve can be recovered using the calibration parameters of the stereoscopic system. These approaches are illustrated by experimental results.>

Deals with the development and implementation of several deformable models (snakes) designed to extract some particular and important features in an image. First, the authors propose polygonal-like snakes which detect corners and triple junctions in an image. In the second part, they describe parametric snakes designed in order to extract curves of degree greater than one: segments, ellipses, superellipses and rational B-spline curves.>

In this article, we describe some of the algorithms for depth and motion analysis which have been developed within ESPRIT project 940. Specifically we discuss edge detection, token tracking in sequences of images, and trinocular stereo. These processes have been implemented in hardware to form the core of the Depth and Motion Analysis (DMA) machine which has been developed to provide sophisticated real time vision capabilities for a large variety of robotics tasks.

A formal representation of corner and vertex detection is presented. In particular, an analytical study is presented which allows one to know exactly what the behavior is of a detector around trihedral vertices. It is shown that near three surfaces, two elliptic maxima of DET exist, and their location is inside extremal contrast surface. The intermediate surface always shows a hyperbolic minima. It is shown that the detector allows to find the exact position of vertex. The approach proposed has been tested on many noisy synthetic data and real images and its robustness seems promising.>

Consideration is given to a corner model, and its behavior in the scale-space is studied. The authors derive results that clarify the behavior of some well known approaches used to detect corners. In particular, they show that some of the approaches are inadequate for an exact localization of the corner. A novel approach is then proposed in order to correct the displacement effect and detect exactly the corner position. Some promising experimental results obtained on real data are shown.>

An investigation is conducted of the relationships that exist between the three-dimensional structure and kinematics, of a line moving rigidly in space and the two-dimensional structure and kinematics (optical flow) of its image in one or two cameras. The authors establish the fundamental equations that relate its three-dimensional motion to its observed image motion. They then assume that stereo matches have been established between image segments and show how the estimation of the optical flows in the two images can be used to compute part of the kinematic screw of the corresponding 3-D line. The equations are linear and provide a very simple way to estimate the full kinematic screw, if several lines of the same object are available. Experimental results using synthetic and real data are presented.>

The authors present an efficient approach for reliably matching a set of points extracted from the environment of a mobile robot by means of passive stereo vision using two or three cameras. First, feature points corresponding to points with high curvature are extracted from each image using an efficient approach. The epipolar geometry and some powerful configuration constraints are then combined to match these points. A correspondence between curves is then established using the figural continuity. Results obtained on real images are given.>

Edge detection in 3D images such as scanner, magnetic resonance, or spatiotemporal data is considered. A two-stage scheme based on separable recursive filtering and edge tracking/closing is proposed. The key point of the filtering stage is to use optimal recursive and separable filters to approximate gradient or Laplacian methods. The recursive nature of the operators enables one to implement infinite 3D impulse response with a computing time roughly similar to a 3*3*3 convolution mask. The principle of the edge tracking/closing is to select from the previous stage only the more reliable edge points and then to apply an edge closing method derived from the idea developed by R. Deriche and J.P. Cocquerez (1988). This makes it possible to substantially improve the results provided by the filtering stage.>

A recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing, performing the first and second directional derivatives, and carrying out the Laplacian of an image. These operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered. The key to the approach is, first, the use of an exponentially based filter family and, second, the use of the recursive filtering. Applications to edge detection problems and multiresolution techniques are considered, and an edge detector allowing the extraction of zero-crossings of an image with only 14 operations per output element at any resolution is proposed. Various experimental results are shown.>

A novel algorithm for three-dimensional edge detection is proposed. This method is an extension to the 3D case of the optimal 2D edge detector recently introduced by R. Deriche (1987). The authors present better theoretical and experimental performances than some classical approaches used previously. Experimental results obtained on magnetic-resonance images and on echographic images are shown. It is pointed out that this approach can be used to detect edges in other multidimensional data, for instance, 2D+t or 3D+t images.>

A computationally efficient recursive filtering structure is presented for smoothing and, calculating the first and second directional derivatives and the Laplacian of an image with a fixed number of operations per output element, independently of the size of the neighborhood considered. It is shown how the recursive approach results on an implementation of low-level vision algorithms that is very efficient in terms of computational effort and how it renders the use of multiresolution techniques very attractive. Applications to edge detection problem are considered, and a novel edge detector allowing zero-crossings of an image, to be extracted with only 14 operations per output element at any resolution is provided. The algorithms have been tested for indoor scenes and noisy images and gave very good results for all of them.>

The elaboration of an early image description based on an adjacency graph of reliable regions is discussed. An optimal edge detector is used first to extract the contours of the analyzed scene. A topological-configuration-based look-up table is then used to determine the extremity points, and a closing-contours process is applied using gradient magnitude information. An efficient connected components labeling algorithm is used to segment the image into reliable regions. A region-based adjacency graph, where radiometric parameters and reliable polygonal approximation of region boundaries are associated with each node, is then created and used as an early image description of the analyzed image.>

A new procedure for 2-D Separable Denominator Recursive (SDR) Filter aesign is introduce. It is based upon the minimization of mean-square error criteria between impulse responses. The algorithm is two fold. First the finite impulse response of the prototype is approximated by a finite sum of separable filters using the Singular Value Decomposition Theorem as described in TREITEL & SHANKS (1) - Second the finite sum is approximated by an SDR filter. In this part we develop a new approach based upon a single input-multi output 1-D filter approximation. In the last part of the paper, we present experimental results that compare our new algorithm to related previous ones.