Hüseyin Tek

Symmetry-Based Indexing of Image Databases

The use of shape as a cue for indexing into pictorial databases has been traditionally based on global invariant statistics and deformable templates, on the one hand, and local edge correlation on the other. This paper proposes an intermediate approach based on a characterization of the symmetry in edge maps. The use of symmetry matching as a joint correlation measure between pairs of edge elements further constrains the comparison of edge maps. In addition, a natural organization of groups of symmetry into a hierarchy leads to a graph-based representation of relational structure of components of shape that allows for deformations by changing attributes of this relational graph. A graduated assignment graph matching algorithm is used to match symmetry structure in images to stored prototypes or sketches. The results of matching sketches and grey-scale images against a small database consisting of a variety of fish, planes, tools, etc., are promising.

Segmentation of carpal bones from CT images using skeletally coupled deformable models.

The in vivo investigation of joint kinematics in normal and injured wrist requires the segmentation of carpal bones from 3D (CT) images, and their registration over time. The non-uniformity of bone tissue, ranging from dense cortical bone to textured spongy bone, the irregular shape of closely packed carpal bones, small inter-bone spaces compared to the resolution of CT images, along with the presence of blood vessels, and the inherent blurring of CT imaging render the segmentation of carpal bones a challenging task. We review the performance of statistical classification, deformable models (active contours), region growing, region competition, and morphological operations for this application. We then propose a model which combines several of these approaches in a unified framework. Specifically, our approach is to use a curve evolution implementation of region growing from initialized seeds, where growth is modulated by a skeletally-mediated competition between neighboring regions. The inter-seed skeleton, which we interpret as the predicted boundary of collision between two regions, is used to couple the growth of seeds and to mediate long-range competition between them. The implementation requires subpixel representations of each growing region as well as the inter-region skeleton. This method combines the advantages of active contour models, region growing, and both local and global region competition methods. We demonstrate the effectiveness of this approach for our application where many of the difficulties presented above are overcome as illustrated by synthetic and real examples. Since this segmentation method does not rely on domain-specific knowledge, it should be applicable to a range of other medical imaging segmentation tasks.

Image segmentation by reaction-diffusion bubbles

Figure-ground segmentation is a fundamental problem in computer vision. The main difficulty is the integration of low-level, pixel-based local image features to obtain global object-based descriptions. Active contours in the form of snakes, balloons, and level-set modeling techniques have been proposed that satisfactorily address this question for certain applications. However, these methods require manual initialization, do not always perform well near sharp protrusions or indentations, or often cross gaps. We propose an approach inspired by these methods and a shock-based representation of shape in terms of parts, protrusions, and bends. Since initially it is not clear where the objects or their parts are, parts are hypothesized in the form of fourth order shocks randomly initialized in homogeneous areas of images. These shocks then form evolving contours, or bubbles, which grow, shrink, merge, split and disappear to capture the objects in the image. In the homogeneous areas of the image bubbles deform by a reaction-diffusion process. In the inhomogeneous areas, indicated by differential properties computed from low-level processes such as edge-detection, texture, optical-flow and stereo, etc., bubbles do not deform. As such, the randomly initialized bubbles integrate low-level information and, in the process, segment the figures from the ground.<<ETX>>

Volumetric Segmentation of Medical Images by Three-Dimensional Bubbles

The segmentation of structure from images is an inherently difficult problem in computer vision and a bottleneck to its widespread application, e.g., in medical imaging. This paper presents an approach for integrating local evidence such as regional homogeneity and edge response to form global structure for figure?ground segmentation. This approach is motivated by a shock-based morphogenetic language, where the growth of four types of shocks results in a complete description of shape. Specifically, objects are randomly hypothesized in the form of fourth-order shocks (seeds) which then grow, merge, split, shrink, and, in general, deform under physically motivated “forces,” but slow down and come to a halt near differential structures. Two major issues arise in the segmentation of 3D images using this approach. First, it is shown that the segmentation of 3D images by 3D bubbles is superior to a slice-by-slice segmentation by 2D bubbles or by “212D bubbles” which are inherently 2D but use 3D information for their deformation. Specifically, the advantages lie in an intrinsic treatment of the underlying geometry and accuracy of reconstruction. Second, gaps and weak edges, which frequently present a significant problem for 2D and 3D segmentation, are regularized by curvature-dependent curve and surface deformations which constitute diffusion processes. The 3D bubbles evolving in the 3D reaction?diffusion space are a powerful tool in the segmentation of medical and other images, as illustrated for several realistic examples.

Evaluation framework for carotid bifurcation lumen segmentation and stenosis grading.

This paper describes an evaluation framework that allows a standardized and objective quantitative comparison of carotid artery lumen segmentation and stenosis grading algorithms. We describe the data repository comprising 56 multi-center, multi-vendor CTA datasets, their acquisition, the creation of the reference standard and the evaluation measures. This framework has been introduced at the MICCAI 2009 workshop 3D Segmentation in the Clinic: A Grand Challenge III, and we compare the results of eight teams that participated. These results show that automated segmentation of the vessel lumen is possible with a precision that is comparable to manual annotation. The framework is open for new submissions through the website http://cls2009.bigr.nl.

Symmetry-based indexing of image databases

The use of shape as a cue for indexing in pictorial databases has been traditionally based on global invariant statistics and deformable templates, on the one hand, and local edge correlation on the other. This paper proposes an intermediate approach based on a characterization of the symmetry in edge maps. The use of symmetry matching as a joint correlation measure between pairs of edge elements further constrains the comparison of edge maps. In addition, a natural organization of groups of symmetry into a hierarchy leads to a graph-based representation of relational structure of components of shape that allows for deformations by changing attributes of this relational graph. A graduate assignment graph matching algorithm is used to match symmetry structure in images to stored prototypes or sketches. The results of matching sketches and grey-scale images against a small database consisting of a variety of fish, planes, tools, etc., are depicted.

Symmetry Maps of Free-Form Curve Segments via Wave Propagation

This paper presents an approach for computing the symmetries (skeletons) of an edge map consisting of a collection of curve segments. This approach is a combination of analytic computations in the style of computational geometry and discrete propagations on a grid in the style of the numerical solutions of PDEs. Specifically, waves from each of the initial curve segments are initialized and propagated as a discrete wavefront along discrete directions. In addition, to avoid error built up due to the discrete nature of propagation, shockwaves are detected and explicitly propagated along a secondary dynamic grid. The propagation of shockwaves, integrated with the propagation of the wavefront along discrete directions, leads to an exact simulation of propagation by the Eikonal equation. The resulting symmetries are simply the collection of shockwaves formed in this process which can be manipulated locally, exactly, and efficiently under local changes in an edge map (gap completion, removal of spurious elements, etc). The ability to express grouping operations in the language of symmetry maps makes it an appropriate intermediate representation between low-level edge maps and high level object hypotheses.

Volumetric segmentation of medical images by three-dimensional bubbles

The segmentation of structure from 3D images is an inherently difficult problem and a bottleneck to the widespread use of computer vision in such applications as medical imaging. Local low-level voxel-based features must somehow be integrated to obtain global object-based descriptions. Deformable models in the form of snakes, balloons, level sets, and bubbles have been proposed for this task. In this paper, we extend the reaction-diffusion segmentation bubble technique to three dimensions. In generalizing this approach to 3D, two separate issues arise. First, should segmentations be achieved by treating images as a series of disjoint 2D slides, as 2D slices with interslice interactions, or intrinsically as a 3D image? We will show that the existence of saps of information in low-level features guides us to make maximal use of continuity in all directions, thus advocating an intrinsic 3D approach. The treatment of bubbles in 3D, however, requires the generalization of the reaction-diffusion space. While the reaction process is trivially extended, the generalization of diffusion is not straightforward. We utilize a particular mean-Gauss curvature deformation to serve as the regularizing diffusion process. The resulting 3D reaction-diffusion bubbles are intrinsic, can deal with a variety of gaps, and place captured surfaces in a hierarchy of scale. The process is illustrated on MRI images of the ventricle cavity and the vascular structure in MRA images

Boundary Smoothing via Symmetry Transforms

This paper proposes a smoothing technique for shape based on a perturbation analysis of the underlying medial axis, and by iteratively removing skeletal branches. While medial axis regularization usually aims at dealing with its sensitivity in the context of applications such as recognition, we use it here to smooth shape. The approach overcomes a basic drawback with current smoothing techniques, namely, the rounding of perceptually salient corners. The key idea is that the instability of the skeleton under a family of deformations can be dealt with via a symmetry transform which is applied to all related symmetry branches so as to effect an appropriate change in the shape. This leads to the notion of a splice transform which removes a branch coupled with simultaneous changes in the skeleton. In contrast to point-based pruning techniques which use local salience and which cannot construct coarse-scale corners, our approach constructs and preserves coarse-scale curvature extrema, leading to a “scale-discrete scale-space” for shape. The approach is also applicable to the smoothing of incomplete shapes represented as a set of curve segments.

Shocks from images: propagation of orientation elements

The extraction of figure symmetry from image contours faces a number of fundamental difficulties: object symmetries are distorted due to (i) gaps in the bounding contour of a shape due to figure-ground blending, weak contrast edges, highlights, noise, etc.; (ii) an introduction of parts and occluders, and (iii) spurious edge elements due to surface markings, texture, etc. A framework for extracting such symmetries from real images is proposed based on the propagation of contour orientation information and the detection of four types of singularities (shocks) arising from the collision of propagating elements. In this paper, we show that an additional labeling of shocks based on whether the colliding wavefronts carry true orientation information (regular vs. rarefaction waves) allows a division of shocks into three sets: regular shocks are the partial shocks of partial contours as they remain invariant to the completion of the contour; semi-degenerate and degenerate shocks depict potential parts and gaps. Finally, shocks altered due to spurious edges, occlusion, and gaps are recovered via a simulation of inter-penetrating waves generated at select shock groups which with the aid of the above shock labels leads to second and further generations of shocks.