Joachim Hornegger

A Linear Programming Relaxation for Binary Tomography with Smoothness Priors

Abstract We focus on the reconstruction of binary functions from a small number of X-ray projections. The linear-programming (LP) relaxation to this combinatorial optimization problem due to Fishburn et al. is extended to objective functionals with quadratic smoothness priors. We show that the regularized LP-relaxation provides a good approximation and thus allows to bias the reconstruction towards solutions with spatially coherent regions. These solutions can be computed with any interior-point solver and a related rounding technique. Our approach provides an alternative to computationally expensive MCMC-sampling (Markov Chain Monte Carlo) techniques and other heuristic rounding schemes.

A Linear Programming Approach to Limited Angle 3D Reconstruction from DSA Projections

OBJECTIVESnWe investigate the feasibility of binary-valued 3D tomographic reconstruction using only a small number of projections acquired over a limited range of angles.nnnMETHODSnRegularization of this strongly ill-posed problem is achieved by (i) confining the reconstruction to binary vessel/non-vessel decisions, and (ii) by minimizing a global functional involving a smoothness prior.nnnRESULTSnOur approach successfully reconstructs volumetric vessel structures from three projections taken within 90 degrees. The percentage of reconstructed voxels differing from ground truth is below 1%.nnnCONCLUSIONnWe demonstrate that for particular applications--like Digital Subtraction Angiography--3D reconstructions are possible where conventional methods must fail, due to a severely limited imaging geometry. This could play an important role for dose reduction and 3D reconstruction using non-conventional technical setups.

Chromoendoscopy in magnetically guided capsule endoscopy

BackgroundDiagnosis of intestinal metaplasia and dysplasia via conventional endoscopy is characterized by low interobserver agreement and poor correlation with histopathologic findings. Chromoendoscopy significantly enhances the visibility of mucosa irregularities, like metaplasia and dysplasia mucosa. Magnetically guided capsule endoscopy (MGCE) offers an alternative technology for upper GI examination. We expect the difficulties of diagnosis of neoplasm in conventional endoscopy to transfer to MGCE. Thus, we aim to chart a path for the application of chromoendoscopy on MGCE via an ex-vivo animal study.MethodsWe propose a modified preparation protocol which adds a staining step to the existing MGCE preparation protocol. An optimal staining concentration is quantitatively determined for different stain types and pathologies. To that end 190 pig stomach tissue samples with and without lesion imitations were stained with different dye concentrations. Quantitative visual criteria are introduced to measure the quality of the staining with respect to mucosa and lesion visibility. Thusly determined optimal concentrations are tested in an ex-vivo pig stomach experiment under magnetic guidance of an endoscopic capsule with the modified protocol.ResultsWe found that the proposed protocol modification does not impact the visibility in the stomach or steerability of the endoscopy capsule. An average optimal staining concentration for the proposed protocol was found at 0.4% for Methylene blue and Indigo carmine. The lesion visibility is improved using the previously obtained optimal dye concentration.ConclusionsWe conclude that chromoendoscopy may be applied in MGCE and improves mucosa and lesion visibility. Systematic evaluation provides important information on appropriate staining concentration. However, further animal and human in-vivo studies are necessary.

Total Variation Regularization Method for 3D Rotational Coronary Angiography

3D rotational coronary angiography plays an important role in the field of diagnosis and treatment planning of coronary artery disease. Due to the cardiac motion, only limited number of projections can be used to reconstruct coronary arteries for each heart phase, which makes the reconstruction problem ill-posed. To reduce the under-sampling artifacts, we apply an iterative method that makes use of total variation regularization. Some different reconstruction algorithms are compared and our method outperforms the others in the experiments.

Localization and classification based on projections

Due to the loss of range information, projections as input data for a 3-D object recognition algorithm are expected to increase the computational complexity. In this work, however, we demonstrate that this deficiency carries potential for complexity reduction of major vision problems. We show that projections provide a reduction of feature dimensions, and lead to structures exhibiting simple combinatorial properties. The theoretical framework is embedded in a probabilistic setting which deals with uncertainties and variations of observed features. In statistics marginal densities and the assumption of independency prove to be the key tools when one encounters projections. The examples discussed in this paper include feature matching, pose estimation as well as classification of 3-D objects. The final experimental evaluation demonstrates the practical importance of the marginalization concept and independency assumptions.

Accurate regression-based 4D mitral valve surface reconstruction from 2D+t MRI slices

Cardiac MR (CMR) imaging is increasingly accepted as the gold standard for the evaluation of cardiac anatomy, function and mass. The multi-plan ability of CMR makes it a well suited modality for evaluation of the complex anatomy of the mitral valve (MV). However, the 2D slice-based acquisition paradigm of CMR limits the 4D capabilities for precise and accurate morphological and pathological analysis due to long through-put times and protracted study. In this paper we propose a new CMR protocol for acquiring MR images for 4D MV analysis. The proposed protocol is optimized regarding the number and spatial configuration of the 2D CMR slices. Furthermore, we present a learning- based framework for patient-specific 4D MV segmentation from 2D CMR slices (sparse data). The key idea with our Regression-based Surface Reconstruction (RSR) algorithm is the use of available MV models from other imaging modalities (CT, US) to train a dynamic regression model which will then be able to infer the absent information pertinent to CMR. Extensive experiments on 200 transesophageal echochardiographic (TEE) US and 20 cardiac CT sequences are performed to train the regression model and to define the CMR acquisition protocol. With the proposed acquisition protocol, a stack of 6 parallel long-axis (LA) planes, we acquired CMR patient images and regressed 4D patient-specific MV model with an accuracy of 1.5±0.2 mm and average speed of 10 sec per volume.

Computational decision support for percutaneous aortic valve implantation

Valve replacement is the most common therapy for diseased aortic valves. Percutaneous approaches are becoming increasingly popular, due to reduced procedural complications and lower follow-up rates. Still there is a lack of efficient tools for valve quantification and preoperative simulation of replacement and repair procedures. Thus the success of the intervention relies to a large portion on experience and skills of the operator. In this paper we propose a novel framework for preoperative planning, intraoperative guidance and post-operative assessment of percutaneous aortic valve replacement procedures with stent mounted devices. A comprehensive model of the aortic valvular complex including aortic valve and aorta ascendens is estimated with fast and robust learning-based techniques from cardiac CT images. Consequently our model is used to perform a in-silico delivery of the valve implant based on deformable simplex meshes and geometrical constraints. The predictive power of the model-based in-silico valve replacement was validated on 3D cardiac CT data from 20 patients through comparison of preoperative prediction against postoperatively imaged real device. In our experiments the method performed with an average accuracy of 2.18 mm and a speed of 55 seconds. To the best of our knowledge, this is the first time a computational framework is validated using real pre- and postoperative patient data.

Abstract: Robust Multi-Scale Anatomical Landmark Detection in Incomplete 3D-CT Data

An essential prerequisite for comprehensive medical image analysis is the robust and fast detection of anatomical structures in the human body. To this point, machine learning techniques are most often applied to address this problem, exploiting large annotated image databases to estimate parametric models for anatomy appearance. However, the performance of these methods is generally limited, due to suboptimal and exhaustive search strategies applied on large volumetric image data, e.g., 3D-CT scans.