Implementation and complexity of the watershed-from-markers algorithm computed as a minimal cost forest

The watershed algorithm belongs to classical algorithms in mathematical morphology. Lotufo et al. published a principle of the watershed computation by means of an Image Foresting Transform (IFT), which computes a shortest path forest from given markers. The algorithm itself was described for a 2D case (image) without a detailed discussion of its computation and memory demands for real datasets. As IFT cleverly solves the problem of plateaus and as it gives precise results when thin objects have to be segmented, it is obvious to use this algorithm for 3D datasets taking in mind the minimizing of a higher memory consumption for the 3D case without loosing low asymptotical time complexity of O(m+C) (and also the real computation speed). The main goal of this paper is an implementation of the IFT algorithm with a priority queue with buckets and careful tuning of this implementation to reach as minimal memory consumption as possible. The paper presents five possible modifications and methods of implementation of the IFT algorithm. All presented implementations keep the time complexity of the standard priority queue with buckets but the best one minimizes the costly memory allocation and needs only 19-45% of memory for typical 3D medical imaging datasets. Memory saving was reached by an IFT algorithm simplification, which stores more elements in temporary structures but these elements are simpler and thus need less memory. The best presented modification allows segmentation of large 3D medical datasets (up to 512x512x680 voxels) with 12-or 16-bits per voxel on currently available PC based workstations.Comment: v1: 10 pages, 6 figures, 7 tables EUROGRAPHICS conference, Manchester, UK, 2001. v2: 12 pages, reformated for letter, corrected IFT to "Image Foresting Tranform

Intuitive visualization technique to support eye tracking data analysis: A user-study

While fixation distribution is conventionally visualized using heat maps, there is still a lack of a commonly accepted technique to visualize saccade distributions. Inspired by wind maps and the Oriented Line Integral Convolution (OLIC) technique, we visualize saccades by drawing ink droplets which follow the direction indicated by a flow direction map. This direction map is computed using a kernel density estimation technique over the tangent directions to each saccade gaze point. The image is further blended with the corresponding heat map. It results in an animation or a static image showing main directions of the transitions between different areas of interest. We also present results from a web-based user study where naive non-expert users where asked to identify the direction of the flow and simple patterns. The results showed that these visualizations can successfully be used to support visual analysis of the eye-tracking data. It also showed that the use of animation allows to ease the task and to improve the performance

Interactive design of nonlinear functions for iterated function systems

The basic reqirement for the functions of an Iterated Function System (IFS for shor) is contractivity. Nevertheless the majority of recent scientific investigations is concentrating on IFSs defined through a set of contractive linear functions. Simpler handling of this kind of functions and a more predictable results is the main reason for this approach. In this work we use distorted grids (representing nonlinear functions) to specify an IFS with a higher degree of flexibility and a higher modeling capability. A program for modeling these grids with so-called high-level operations is presented. Attention is directed to the interactivity of designing the IFS and rendering its limit set. Therefore a z-Buffer for displaying the result of a stochastic algorithm is included. Example images designed with the implemented software system are presented

Analysis of four-dimensional cardiac data sets using skeleton-based segmentation

Computer-aided analysis of four-dimensional tomography data has become an important tool in modern cardiology. In order to examine the capability and health of a patient’s cardiac system, scans are taken at a number of time points evenly distributed over one cardiac cycle. A key task for understanding the dynamics involved within a recorded cardiac cycle is to segment the acquired data to identify objects of interest in each volume of the sequence. This paper presents an algorithm to segment the heart muscle and the left ventricle from a sequence of cardiac CT images using only a minimum of user interaction. Furthermore, the paper introduces methods to process the segmentation result for extraction of important properties of the cardiac cycle, which are helpful for diagnosis

Fast Oriented Line Integral Convolution for Vector Field Visualization via the Internet

Oriented Line Integral Convolution (OLIC) illustrates flow fields by convolving a sparse texture with an anisotropic convolution kernel. The kernel is aligned to the underlying flow of the vector field. OLIC does not only show the direction of the flow but also its orientation. This paper presents Fast Rendering of Oriented Line Integral Convolution (FROLIC), which is approximately two orders of magnitude faster than OLIC. Costly convolution operations as done in OLIC are replaced in FROLIC by approximating a streamlet through a set of disks with varying intensity. The issue of overlapping streamlets is discussed. Two efficient animation techniques for animating FROLIC images are described. FROLIC has been implemented as a Java applet. This allows researchers from various disciplines (typically with inhomogenous hardware environments) to conveniently explore and investigate analytically defined 2D vector fields. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics ]: Pictur..

EndoView: a phantom study of a tracked virtual bronchoscopy

Virtual endoscopy can be used for preoperative planning, for training and intraoperatively. Surface rendering displays the inner lumen very well. Volume rendering has to be used if the external structures are of interest. For certain applications, e.g. endoluminal biopsy, it is of great advantage to be able to use both techniques at once. In this work we describe an approach that allows using these two methods in combination on a low-end standard personal computer. Since image generation is done in a preprocessing step, any high quality volume or polygonal rendering technique can be used and mixed together without any loss in performance at run-time. This work extends a previous image based rendering system for virtual bronchoscopy to include tracking of a rigid or flexible endoscope and finding one's way in the tracheal tree by displaying the endoscope's position in a top-view map of the trachea. Natural landmarks, i.e. bifurcations in the bronchial tree, are used for registration. Properties of the technique are explored on a phantom data set