Optimal Geodesic Active Contours: Application to Heart Segmentation

We develop a semiautomated segmentation method to assist in the analysis of functional pathologies of the left ventricle of the heart. The segmentation is performed using an optimal geodesic active contour with minimal structural knowledge to choose the most likely surfaces of the myocardium. The use of an optimal segmentation algorithm avoids the problems of contour leakage and false minima associated with variational active contour methods. The resulting surfaces may be analysed to obtain quantitative measures of the heart's function. We have applied the proposed segmentation method to multislice MRI data. The results demonstrate the reliability and efficiency of this scheme as well as its robustness to noise and background clutter

Globally Optimal Surfaces By Continuous Maximal Flows

In this paper we consider the problem of computing globally minimal continuous curves and surfaces for image segmentation and 3D reconstruction. This is solved using a maximal flow approach expressed as a PDE model. Previously proposed techniques yield either grid-biased solutions (graph based approaches) or sub-optimal solutions (active contours and surfaces). The proposed algorithm simulates the flow of an ideal fluid with a spatially varying velocity constraint derived from image data. A proof is given that the algorithm gives the globally maximal flow at convergence, along with an implementation scheme. The globally minimal surface may be obtained trivially from its output. The new algorithm is applied to segmentation in 2D and 3D medical images and to 3D reconstruction from a stereo image pair. The results in 2D agree remarkably well with an existing planar minimal contour algorithm and the results in 3D segmentation and reconstruction demonstrate that the new algorithm is free from grid bias

Globally minimal surfaces by continuous maximal flows

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 sub-optimal (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

Fast Stereo Matching by Iterated Dynamic Programming and Quadtree Subregioning

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 or even hours of computation. We propose a fast minimisation scheme that produces strongly competitive results for significantly reduced computation, requiring only a few seconds of computation. In this paper, we present our iterated dynamic programming algorithm along with a quadtree subregioning process for fast stereo matching

Embedded Voxel Colouring

The reconstruction of a complex scene from multiple images is a fundamental problem in the field of computer vision. Volumetric methods have proven to be a strong alternative to traditional correspondence-based methods due to their flexible visibility models. In this paper we analyse existing methods for volumetric reconstruction and identify three key properties of voxel colouring algorithms: a water-tight surface model, a monotonic carving order, and causality. We present a new Voxel Colouring algorithm which embeds all reconstructions of a scene into a single output. While modelling exact visibility for arbitrary camera locations, Embedded Voxel Colouring removes the need for a priori threshold selection present in previous work. An efficient implementation is given along with results demonstrating the advantages of posteriori threshold selection

Circular Shortest Paths by Branch and Bound

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 $O(u^{1.6} v)$ 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$\times$256 image is in the order of 0.1 seconds on a 1GHz Dell P3 workstation under the Linux operating system. Applications to crack detection and object segmentation are presented

Autonomous Direct 3D Segmentation of Articular Knee Cartilage

The aim of the work presented here, is to speed up the entire evaluation process of articular knee cartilage and the associated medication developments for Osteoarthritis. To enable this, the development of an automated direct 3D segmentation is described that incorporates non-linear diffusion for efficient image denoising. Cartilage specific magnetic resonance imaging is used, which allows acquiring the entire cartilage volume as one 3D image. The segmentation itself is based on level sets for their accuracy, stability and topological flexibility. By using this kind of segmentation, it is hoped to improve the time efficiency and accuracy for quantitative and qualitative integrity evaluation of cartilage and to enable an earlier diagnosis and treatment of Osteoarthritis

Estimating specific surface area of fine stream bed sediments from geochemistry

Specific surface area (SSA) of headwater stream bed sediments is a fundamental property which determines the nature of sediment surface reactions and influences ecosystem-level, biological processes. Measurements of SSA – commonly undertaken by BET nitrogen adsorption – are relatively costly in terms of instrumentation and operator time. A novel approach is presented for estimating fine (2.5 mg kg−1), four elements were identified as significant predictors of SSA (ordered by decreasing predictive power): V > Ca > Al > Rb. The optimum model from these four elements accounted for 73% of the variation in bed sediment SSA (range 6–46 m2 g−1) with a root mean squared error of prediction – based on leave-one-out cross-validation – of 6.3 m2 g−1. It is believed that V is the most significant predictor because its concentration is strongly correlated both with the quantity of Fe-oxides and clay minerals in the stream bed sediments, which dominate sediment SSA. Sample heterogeneity in SSA – based on triplicate measurements of sub-samples – was a substantial source of variation (standard error = 2.2 m2 g−1) which cannot be accounted for in the regression model. The model was used to estimate bed sediment SSA at the other 1792 sites and at 30 duplicate sites where an extra sediment sample had been collected, 25 m from the original site. By delineating sub-catchments for the headwater sediment sites only those sub-catchments were selected with a dominant (>50% of the sub-catchment area) bedrock formation and land use type; the bedrock and land use classes accounted for 39% and 7% of the variation in bed sediment SSA, respectively. Variation in estimated, fine bed sediment SSA from the paired, duplicate sediment sites was small (2.7 m2 g−1), showing that local variation in SSA at stream sites is modest when compared to that between catchments. How the approach might be applied in other environments and its potential limitations are discussed

Registration evaluation of dynamic breast MR images

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