We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

/pdf/active-contours-without-edges-2tt3qz9lq0.pdf

Active contours without edges

http://midag.cs.unc.edu/pubs/papers/Neuroimage06_Yushkevich.pdf

User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability

A novel scheme for the detection of object boundaries is presented. The technique is based on active contours deforming according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric as defined by the image content. This geodesic approach for object segmentation allows to connect classical "snakes" based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved as showed by a number of examples. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. >

/pdf/geodesic-active-contours-4wqlqxa13k.pdf

Geodesic active contours

A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object segmentation allows to connect classical “snakes” based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved, allowing stable boundary detection when their gradients suffer from large variations, including gaps. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. The scheme was implemented using an efficient algorithm for curve evolution. Experimental results of applying the scheme to real images including objects with holes and medical data imagery demonstrate its power. The results may be extended to 3D object segmentation as well.

Geodesic Active Contours

The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics In spite of the sophistication of the recently proposed methods, m

/pdf/a-review-of-image-denoising-algorithms-with-a-new-one-4vfxkcsntt.pdf

A Review of Image Denoising Algorithms, with a New One

We propose a new model for active contours based on a geometric partial differential equation. Our model is intrinsec, stable (satisfies the maximum principle) and permits a rigorous mathematical analysis. It enables us to extract smooth shapes (we cannot retrieve angles) and it can be adapted to find several contours simultaneously. Moreover, as a consequence of the stability, we can design robust algorithms which can be engineed with no parameters in applications. Numerical experiments are presented.

A geometric model for active contours in image processing

In this paper, we propose a novel example-based method for denoising and super-resolution of medical images. The objective is to estimate a high-resolution image from a single noisy low-resolution image, with the help of a given database of high and low-resolution image patch pairs. Denoising and super-resolution in this paper is performed on each image patch. For each given input low-resolution patch, its high-resolution version is estimated based on finding a nonnegative sparse linear representation of the input patch over the low-resolution patches from the database, where the coefficients of the representation strongly depend on the similarity between the input patch and the sample patches in the database. The problem of finding the nonnegative sparse linear representation is modeled as a nonnegative quadratic programming problem. The proposed method is especially useful for the case of noise-corrupted and low-resolution image. Experimental results show that the proposed method outperforms other state-of-the-art super-resolution methods while effectively removing noise.

Novel Example-Based Method for Super-Resolution and Denoising of Medical Images

This paper introduces a discrete scheme for mean curvature motion using a morphological image processing approach. An axiomatic approach of image processing and the mean curvature partial differential equation (PDE) are briefly presented, then the properties of the proposed scheme are studied. In particular, consistency and convergence are proved. The applications of mean curvature motion in image denoising and form evolution are developed and experiences are presented.

A morphological scheme for mean curvature motion and applications to anisotropic diffusion and motion of level sets

We introduce a discrete scheme using a morphological image processing approach. After briefly presenting the axiomatic approach of image processing and the mean curvature motion partial differential equation (PDE), the properties of the proposed scheme are studied. We show that this morphological scheme performs mean curvature evolution on a gray level image. Then we notice that the same scheme can be applied to forms. To conclude we present experimental results. >

The minimization of the total variation is an important tool of image processing. A lot of authors have addressed the problem and developed algorithms for image denoising. In this paper we present an alternative approach of the total variation minimization problem. After an introduction to the topic and a review of related work, we give a short development of the bounded variation (BV) background. Then we present our global total variation minimization model and proof its validity. Furthermore we introduce a practical algorithm which handles digital image data and we give experimental results.

/pdf/global-total-variation-minimization-58w3zwqueb.pdf

Françoise Dibos

Papers

A geometric model for active contours in image processing

Novel Example-Based Method for Super-Resolution and Denoising of Medical Images

A morphological scheme for mean curvature motion and applications to anisotropic diffusion and motion of level sets

A morphological scheme for mean curvature motion and applications to anisotropic diffusion and motion of level sets

Global Total Variation Minimization