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

https://www.cs.ucla.edu/~dt/papers/mia96/mia96.pdf

Deformable models in medical image analysis: a survey

Combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics. This paper focusses on possibly the simplest application of graph-cuts: segmentation of objects in image data. Despite its simplicity, this application epitomizes the best features of combinatorial graph cuts methods in vision: global optima, practical efficiency, numerical robustness, ability to fuse a wide range of visual cues and constraints, unrestricted topological properties of segments, and applicability to N-D problems. Graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes, geodesic active contours, and level-sets. The segmentation energies optimized by graph cuts combine boundary regularization with region-based properties in the same fashion as Mumford-Shah style functionals. We present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s/t graph cuts. After the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in Boykov and Jolly (2001), this idea was widely studied in computer vision and graphics communities. We provide links to a large number of known extensions based on iterative parameter re-estimation and learning, multi-scale or hierarchical approaches, narrow bands, and other techniques for demanding photo, video, and medical applications.

/pdf/graph-cuts-and-efficient-n-d-image-segmentation-15v3dgbexd.pdf

Graph Cuts and Efficient N-D Image Segmentation

Vessel segmentation algorithms are the critical components of circulatory blood vessel analysis systems. We present a survey of vessel extraction techniques and algorithms. We put the various vessel extraction approaches and techniques in perspective by means of a classification of the existing research. While we have mainly targeted the extraction of blood vessels, neurosvascular structure in particular, we have also reviewed some of the segmentation methods for the tubular objects that show similar characteristics to vessels. We have divided vessel segmentation algorithms and techniques into six main categories: (1) pattern recognition techniques, (2) model-based approaches, (3) tracking-based approaches, (4) artificial intelligence-based approaches, (5) neural network-based approaches, and (6) tube-like object detection approaches. Some of these categories are further divided into subcategories. We have also created tables to compare the papers in each category against such criteria as dimensionality, input type, preprocessing, user interaction, and result type.

/pdf/a-review-of-vessel-extraction-techniques-and-algorithms-1qqzv9f4am.pdf

A review of vessel extraction techniques and algorithms

The problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision. Terzopoulos et al. (1987) proposed an approach to detect the contour regions of complex shapes, assuming a user selected initial contour not very far from the desired solution. We propose to further explore the information provided by the user's selected points and apply an optimal method to detect contours which allows a segmentation of the image. The method is based on dynamic programming (DP), and applies to a wide variety of shapes. It is exact and not iterative. We also consider a multiscale approach capable of speeding up the algorithm by a factor of 20, although at the expense of losing the guaranteed optimality characteristic. The problem of tracking and matching these contours is addressed. For tracking, the final contour obtained at one frame is sampled and used as initial points for the next frame. Then, the same DP process is applied. For matching, a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not. The algorithm is again based on DP and the optimal solution is guaranteed. We have demonstrated the algorithms on natural objects in a large spectrum of applications, including interactive segmentation and automatic tracking of the regions of interest in medical images. >

J. Vlontzos

Papers

Dynamic programming for detecting, tracking, and matching deformable contours