We describe a consistent hashing algorithm which performs multiple lookups per key in a hash table of nodes. It requires no additional storage beyond the hash table, and achieves a peak-to-average load ratio of 1 + epsilon with just 1 + 1/epsilon lookups per key.

Image-based 3D reconstruction remains a competitive field of research as state-of-the-art algorithms continue to improve. This paper presents a voxel-based algorithm that adapts the earliest space-carving methods and utilises a minimal surface technique to obtain a cleaner result. Embedded Voxel Colouring is built in two stages: (a) progressive voxel carving is used to build a volume of embedded surfaces and (b) the volume is processed to obtain a surface that maximises photo-consistency data in the volume. This algorithm combines the strengths of classical carving techniques with those of minimal surface approaches. We require only a single pass through the voxel volume, this significantly reduces computation time and is the key to the speed of our approach. We also specify three requirements for volumetric reconstruction: monotonic carving order, causality of carving and water-tightness. Experimental results are presented that demonstrate the strengths of this approach.

The application of energy minimisation methods for stereo matching has been demonstrated to produce high quality disparity maps. However, the majority of these methods are known to be computationally expensive requiring minutes of computation. In this paper, we propose a fast minimisation scheme that produces high quality stereo reconstructions for significantly reduced running time, requiring only a few seconds of computation. The minimisation scheme is carried out using our iterated dynamic programming algorithm, which iterates over entire rows and columns for fast stereo matching. A quadtree subregioning process is also used for efficient computation of a matching cost volume where iterated dynamic programming operates on.

Path openings and closings are algebraic morphological operators using families of thin and oriented structuring elements that are not necessarily perfectly straight. These operators can typically be used in filtering applications in lieu of operators based on the more standard families of straight line structuring elements. They yield results which are less constrained than filters based on straight line segments, yet more constrained than connected area or other attribute-based operators. Furthermore, path operators can be parametrised to behave more like either extreme.Natural implementations of this idea using actual suprema or infima of morphological operators with paths as structuring elements would imply exponential complexity. Fortunately, a linear complexity algorithm exists in the literature. This algorithm has similar running times as the best known implementation of morphological operators using straight lines as structuring elements.However, even this implementation is sometimes not fast enough, leading practitioners to favour some attribute-based operators instead, which in some applications is not the best solution.In this paper, we propose an implementation of path-based morphological operators that is shown experimentally to exhibit a logarithmic complexity and comparable computing times with those of attribute-based operators. This implementation has the added benefit of allowing the computation of the related opening transform at no extra computational cost.In order to give additional flexibility and noise-robustness to these operators, we also investigate the case when some pixels are left ignored from the path (i.e. “jumps” are allowed) and form incomplete paths.

This paper describes an electrical model of cardiac ventricles incorporating real geometry and motion. The heart anatomy and its motion through the cardiac cycle are obtained from segmentations of multiple-slice MRI time sequences; the special conduction system is constructed using an automated mapping procedure from an existing static heart model. The heart model is mounted in an anatomically realistic voxel model of the human body. The cardiac electrical source and surface potentials are determined numerically using both a finite-difference scheme and a boundary-element method with the incorporation of the motion of the heart. The electrocardiograms (ECG) and body surface potential maps are calculated and compared to the static simulation in the resting heart. The simulations demonstrate that introducing motion into the cardiac model modifies the ECG signals, with the most obvious change occurring during the T-wave at peak contraction of the ventricles. Body surface potential maps differ in some local positions during the T-wave, which may be of importance to a number of cardiac models, including those incorporating inverse methods.

positioning of the short-axis planes. We may segment the LV lumen in the long-axis plane. The segmentation method for the long-axis slices is identical to that for the short-axis slices. Following the segmentation of the LV endocardium, the LV epicardium and septal wall may be extracted either automatically or semi-automatically. After segmenting the LV contours the right ventricular (RV) endocardium may be extracted. On the RV segmentation, it makes use of the LV myocardial segmentation to track the septal wall and provide further guidance to the RV segmentation. A dedicated user interface and image processing platform is designed for the implementation of the contour detections. Fig.1 illustrates the contour extraction and reconstructed heart model. Special Conduction System Setup: The special conduction system (SCS) of the heart is obtained from an existing SCS model [2]. We deform a previously developed static heart model [2] to match the new heart geometry and then attach the SCS to obtain a similar activation sequence in the new heart model. The deformation is based on a stable regularization procedure. Cardiac Electric Source Modeling: After the SCS is incorporated into the heart model, we modify a dipolebased static electric source modeling algorithm [2] to the moving heart model. The fiber structure has been considered for the determination of the activation sequences over the myocardium wall, the dipole currents in each cardiac element is the source of the cardiac field. Calculation of Body Surface ECG Potentials: In the simulation, the heart model is mounted in a 2mm resolution MRI-based human model (NORMAN). To calculate the torso surface ECG potentials generated by the moving cardiac sources, the governing equation may be expressed as () 0 f σφ ∇+ = where φ represents the potential function, σ the conductivity tensor and f the current density source. In this study the finite-volume formulation was chosen to solve the forward problem.

In this paper, we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction. We present a solution, simulating a continuous maximal flow by a novel system of partial differential equations. Existing methods are either grid-biased (graph-based methods) or suboptimal (active contours and surfaces). The solution simulates the flow of an ideal fluid with isotropic velocity constraints. Velocity constraints are defined by a metric derived from image data. An auxiliary potential function is introduced to create a system of partial differential equations. It is proven that the algorithm produces a globally maximal continuous flow at convergence, and that the globally minimal surface may be obtained trivially from the auxiliary potential. The bias of minimal surface methods toward small objects is also addressed. An efficient implementation is given for the flow simulation. The globally minimal surface algorithm is applied to segmentation in 2D and 3D as well as to stereo matching. Results in 2D agree with an existing minimal contour algorithm for planar images. Results in 3D segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias.

Path openings and closings are algebraic morphological operators using families of thin and oriented structuring elements that are not necessarily perfectly straight. These operators are naturally translation invariant and can be used in filtering applications instead of operators based on the more standard families of straight line structuring elements. They give similar results to area or attribute-based operators but with more flexibility in the constraints.

This paper describes an electrical model of the ventricles incorporating real geometry and motion. Cardiac geometry and motion is obtained from segmentations of multiple-slice MRI time sequences. A static heart model developed previously is deformed to match the observed geometry using a novel shape registration algorithm. The resulting electrocardiograms and body surface potential maps are compared to a static simulation in the resting heart. These results demonstrate that introducing motion into the cardiac model modifies the ECG during the T wave at peak contraction of the ventricles

The interpretation of dynamic contrast-enhanced breast MR images is predicated on the assumption of minimal voxel movement during the time course of the image acquisition. Misalignment of the dynamic image sequence as a result of movement during image acquisition can lead to potentially misleading diagnostic conclusions. In this paper a new methodology is presented for assessing the degree of in-plane (intra-slice) movement in a dynamic image sequence. The method is demonstrated on data from six subjects. The conclusion is that the method makes it possible to quantitatively qualify the accuracy of computed enhancement curves and more importantly to identify unacceptably poor registration.

In this paper we present a system for the automatic segmentation of the left ventricle (LV) of the heart from breath hold MRI images with subsequent ejection fraction (EF) calculations. The ventricular luminal contours in short and long-axis slices are enhanced with morphological image processing methods and extracted using a novel Global Optimal Closed Path algorithm. In this study, contours both including and excluding LV trabeculations and papillary muscles are considered. Ventricular 3D-reconstructions are based on the use of both short-axis and long-axis contours, with the long-axis contours also being used as an internal skeleton template of the LV to correct for through plane motion. A series of volumes of the reconstructed 3D ventricle is evaluated at different times during the cycle and the EF calculated. By comparing our numerical results with those derived from manual segmentations on eight normal subjects, we conclude that the automated system performance is reliable and consistent.

Recursive filters are widely used in image analysis due to their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually.In this paper, we describe a method for the recursive filtering of symmetrically extended images for filters with symmetric denominator. We begin with an analysis of symmetric extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on symmetric domains as a linear but spatially varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system, along with a proof that this decomposition always exists.This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring less computation than the standard recursive filtering. We give experimental evidence to verify these claims.

In this paper we examine a new prospect for volumetric image segmentation, the globally minimal surface algorithm, and its application to segmenting anatomical structures in the brain. Existing minimal surface algorithms typically use a variational approach and so are prone to becoming stuck in local minima. The globally minimal surface algorithm used here is based on a maximal flow approach which has been mathematically proven to obtain optimal segmentations. We present the application of globally minimal surfaces to segmenting a number of structures in the brain, as well as to tracking changes in the shape of the brain in a study of elderly patients. The results demonstrate that this new method is able to obtain robust and accurate segmentations with little user interaction. We conclude that a wide range of medical segmentation problems may benefit from the application of globally minimal surfaces.

Single shortest path extraction algorithms have been used in a number of areas such as network flow and image analysis. In image analysis, shortest path techniques can be used for object boundary detection, crack detection, or stereo disparity estimation. Sometimes one needs to find multiple paths as opposed to a single path in a network or an image where the paths must satisfy certain constraints. In this paper, we propose a new algorithm to extract multiple paths simultaneously within an image using a constrained expanded trellis (CET) for feature extraction and object segmentation. We also give a number of application examples for our multiple paths extraction algorithm.

In this paper we present an image stitching method based on dynamic programming and describe its application to automated slide acquisition for Virtual Microscopy (VM). Given a large number of fields of view (FOVs) acquired from a single microscope slide, we composite these images into a single large ‘virtual slide’ image. The location of each FOV is determined using a new algorithm based on dynamic programming. We compare the performance of the proposed algorithm to an existing greedy algorithm. In a visual trial it is shown that the new algorithm provides a significant improvement in perceived image quality at image boundaries compared to the existing algorithm.

In this paper we present an algorithm as the combination of a low level morphological operation and model based global circular shortest path scheme to explore the segmentation of the right ventricle. Traditional morphological operations were employed to obtain the region of interest, and adjust it to generate a mask. The image cropped by the mask is then partitioned into a few overlapping regions. Global circular shortest path algorithm is then applied to extract the contour from each partition. The final step is to re-assemble the partitions to create the whole contour. The technique is deemed quite reliable and robust, as this is illustrated by a very good agreement between the extracted contour and the expert manual drawing output.

An approach to optimal object segmentation in the geodesic active contour framework is presented with application to automated image segmentation. The new segmentation scheme seeks the geodesic active contour of globally minimal energy under the sole restriction that it contains a specified internal point pint. This internal point selects the object of interest and may be used as the only input parameter to yield a highly automated segmentation scheme. The image to be segmented is represented as a Riemannian space S with an associated metric induced by the image. The metric is an isotropic and decreasing function of the local image gradient at each point in the image, encoding the local homogeneity of image features. Optimal segmentations are then the closed geodesics which partition the object from the background with minimal similarity across the partitioning. An efficient algorithm is presented for the computation of globally optimal segmentations and applied to cell microscopy, x-ray, magnetic resonance and cDNA microarray images.

We propose a novel energy minimisation framework for the dense reconstruction of stereo image sequences that incorporates data fidelity as well as spatial and temporal regularity. An iterated dynamic programming scheme is proposed to minimise the energy function. We also present an efficient implementation of the minimisation scheme by introducing morphological decomposition techniques to solve the dynamic programming subproblem. Our proposed method is capable of reconstructing dynamic scenes with complex motion. Results are presented demonstrating the strength of our proposed algorithm.

Shortest path algorithms are used for a large variety of optimisation problems in network and transportation analysis. They are also used in image analysis for object segmentation, disparity estimation, path finding and crack detection. Sometimes the topology of the problem demands that the path be circular. Such circular path constraints occur in polar object segmentation, disparity estimation for panoramic stereo images and in shortest paths around a cylinder. In this paper we present a new efficient algorithm for circular shortest path determination on a u-by-v trellis in O(u1.6v) average time. We impose a binary search tree on the set of path endpoints and use a best-first Branch and Bound search technique to efficiently obtain the global minimum circular path. The typical running time of our circular shortest path algorithm on a 256×256 image is in the order of 0.1s on a 1GHz Dell P3 workstation under the Linux operating system. Applications to crack detection and object segmentation are presented.

Recursive filters are commonly used in scale space construction for their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of reflectively extended images for filters with symmetric denominator. We begin with an analysis of reflective extensions and their effect on nonrecursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on reflective domains as a linear but time-varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring the same order of computation as the standard recursive filtering. We give experimental evidence to verify these claims.