Dragan Tubic

Automated seed detection and three-dimensional reconstruction. II. Reconstruction of permanent prostate implants using simulated annealing

We present an algorithm, based on simulated annealing, for automatic seed matching and three-dimensional spatial coordinate reconstruction using either three radiographic films or three fluoroscopic images taken from different perspectives. The matching problem is defined in the framework of combinatorial optimization, which allows robust reconstruction in presence of calibration imprecision, patient movements, and isometric distortions. Furthermore, by using a global criterion to select the correct matching, we evade common problems of the three-film method and its variants in presence of noise. The algorithm has been tested on 112 clinical cases and 100 simulated implants and used clinically on more than 100 cases. Simulated implants were reconstructed with an average error of 0.21 mm. For clinical cases, comparison of the precision is performed between results obtained with this new method and results obtained using the three-film technique. Compared to the latter technique, the reconstruction precision was improved in 62% of the clinical cases.

Automated seed detection and three-dimensional reconstruction. I. Seed localization from fluoroscopic images or radiographs

An automated procedure for the detection of the position and the orientation of radioactive seeds on fluoroscopic images or scanned radiographs is presented. The extracted positions of seed centers and the orientations are used for three-dimensional reconstruction of permanent prostate implants. The extraction procedure requires several steps: correction of image intensifier distortions, normalization, background removal, automatic threshold selection, thresholding, and finally, moment analysis and classification of the connected components. The algorithm was tested on 75 fluoroscopic images. The results show that, on average, 92% of the seeds are detected automatically. The orientation is found with an error smaller than 50 for 75% of the seeds. The orientation of overlapping seeds (10%) should be considered as an estimate at best. The image processing procedure can also be used for seed or catheter detection in CT images, with minor modifications.

Octree indexing of DICOM images for voxel number reduction and improvement of Monte Carlo simulation computing efficiency.

The purpose of the present study is to introduce a compression algorithm for the CT (computed tomography) data used in Monte Carlo simulations. Performing simulations on the CT data implies large computational costs as well as large memory requirements since the number of voxels in such data reaches typically into hundreds of millions voxels. CT data, however, contain homogeneous regions which could be regrouped to form larger voxels without affecting the simulations accuracy. Based on this property we propose a compression algorithm based on octrees: in homogeneous regions the algorithm replaces groups of voxels with a smaller number of larger voxels. This reduces the number of voxels while keeping the critical high-density gradient area. Results obtained using the present algorithm on both phantom and clinical data show that compression rates up to 75% are possible without losing the dosimetric accuracy of the simulation.

Sliding slice: A novel approach for high accuracy and automatic 3D localization of seeds from CT scans

We present a conceptually novel principle for 3D reconstruction of prostate seed implants. Unlike existing methods for implant reconstruction, the proposed algorithm uses raw CT data (sinograms) instead of reconstructed CT slices. Using raw CT data solves several inevitable problems related to the reconstruction from CT slices. First, the sinograms are not affected by reconstruction artifacts in the presence of metallic objects and seeds in the patient body. Second, the scanning axis is not undersampled as in the case of CT slices; as a matter of fact the scanning axis is the most densely sampled and each seed is typically represented by several hundred samples. Moreover, the shape of a single seed in a sinogram can be modeled exactly, thus facilitating the detection. All this allows very accurate 3D reconstruction of both position and the orientation of the seeds. Preliminary results indicate that the seed position can be estimated with 0.15 mm accuracy (average), while the orientation estimate accuracy is within 3 deg on average. Although the main contribution of the paper is to present a new principle of reconstruction, a preliminary implementation is also presented as a proof of concept. The implemented algorithm has been tested on a phantom and the obtained results are presented to validate the proposed approach.

A volumetric approach for interactive 3D modeling

Range image registration and surface reconstruction have been traditionally considered as two independent processes where the latter relies on the results of the former. This paper presents a new approach to surface recovery from range images where the two processes are unified and performed in a common volumetric representation. While the reconstructed surface is described in its implicit form as a signed distance field within a volume, registration information for matching partial surfaces is encoded in the same volume as the gradient of the distance field. This allows coupling of both reconstruction and registration and leads to an algorithm whose complexity is linear with respect to the number of images and the number of measured 3D points. The close integration and performance gain improve interactivity in the process of modeling from range image acquisition to surface reconstruction. The distances computed in the direction of filtered normals improve robustness while preserving the sharp details of the initial range images. It is shown that the integrated algorithm is tolerant to initial registration errors as well as to measurement errors. The paper describes the representation and formalizes the approach. Experimental results demonstrate performance advantages and tolerance to aforementioned types of errors.

A unified representation for interactive 3D modeling

Interactive 3D modeling is the process of building a 3D model of an object or a scene in real-time while the 3D (range) data is acquired. This is possible only if the computational complexity of all involved algorithms is linear with respect to the amount of data. We propose a new framework for 3D modeling where a complete modeling chain meets with this requirement. The framework is based on the use of vector fields as an implicit surface representation. Each modeling step, registration, surface reconstruction, geometric fusion, compression and visualization is solved and explained using the vector fields without any intermediate representations. The proposed framework allows model reconstruction from any type of 3D data, surface patches, curves, unorganized sets of points or a combination of these.

Automatic post-implant needle reconstruction algorithm to characterize and improve implant robustness analyses.

Post-implant analysis in permanent implant brachytherapy is an important process that provides a feedback on treatment quality. Random seed movements, edema, and needle related factors contribute to deteriorate dose coverage. For a complete study of these movements, it is important to reconstruct the post-implant seeds clusters but, up to now, this task was only possible via a long and difficult manual process. To facilitate post-implant analysis a simulated annealing algorithm was developed to perform automatic reconstructions. This process is fast (30-60 s on a 1.3 GHz pentium) and has a high level of success, even with up to 5% of seed loss. Tests on 21 clinical cases show that the algorithm yields exactly the same results as manual reconstructions. A realistic simulation tool was used to generate 58 synthetic post-implant data, in which cases the exact configuration was known. Even if some errors were found, pertinent information was extracted. For medium seed density [corresponding to seeds of 0.6 mCi (0.762 U)], 97% of seeds are matched with their correct needle and 89% are matched with their correct planned position. This method provides pertinent information that can be used to understand inhomogenous dose coverage in specific prostate quadrants; to make realistic post-implant simulations or to identify seeds belonging to a needle loaded with different seed types or activity.

3D surface modeling from range curves

Traditional approaches for surface reconstruction from range data require that the input data be either range images or unorganized sets of points. Since a large number of range sensors provide data along curvilinear patterns such as profiles, this paper presents an approach for reconstructing a surface from a set of unorganized curves. A strategy for updating the reconstructed surface during data acquisition is described as well. Curves are accumulated in a volumetric structure in which a vector field is built and updated. The information that is needed for efficient curve registration is also directly available in this vector field. This leads to a unified modeling approach combining surface reconstruction and curve registration. The algorithm implementing the approach is of linear complexity with respect to the number of input curves and makes it suitable for interactive modeling. Simulated data based on a set of six curvilinear patterns as well as data acquired with a range sensor are used to illustrate the various steps of the algorithm.

3D Surface Modeling from Curves

Traditional approaches for surface reconstruction from range data require that the input data be either range images or unorganized sets of points. With these methods, range data acquired along curvilinear patterns cannot be used for surface reconstruction unless constraints are imposed on the shape of the patterns or on sensor displacement. This paper presents a novel approach for reconstructing a surface from a set of arbitrary, unorganized and intersecting curves. A strategy for updating the reconstructed surface during data acquisition is described as well. Curves are accumulated in a volumetric structure in which a vector field is built and updated. The information that is needed for efficient curve registration is also directly available in the vector field. The proposed modeling approach combines surface reconstruction and curve registration into a unified procedure. The algorithm implementing the approach is of linear complexity with respect to the number of input curves and makes it suitable for interactive modeling. Simulated data based on a set of six curvilinear patterns as well as data acquired with a range sensor are used to illustrate the various steps of the algorithm.

A volumetric approach for the registration and integration of range images: towards interactive modeling systems

This paper presents a new approach for registering and integrating range images where these two processes are merged and performed in a common volumetric representation. The proposed approach allows both simultaneous and incremental registration where matching complexity is linear with respect to the number of images. This improvement leads to incremental modeling from range image acquisition to surface reconstruction. It is shown that the approach is tolerant to initial registration errors as well as to measurement errors while keeping the details of the initial range images. The paper describes the formalism of the approach. Experimental results demonstrate the performance advantages and tolerance to aforementioned types of errors for free form objects.