Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape

We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing

Extracting 3D parametric curves from 2D images of Helical objects

Helical objects occur in medicine, biology, cosmetics, nanotechnology, and engineering. Extracting a 3D parametric curve from a 2D image of a helical object has many practical applications, in particular being able to extract metrics such as tortuosity, frequency, and pitch. We present a method that is able to straighten the image object and derive a robust 3D helical curve from peaks in the object boundary. The algorithm has a small number of stable parameters that require little tuning, and the curve is validated against both synthetic and real-world data. The results show that the extracted 3D curve comes within close Hausdorff distance to the ground truth, and has near identical tortuosity for helical objects with a circular profile. Parameter insensitivity and robustness against high levels of image noise are demonstrated thoroughly and quantitatively

Stochastic Distance Transform

The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the DT, which is highly sensitive to spurious noise points. In this study, we consider images represented as discrete random sets and observe statistics of DT computed on such representations. We, thus, define a stochastic distance transform (SDT), which has an adjustable robustness to noise. Both a stochastic Monte Carlo method and a deterministic method for computing the SDT are proposed and compared. Through a series of empirical tests, we demonstrate that the SDT is effective not only in improving the accuracy of the computed distances in the presence of noise, but also in improving the performance of template matching and watershed segmentation of partially overlapping objects, which are examples of typical applications where DTs are utilized.Comment: 12 pages, 4 figures, 3 table

Tomography: mathematical aspects and applications

In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford-Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.Comment: 11 pages, 5 figure

Multi-atlas segmentation in head and neck CT scans

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 45-46).We investigate automating the task of segmenting structures in head and neck CT scans, to minimize time spent on manual contouring of structures of interest. We focus on the brainstem and left and right parotids. To generate contours for an unlabeled image, we employ an atlas of labeled training images. We register each of these images to the unlabeled target image, transform their structures, and then use a weighted voting method for label fusion. Our registration method starts with multi-resolution translational alignment, then applies a relatively higher resolution affine alignment. We then employ a diffeomorphic demons registration to deform each atlas to the space of the target image. Our weighted voting method considers one structure at a time to determine for each voxel whether or not it belongs to the structure. The weight for a voxel's vote from each atlas depends on the intensity difference of the target and the transformed gray scale atlas image at that voxel, in addition to the distance of that voxel from the boundary of the structure. We evaluate the method on a dataset of sixteen labeled images, generating automatic segmentations for each using the other fifteen images as the atlas. We evaluated the weighted voting method and a majority voting method by comparing the resulting segmentations to the manual segmentations using a volume overlap metric and the distances between contours. Both methods produce accurate segmentations, our method producing contours with boundaries usually only a few millimeters away from the manual contour. This could save physicians considerable time, because they only have to make small modifications to the outline instead of contouring the entire structure.by Amelia M. Arbisser.M.Eng

Evaluation of Image Registration Accuracy for Tumor and Organs at Risk in the Thorax for Compliance With TG 132 Recommendations

Purpose To evaluate accuracy for 2 deformable image registration methods (in-house B-spline and MIM freeform) using image pairs exhibiting changes in patient orientation and lung volume and to assess the appropriateness of registration accuracy tolerances proposed by the American Association of Physicists in Medicine Task Group 132 under such challenging conditions via assessment by expert observers. Methods and Materials Four-dimensional computed tomography scans for 12 patients with lung cancer were acquired with patients in prone and supine positions. Tumor and organs at risk were delineated by a physician on all data sets: supine inhale (SI), supine exhale, prone inhale, and prone exhale. The SI image was registered to the other images using both registration methods. All SI contours were propagated using the resulting transformations and compared with physician delineations using Dice similarity coefficient, mean distance to agreement, and Hausdorff distance. Additionally, propagated contours were anonymized along with ground-truth contours and rated for quality by physician-observers. Results Averaged across all patients, the accuracy metrics investigated remained within tolerances recommended by Task Group 132 (Dice similarity coefficient \u3e0.8, mean distance to agreement \u3c3 \u3emm). MIM performed better with both complex (vertebrae) and low-contrast (esophagus) structures, whereas the in-house method performed better with lungs (whole and individual lobes). Accuracy metrics worsened but remained within tolerances when propagating from supine to prone; however, the Jacobian determinant contained regions with negative values, indicating localized nonphysiologic deformations. For MIM and in-house registrations, 50% and 43.8%, respectively, of propagated contours were rated acceptable as is and 8.2% and 11.0% as clinically unacceptable. Conclusions The deformable image registration methods performed reliably and met recommended tolerances despite anatomically challenging cases exceeding typical interfraction variability. However, additional quality assurance measures are necessary for complex applications (eg, dose propagation). Human review rather than unsupervised implementation should always be part of the clinical registration workflow