Exact Geosedics and Shortest Paths on Polyhedral Surface

We present two algorithms for computing distances along a non-convex polyhedral surface. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimalgeodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.National Institute for Biomedical Imaging and Bioengineering (R01 EB001550

ANATOMICAL LOCALIZATION OF DEEP INFILTRATING ENDOMETRIOSIS: 3D MRI RECONSTRUCTIONS

1. Abstract Purpose The goal of this study was to determine the accuracy of 3D MRI reconstructions obtained with segmentation technique in the preoperative assessment of deep infiltrating endometriosis (DIE) and in particular to evaluate rectosigmoid and bladder wall involvement. Materials and methods Institutional review board approval for this study was obtained, and each patient gave written informed consent. Fifty-seven consecutive patients with diagnosis of DIE who had undergone pelvic MRI at 1.5 T before surgery between 2007 and 2011, were retrospectively evaluated and 3D post-processed in order to obtain a detailed mapping of DIE. A blinded reader interpreted images. MRI results were compared with surgical findings and were scored by using a four-point scale (0_3 score). Results 36/57 patients with symptomatic DIE underwent surgery: 18/36 had endometriotic nodules infiltrating the recto-uterine pouch, 12/36 the vescico-uterine pouch and 6/36 the rectovaginal pouch. The sensitivity of MRI and 3D-MRI versus surgery was respectively 64% versus 83%; diagnostic accuracy of 3D-MRI respect to MRI alone was 86% versus 67% for localization; 86% versus 67% for dimension; 79% versus 58% for rectosigmoid infiltration; 92% versus 75% for bladder infiltration. Conclusions In this preliminary study 3D MRI reconstructions obtained with semi-automatic method of segmentation provided encouraging results for staging DIE preoperatively. In fact, the addition of 3D MRI reconstructions improved diagnostic accuracy and staging of DIE providing the exact volume of the lesions and enabling a precise mapping of these before surgery. Key words: Endometriosis; MRI; 3D reconstructions; semi-automatic segmentation; wall infiltration; laparoscopyc or robotic surgery

Constructing morphometric profiles along the human brain cortex using in vivo Magnetic Resonance Imaging (MRI)

The geometry of the brain cortex is comprised of gyri (outward folds) and sulci (inward folds). Several biological properties about the anatomy and physiology of the brain cortex have been measured at the top of the sulci and at the bottom of the gyri; however, no one has yet measured how the values of these properties (called biomarkers) change along the path joining the top of the sulci and the bottom of the gyri. In this work, a methodology to display that information is shown, using different modalities of MRI images as input. There are four main steps to the methodology: the first two consist on obtaining the lines that run on top of the gyri and at the bottom of the sulci, while the next two make use of these lines to create a geodesic path between the top of the gyri and the bottom of the sulci and assigning biomarker values to each point of this geodesic path. The results of this work are composed of the validation of the methodology and three examples of possible applications of the methodology. These applications could be applied in future work to improve the detection and study the neurodevelopment of neurodegenerative diseases.Ingeniería Biomédic

Statistical Study on Cortical Sulci of Human Brains

Abstract. A method for building a statistical shape model of sulci of the human brain cortex is described. The model includes sulcal fundi that are defined on a spherical map of the cortex. The sulcal fundi are first extracted in a semi-automatic way using an extension of the fast march-ing method. They are then transformed to curves on the unit sphere via a conformal mapping method that maps each cortical point to a point on the unit sphere. The curves that represent sulcal fundi are parameterized with piecewise constant-speed parameterizations. Intermediate points on these curves correspond to sulcal landmarks, which are used to build a point distribution model on the unit sphere. Statistical information of local properties of the sulci, such as curvature and depth, are embedded in the model. Experimental results are presented to show how the models are built.

3D minutiae extraction in 3D fingerprint scans.

Traditionally, fingerprint image acquisition was based on contact. However the conventional touch-based fingerprint acquisition introduces some problems such as distortions and deformations to the fingerprint image. The most recent technology for fingerprint acquisition is touchless or 3D live scans introducing higher quality fingerprint scans. However, there is a need to develop new algorithms to match 3D fingerprints. In this dissertation, a novel methodology is proposed to extract minutiae in the 3D fingerprint scans. The output can be used for 3D fingerprint matching. The proposed method is based on curvature analysis of the surface. The method used to extract minutiae includes the following steps: smoothing; computing the principal curvature; ridges and ravines detection and tracing; cleaning and connecting ridges and ravines; and minutiae detection. First, the ridges and ravines are detected using curvature tensors. Then, ridges and ravines are traced. Post-processing is performed to obtain clean and connected ridges and ravines based on fingerprint pattern. Finally, minutiae are detected using a graph theory concept. A quality map is also introduced for 3D fingerprint scans. Since a degraded area may occur during the scanning process, especially at the edge of the fingerprint, it is critical to be able to determine these areas. Spurious minutiae can be filtered out after applying the quality map. The algorithm is applied to the 3D fingerprint database and the result is very encouraging. To the best of our knowledge, this is the first minutiae extraction methodology proposed for 3D fingerprint scans

A Second Order Variational Approach For Diffeomorphic Matching Of 3D Surfaces

In medical 3D-imaging, one of the main goals of image registration is to accurately compare two observed 3D-shapes. In this dissertation, we consider optimal matching of surfaces by a variational approach based on Hilbert spaces of diffeomorphic transformations. We first formulate, in an abstract setting, the optimal matching as an optimal control problem, where a vector field flow is sought to minimize a cost functional that consists of the kinetic energy and the matching quality. To make the problem computationally accessible, we then incorporate reproducing kernel Hilbert spaces with the Gaussian kernels and weighted sums of Dirac measures. We propose a second order method based the Bellman's optimality principle and develop a dynamic programming algorithm. We apply successfully the second order method to diffeomorphic matching of anterior leaflet and posterior leaflet snapshots. We obtain a quadratic convergence for data sets consisting of hundreds of points. To further enhance the computational efficiency for large data sets, we introduce new representations of shapes and develop a multi-scale method. Finally, we incorporate a stretching fraction in the cost function to explore the elastic model and provide a computationally feasible algorithm including the elasticity energy. The performance of the algorithm is illustrated by numerical results for examples from medical 3D-imaging of the mitral valve to reduce excessive contraction and stretching.Mathematics, Department o

Ridges and umbilics of a sampled smooth surface: a complete picture gearing toward topological coherence

Consider a smooth surface, and at each point which is not an umbilic, respectively paint in blue (red) anything related to the maximum (minimum) principal curvature. Given such a surface, a blue (red) ridge is a curve on the surface such that at each of its points, the principal blue (red) curvature has an extremum along its blue (red) curvature line. Ridges are curves of extremal curvature and therefore encode important informations used in segmentation, registration, matching and surface analysis. Surprisingly, no method developed so far to report ridges from a mesh approximating a smooth surface comes with a careful analysis, which entails that one does not know whether the ridges are reported in a coherent fashion. This paper aims at bridging this gap with the following contributions. First, a careful analysis of the Acute rule - an orientation procedure used in most algorithms - is presented. Second, given a triangulation $T$ approximating a smooth generic surface $S$, we present sufficient conditions on $T$ together with a certified algorithm reporting ridges in a topologically coherent fashion. Third, we develop an algorithm and a filtering procedure aiming at reporting the most salient features of a coarse mesh $T$

Shape analysis of the human brain.

Autism is a complex developmental disability that has dramatically increased in prevalence, having a decisive impact on the health and behavior of children. Methods used to detect and recommend therapies have been much debated in the medical community because of the subjective nature of diagnosing autism. In order to provide an alternative method for understanding autism, the current work has developed a 3-dimensional state-of-the-art shape based analysis of the human brain to aid in creating more accurate diagnostic assessments and guided risk analyses for individuals with neurological conditions, such as autism. Methods: The aim of this work was to assess whether the shape of the human brain can be used as a reliable source of information for determining whether an individual will be diagnosed with autism. The study was conducted using multi-center databases of magnetic resonance images of the human brain. The subjects in the databases were analyzed using a series of algorithms consisting of bias correction, skull stripping, multi-label brain segmentation, 3-dimensional mesh construction, spherical harmonic decomposition, registration, and classification. The software algorithms were developed as an original contribution of this dissertation in collaboration with the BioImaging Laboratory at the University of Louisville Speed School of Engineering. The classification of each subject was used to construct diagnoses and therapeutic risk assessments for each patient. Results: A reliable metric for making neurological diagnoses and constructing therapeutic risk assessment for individuals has been identified. The metric was explored in populations of individuals having autism spectrum disorders, dyslexia, Alzheimers disease, and lung cancer. Conclusion: Currently, the clinical applicability and benefits of the proposed software approach are being discussed by the broader community of doctors, therapists, and parents for use in improving current methods by which autism spectrum disorders are diagnosed and understood