44690610
Spatio-temporal Prior Shape Constraint for Level Set Segmentation
This paper exposes a novel formulation of prior shape constraint incorporation for the level set segmentation of objects from corrupted images. Applicable to variational frameworks, the proposed scheme consists in weighting the prior shape constraint by a function of time and space to overcome local minima issues of the energy functional. Pose parameters which make the prior shape constraint invariant from global transformations are estimated by the downhill simplex algorithm, which is more tractable and robust than the traditional gradient descent. The proposed scheme is simple, easy to implement and can be generalized to any variational approach incorporating a single prior shape. Results illustrated with different kinds of images demonstrate the efficiency of the method.
9209299
Boundary Finding with Parametrically Deformable Models
Segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model-based global shape information. The authors apply flexible constraints, in the form of a probabilistic deformable model, to the problem of segmenting natural 2-D objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form. The parametric model is based on the elliptic Fourier decomposition of the boundary. Probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations. Boundary finding is formulated as an optimization problem using a maximum a posteriori objective function. Results of the method applied to real and synthetic images are presented, including an evaluation of the dependence of the method on prior information and image quality. >
125385001
Statistical shape influence in geodesic active contours
A novel method of incorporating shape information into the image segmentation process is presented. We introduce a representation for deformable shapes and define a probability distribution over the variances of a set of training shapes. The segmentation process embeds an initial curve as the zero level set of a higher dimensional surface, and evolves the surface such that the zero level set converges on the boundary of the object to be segmented. At each step of the surface evolution, we estimate the maximum a posteriori (MAP) position and shape of the object in the image, based on the prior shape information and the image information. We then evolve the surface globally, towards the MAP estimate, and locally, based on image gradients and curvature. Results are demonstrated on synthetic data and medical imagery, in 2D and 3D.
7911344
Using Prior Shapes in Geometric Active Contours in a Variational Framework
In this paper, we report an active contour algorithm that is capable of using prior shapes. The energy functional of the contour is modified so that the energy depends on the image gradient as well as the prior shape. The model provides the segmentation and the transformation that maps the segmented contour to the prior shape. The active contour is able to find boundaries that are similar in shape to the prior, even when the entire boundary is not visible in the image (i.e., when the boundary has gaps). A level set formulation of the active contour is presented. The existence of the solution to the energy minimization is also established.We also report experimental results of the use of this contour on 2d synthetic images, ultrasound images and fMRI images. Classical active contours cannot be used in many of these images.
6972902
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes. We propose a closed-form, parameter-free solution for incorporating invariance with respect to similarity transformations in the variational framework. We show segmentation results on artificial and real-world images with and without prior shape information. In the cases of noise, occlusion or strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by a level set implementation of geodesic active contours.
897936
Shape Priors for Level Set Representations
Level Set Representations, the pioneering framework introduced by Osher and Sethian [14] is the most common choice for the implementation of variational frameworks in Computer Vision since it is implicit, intrinsic, parameter and topology free. However, many Computer vision applications refer to entities with physical meanings that follow a shape form with a certain degree of variability. In this paper, we propose a novel energetic form to introduce shape constraints to level set representations. This formulation exploits all advantages of these representations resulting on a very elegant approach that can deal with a large number of parametric as well as continuous transformations. Furthermore, it can be combined with existing well known level set-based segmentation approaches leading to paradigms that can deal with noisy, occluded and missing or physically corrupted data. Encouraging experimental results are obtained using synthetic and real images.
6428775
Level set based shape prior segmentation
We propose a level set based variational approach that incorporates shape priors into Chan-Vese's model for the shape prior segmentation problem. In our model, besides the level set function for segmentation, as in Cremers' work, we introduce another labelling level set function to indicate the regions on which the prior shape should be compared. Our model can segment an object, whose shape is similar to the given prior shape, from a background where there are several objects. Moreover, we provide a proof for a fast solution principle, which was mentioned by F. Gibou et al., and similar to the one proposed in [B. Song et al., (2002)], for minimizing Chan-Vese's segmentation model without length term. We extend the principle to the minimization of our prescribed functionals.
10695770
Towards Recognition-Based Variational Segmentation Using Shape Priors and Dynamic Labeling
We propose a novel variational approach based on a level set formulation of the Mumford-Shah functional and shape priors. We extend the functional by a labeling function which indicates image regions in which the shape prior is enforced. By minimizing the proposed functional with respect to both the level set function and the labeling function, the algorithm selects image regions where it is favorable to enforce the shape prior. By this, the approach permits to segment multiple independent objects in an image, and to discriminate familiar objects from unfamiliar ones by means of the labeling function. Numerical results demonstrate the performance of our approach.
10276646
A Pseudo-distance for Shape Priors in Level Set Segmentation
We study the question of integrating prior shape knowledge into level set based segmentation methods. In particular, we investigate dissimilarity measures for shapes encoded by the signed distance function. We consider extensions and improvements of existing measures. As a result, we propose a novel dissimilarity measure which constitutes a pseudo-distance. Compared to alternative approaches, this measure is symmetric and not biased toward small area. Based on this pseudo-distance, we propose a shape prior for level set segmentation methods which is pose invariant. In numerical experiments, we demonstrate that the resulting prior permits the segmentation of corrupted versions of a familiar object which is independent of the pose of the object. Moreover, we demonstrate the advantage of the symmetric formulation of the dissimilarity measure when segmenting corrupted images of known objects which consist of multiple components.
1369652
Kernel Density Estimation and Intrinsic Alignment for Knowledge-Driven Segmentation: Teaching Level Sets to Walk
We address the problem of image segmentation with statistical shape priors in the context of the level set framework. Our paper makes two contributions: Firstly, we propose a novel multi-modal statistical shape prior which allows to encode multiple fairly distinct training shapes. This prior is based on an extension of classical kernel density estimators to the level set domain. Secondly, we propose an intrinsic registration of the evolving level set function which induces an invariance of the proposed shape energy with respect to translation. We demonstrate the advantages of this multi-modal shape prior applied to the segmentation and tracking of a partially occluded walking person.
35034127
Model-based curve evolution technique for image segmentation
We propose a model-based curve evolution technique for segmentation of images containing known object types. In particular, motivated by the work of Leventon et al. (2000), we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data, The parameters of this representation are then calculated to minimize an objective function for segmentation. We found the resulting algorithm to be computationally efficient, able to handle multidimensional data, robust to noise and initial contour placements, while at the same time, avoiding the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications.
205007680
Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. Final report
New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.
15315786
DIGITAL BUILDING MAP REFINEMENT FROM KNOWLEDGE-DRIVEN ACTIVE CONTOURS AND VERY HIGH RESOLUTION OPTICAL IMAGERY
We propose a novel approach for digital building map refinement based on the use of knowledge-driven active contours and very high resolution panchromatic optical imagery. This methodology is designed to finely match each building symbolized in an urban Geographical Information System (GIS) database onto its counterpart representation in remote sensing data. This method is GIS mapdriven: GIS data globally registered to the image allows to initialize an active contour near the target building in the image to achieve subsequent refinement. Moreover the digital map provides valuable shape information about the object in the image we aim at matching. This geometric and specific prior knowledge is embedded as a shape constraint into the active contour and enables to overcome urban artifacts issues. Besides, we propose to embed a coarse Digital Surface Model (DSM) as well as a spatio-temporal shape prior constraint within the active contour model. Experimental results carried out over Beijing city area and illustrated in this paper show how these latter contributions improve the robustness and speed of the map refinement process. Map refinement addressed in this paper is becoming an essential issue for urban planning, telecommunications, automobile navigation, crisis and pollution management, which all rely on up-to-date and precise digital maps of a city.
122055904
On the incorporation of shape priors into geometric active contours
A novel model for boundary determination that incorporates prior shape information into geometric active contours is presented. The basic idea of this model is to minimize the energy functional depending on the information of the image gradient and the shape of interest, so that the boundary of the object can be captured either by higher magnitude of the image gradient or by the prior knowledge of its shape. The level set form of the proposed model is also provided. We present our experimental results on some synthetic images, functional MR brain images, and ultrasound images for which the existing active contour methods are not applicable. The existence of the solution to the proposed minimization problem is also discussed.
2208295
A Simplex Method for Function Minimization
A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.
206631161
Matching Distance Functions: A Shape-to-Area Variational Approach for Global-to-Local Registration
This paper deals with the matching of geometric shapes. Our primary contribution is the use of a simple, robust, rich and efficient way to represent shapes, the level set representations according to singed distance transforms. Based on these representations we propose a variational framework for global as well as local shape registration that can be extended to deal with structures of higher dimension. The optimization criterion is invariant to rotation, translation and scale and combines efficiently a global motion model with local pixel-wise deformations. Promising results are obtained on examples showing small and large global deformations as well as arbitrary topological changes.