For diagnosis and risk assessment in patients with stable ischemic heart disease, myocardial perfusion scintigraphy is one of the most common cardiological examinations performed today. There are however many motivations for why an artificial intelligence algorithm would provide useful input to this task. For example to reduce the subjectiveness and save time for the nuclear medicine physicians working with this time consuming task. In this work we have developed a deep learning algorithm for multi-label classification based on a convolutional neural network to estimate the probability of obstructive coronary artery disease in the left anterior artery, left circumflex artery and right coronary artery. The prediction is based on data from myocardial perfusion scintigraphy studies conducted in a dedicated Cadmium-Zinc-Telluride cardio camera (D-SPECT Spectrum Dynamics). Data from 588 patients was available, with stress images in both upright and supine position, as well as a number of auxiliary parameters such as angina symptoms and age. The data was used to train and evaluate the algorithm using 5-fold cross-validation. We achieve state-of-the-art results for this task with an area under the receiver operating characteristics curve of 0.89 as average on per-vessel level and 0.95 on per-patient level.

A new proof of the equivalence of the Taut String Algorithm and the one-dimensional Rudin–Osher–Fatemi model is presented. Based on duality and the projection theorem in Hilbert space, the proof is strictly elementary. Existence and uniqueness of solutions (in the continuous case) to both denoising models follow as by-products. The standard convergence properties of the denoised signal, as the regularizing parameter tends to zero, are recalled and efficient proofs provided. Moreover, a new and fundamental estimate on the denoised signal is derived. It implies, among other things, the strong convergence (in the space of functions of bounded variation) of the denoised signal to the in-signal as the regularization parameter vanishes.

Patients waiting for heart transplantation due to a failing heart can get a left ventricular assist device (LVAD) implanted through open chest surgery. The device consists of a pump that pumps blood from the left ventricle into the aorta. To get the correct rotation speed of the pump, the physicians consider a number of measurements as well as a sequence of echocardiographic images. The important information obtained from the images is the shape of the inter-ventricular septum. For instance, if the septum bulges towards the left ventricle the speed is too high and it might harm the right ventricular function. To get a measure of the shape of the septum, which can be incorporated in a decision support system, we perform a segmentation of the septum using a shortest path method. To reduce user interaction, the user only needs to annotate two anchor points in the first frame. They mark the endpoints of the septum and they are tracked through the sequence with our tracking algorithm. After the segmentation the septum is divided into two regions, the one closest to the right ventricle and the one closest to the left ventricle, and the desired measure is the difference between the areas of these regions divided by the total septum area. The performance of the segmentation algorithm is acceptable and the obtained septum measure corresponds in most cases to the assessments from a physician.

The concept of graph cuts is by now a standard method for all sorts of low level vision problems. Its popularity is largely due to the fact that globally or near globally optimal solutions can be computed using efficient max flow algorithms. On the other hand it has been observed that this method may suffer from metrication errors. Recent work has begun studying continuous versions of graph cuts, which give smaller metrication errors. Another advantage is that continuous cuts are straightforward to parallelize. In this paper we extend the class of functionals that can be optimized in the continuous setting to include anisotropic TV-norms. We show that there is a so called coarea formula for these functionals making it possible to minimize them by solving a convex problem. We also show that the concept of a-expansion moves can be reformulated to fit the continuous formulation, and we derive approximation bounds in analogy with the discrete case. A continuous version of the Potts model for multi-class segmentation problems is presented, and it is shown how to obtain provably good solutions using continuous α-expansions.

One of the key factors for the success of recent energy minimization methods is that they seek to compute global solutions. Even for non-convex energy functionals, optimization methods such as graph cuts have proven to produce high-quality solutions by iterative minimization based on large neighborhoods, making them less vulnerable to local minima. Our approach takes this a step further by enlarging the search neighborhood with one dimension. In this paper we consider binary total variation problems that depend on an additional set of parameters. Examples include: (i) the Chan-Vese model that we solve globally (ii) ratio and constrained minimization which can be formulated as parametric problems, and (iii) variants of the Mumford-Shah functional. Our approach is based on a recent theorem of Chambolle which states that solving a one-parameter family of binary problems amounts to solving a single convex variational problem. We prove a generalization of this result and show how it can be applied to parametric optimization.

In this paper we present the Coupled Active Contours (CAC) model, which is applied to segmentation of the endocardium in ultrasonic images assuming Rayleigh distributed intensities. Comparative experiments, both real and synthetic, with a standard prior model are presented. In the CAC model the prior acts, by affine transformation, on the same image information as the active contour, in addition to the traditional interaction between prior and active contour. By this higher convergence rate and robustness, w.r.t artifacts and poor initialization, is achieved.

In this paper we propose a new method for variational segmentation of image sequences containing nonrigid, moving objects. The method is based on the Chan-Vese model augmented with a novel frame-to-frame interaction term, which allow us to update the segmentation result from one image frame to the next using the previous segmentation result as a shape prior. The interaction term is constructed to be pose-invariant and to allow moderate deformations in shape. It can handle the appearance of occlusions which otherwise can make segmentation fail. The performance of the model is illustrated with experiments on synthetic and real image sequences.

In this paper we consider region-based variational segmentation of two- and three-dimensional images by the minimization of functionals whose fidelity term is the quotient of two integrals. Users often refrain from quotient functionals, even when they seem to be the most natural choice, probably because the corresponding gradient descent PDEs are nonlocal and hence require the computation of global properties. Here it is shown how this problem may be overcome by employing the structure of the Euler-Lagrange equation of the fidelity term to construct a good initialization for the gradient descent PDE, which will then converge rapidly to the desired (local) minimum. The initializer is found by making a one-dimensional search among the level sets of a function related to the fidelity term, picking the level set which minimizes the segmentation functional. This partial extremal initialization is tested on a medical segmentation problem with velocity- and intensity data from MR images. In this particular application, the partial extremal initialization speeds up the segmentation by two orders of magnitude compared to straight forward gradient descent.

In this paper a theory is developed for variational segmentation of images using area-based segmentation functionals with non-quadratic penalty functions in the fidelity term. Two small theorems, which we believe are new to the vision community, allow us to compute the Gateaux derivative of the considered functional, and to construct the corresponding gradient descent flow. The functional is minimized by evolving an initial curve using this gradient descent flow. If the penalty function is sub-quadratic, i.e. behaves like the p'th power of the error for p<2, the obtained segmentation model is more robust with respect to noise and outliers than the classical Chan-Vese model and the curve evolution has better convergence properties.