Dense Deformation Field Estimation for Atlas Registration using the Active Contour Framework

In this paper, we propose a new paradigm to carry outthe registration task with a dense deformation fieldderived from the optical flow model and the activecontour method. The proposed framework merges differenttasks such as segmentation, regularization, incorporationof prior knowledge and registration into a singleframework. The active contour model is at the core of ourframework even if it is used in a different way than thestandard approaches. Indeed, active contours are awell-known technique for image segmentation. Thistechnique consists in finding the curve which minimizesan energy functional designed to be minimal when thecurve has reached the object contours. That way, we getaccurate and smooth segmentation results. So far, theactive contour model has been used to segment objectslying in images from boundary-based, region-based orshape-based information. Our registration technique willprofit of all these families of active contours todetermine a dense deformation field defined on the wholeimage. A well-suited application of our model is theatlas registration in medical imaging which consists inautomatically delineating anatomical structures. Wepresent results on 2D synthetic images to show theperformances of our non rigid deformation field based ona natural registration term. We also present registrationresults on real 3D medical data with a large spaceoccupying tumor substantially deforming surroundingstructures, which constitutes a high challenging problem

Convergence and Energy Landscape for Cheeger Cut Clustering

This paper provides both theoretical and algorithmic results for the l 1-relaxation of the Cheeger cut problem. The l2- relaxation, known as spectral clustering, only loosely relates to the Cheeger cut; however, it is convex and leads to a simple optimization problem. The l1-relaxation, in contrast, is non-convex but is provably equivalent to the original problem. The l1-relaxation therefore trades convexity for exactness, yielding improved clustering results at the cost of a more challenging optimization. The first challenge is understanding convergence of algorithms. This paper provides the first complete proof of convergence for algorithms that minimize the l1-relaxation. The second challenge entails comprehending the l1-energy landscape, i.e. the set of possible points to which an algorithm might converge. We show that l 1-algorithms can get trapped in local minima that are not globally optimal and we provide a classification theorem to interpret these local minima. This classification gives meaning to these suboptimal solutions and helps to explain, in terms of graph structure, when the l1-relaxation provides the solution of the original Cheeger cut problem

Image Segmentation Model Using Active contour and Image Decomposition

This paper proposes an image segmentation model based on the active contour model, the Mumford-Shah functional and the image decomposition process. Generally speaking, the active contour model detects boundaries in images from sharp intensities variations and the Mumford-Shah model finds smooth regions from homogeneous intensities. Our model merges these two complementary approaches while considering the Four Color Theorem to globally partition any given image. We also consider the textural part lying in natural images by separating it from the geometric part, which contains the meaningful objects, to help the segmentation process. Our segmentation model is experimented with a 1-D signal and 2-D images

Decreasing time consumption of microscopy image segmentation through parallel processing on the GPU

The computational performance of graphical processing units (GPUs) has improved significantly. Achieving speedup factors of more than 50x compared to single-threaded CPU execution are not uncommon due to parallel processing. This makes their use for high throughput microscopy image analysis very appealing. Unfortunately, GPU programming is not straightforward and requires a lot of programming skills and effort. Additionally, the attainable speedup factor is hard to predict, since it depends on the type of algorithm, input data and the way in which the algorithm is implemented. In this paper, we identify the characteristic algorithm and data-dependent properties that significantly relate to the achievable GPU speedup. We find that the overall GPU speedup depends on three major factors: (1) the coarse-grained parallelism of the algorithm, (2) the size of the data and (3) the computation/memory transfer ratio. This is illustrated on two types of well-known segmentation methods that are extensively used in microscopy image analysis: SLIC superpixels and high-level geometric active contours. In particular, we find that our used geometric active contour segmentation algorithm is very suitable for parallel processing, resulting in acceleration factors of 50x for 0.1 megapixel images and 100x for 10 megapixel images

Geometric Moments in Scale-Spaces

In this paper we present a generalization of geometric moments in scale-spaces derived from the general heat diffusion equation, with a particular interest for th

A Variational Model for Object Segmentation Using Boundary Information, Statistical Shape Prior and the Mumford-Shah Functional

In this paper, we propose a variational model to segment an object belonging to a given scale space using the active contour method, a geometric shape prior and the Mumford-Shah functional. We define an energy functional composed by three complementary terms. The first one detects object boundaries from image gradients. The second term constrains the active contour to get a shape compatible with a statistical shape model of the shape of interest. And the third part drives globally the shape prior and the active contour towards a homogeneous intensity region. The segmentation of the object of interest is given by the minimum of our energy functional. This minimum is computed with the calculus of variations and the gradient descent method that provide a system of evolution equations solved with the well-known level set method. We also prove the existence of this minimum in the space of functions with bounded variation. Applications of the proposed model are presented on synthetic and medical images

Multiscale Image Segmentation Using Active Contours

We propose a new approach for image segmentation at different scales of observation, based on a multiscale image decomposition and on the active contour segmentation model. The proposed method consists of two steps. Firstly, a representation of a given image at multiple scales is derived, by means of a smoothing method which minimizes the weighted total variation norm of the image. This method allows the longtime preservation of edges and contrast with increasing scale, facilitating the detection of underlying structures. Secondly, image structures are extracted at each scale, using a level set formulation of active contours, minimizing the Mumford-Shah functional. Promising results of the proposed segmentation approach on natural images are reported

Leaf segmentation and tracking using probabilistic parametric active contours

Active contours or snakes are widely used for segmentation and tracking. These techniques require the minimization of an energy function, which is generally a linear combination of a data fit term and a regularization term. This energy function can be adjusted to exploit the intrinsic object and image features. This can be done by changing the weighting parameters of the data fit and regularization term. There is, however, no rule to set these parameters optimally for a given application. This results in trial and error parameter estimation. In this paper, we propose a new active contour framework defined using probability theory. With this new technique there is no need for ad hoc parameter setting, since it uses probability distributions, which can be learned from a given training dataset