Thin Plate Spline Robust Point Matching Research Articles

Modeling Complex Deformations of the Sigmoid Colon Between External Beam Radiation Therapy and Brachytherapy Images of Cervical Cancer

In this study, we investigated registration methods for estimating the large interfractional sigmoid deformations that occur between external beam radiation therapy (EBRT) and brachytherapy (BT) for cervical cancer. Sixty-three patients were retrospectively analyzed. The sigmoid colon was delineated on 2 computed tomography images acquired during EBRT (without applicator) and BT (with applicator) for each patient. Five registration approaches were compared to propagate the contour of the sigmoid from BT to EBRT anatomies: rigid registration, commercial hybrid (ANAtomically CONstrained Deformation Algorithm), controlling ROI surface projection of RayStation, and the classical and constrained symmetrical thin-plate spline robust point matching (sTPS-RPM) methods. Deformation of the sigmoid due to insertion of the BT applicator was reported. Registration performance was compared by using the Dice similarity coefficient (DSC), distance to agreement, and Hausdorff distance. The 2 sTPS-RPM methods were compared by using surface triangle quality criteria between deformed surfaces. Using the deformable approaches, the BT dose of the sigmoid was deformed toward the EBRT anatomy. The displacement and discrepancy between the deformable methods to propagate the planned D1cm3 and D2cm3 of the sigmoid from BT to EBRT anatomies were reported for 55 patients. Large and complex deformations of the sigmoid were observed for each patient. Rigid registration resulted in poor sigmoid alignment with a mean DSC of 0.26. Using the contour to drive the deformation, ANAtomically CONstrained Deformation Algorithm was able to slightly improve the alignment of the sigmoid with a mean DSC of 0.57. Using only the sigmoid surface as controlling ROI, the mean DSC was improved to 0.79. The classical and constrained sTPS-RPM methods provided mean DSCs of 0.95 and 0.96, respectively, with an average inverse consistency error <1 mm. The constrained sTPS-RPM provided more realistic deformations and better surface topology of the deformed sigmoids. The planned mean (range) D1cm3 and D2cm3 of the sigmoid were 13.4 Gy (1-24.1) and 12.2 Gy (1-21.5) on the BT anatomy, respectively. Using the constrained sTPS-RPM to deform the sigmoid from BT to EBRT anatomies, these hotspots had a mean (range) displacement of 27.1 mm (6.8-81). Large deformations of the sigmoid were observed between the EBRT and BT anatomies, suggesting that the D1cm3 and D2cm3 of the sigmoid would unlikely to be at the same position throughout treatment. The proposed constrained sTPS-RPM seems to be the preferred approach to manage the large deformation due to BT applicator insertion. Such an approach could be used to map the EBRT dose to the BT anatomy for personalized BT planning optimization.

Anatomical decomposition of human liver volume to build accurate statistical shape models

Liver is considered as a tissue with large shape variations. Representation of such a complex shape cannot be accurately performed using conventional SSM algorithms. We propose to decompose a human liver into its anatomical parts and use them as a guide when considering point correspondences. To cope with shape complexity, a modified coherent point drift (CPD) algorithm is proposed too. The modified CPD algorithm assigns fuzzy correspondences to points and follows a simulated annealing approach to convert fuzzy correspondences into binary ones. Our modification includes automatic parameter settings which results in robustness of the algorithm. The proposed algorithm was compared to the thin plate spline-robust point matching (TPS-RPM) and minimum description length (MDL) techniques. Our method is twice faster than the MDL algorithm. Compared to the TPS-RPM algorithm, our method improved mean Specificity of the right lobe by 0.09 and Compactness of the model by two less modes.

Accurate point correspondences using a modified coherent point drift algorithm

A crucial challenge of statistical shape modeling is to find corresponding points. The task is much more difficult especially in cases of objects with greater shape diversities (such as liver). In this paper, we propose a new fast algorithm to find corresponding points based on modified Coherent Point Drift technique which is comparable to the state-of-the-art “Minimum Description Length” (MDL) algorithm. Combining fuzzy correspondence and deterministic annealing method together with non-rigid registration of shapes helps to find corresponding points of different liver shapes. We optimized the algorithm parameters to prevent it from producing unacceptable results. Evaluation of the results was performed using Compactness, Generality, Specificity, and run-time measures. We compared our method using both conventional and state-of-the-art techniques including “Iterative Closest Point” (ICP), “Thin Plate Spline-Robust Point Matching” (TPS-RPM) and MDL. The performance of our method is superior to ICP and TPS-RPM algorithms and our results are close to the MDL results. The Generality of ICP, TPS-RPM, MDL and our method are 7.1±1.80, 3.78±0.96, 2.64±0.65 and 3.64±0.85 respectively. The Specificity of MDL and TPS-RPM is the same as ours (0.21±0.06) and the ICP stands in the fourth rank (0.30±0.18). The Compactness of ICP, TPS-RPM, MDL and our method are 23, 19, 16 and 18 respectively. The run-time of ICP, TPS-RPM, MDL and our method are 30, 390, 3600 and 68s. Contrary to the MDL, our algorithm does not trap into degenerate cases.

Validation of non-rigid point-set registration methods using a porcine bladder pelvic phantom

The problem of accurate dose accumulation in fractionated radiotherapy treatment for highly deformable organs, such as bladder, has garnered increasing interest over the past few years. However, more research is required in order to find a robust and efficient solution and to increase the accuracy over the current methods. The purpose of this study was to evaluate the feasibility and accuracy of utilizing non-rigid (affine or deformable) point-set registration in accumulating dose in bladder of different sizes and shapes. A pelvic phantom was built to house an ex vivo porcine bladder with fiducial landmarks adhered onto its surface. Four different volume fillings of the bladder were used (90, 180, 360 and 480 cc). The performance of MATLAB implementations of five different methods were compared, in aligning the bladder contour point-sets. The approaches evaluated were coherent point drift (CPD), gaussian mixture model, shape context, thin-plate spline robust point matching (TPS-RPM) and finite iterative closest point (ICP-finite). The evaluation metrics included registration runtime, target registration error (TRE), root-mean-square error (RMS) and Hausdorff distance (HD). The reference (source) dataset was alternated through all four points-sets, in order to study the effect of reference volume on the registration outcomes. While all deformable algorithms provided reasonable registration results, CPD provided the best TRE values (6.4 mm), and TPS-RPM yielded the best mean RMS and HD values (1.4 and 6.8 mm, respectively). ICP-finite was the fastest technique and TPS-RPM, the slowest.

Robust track-to-track association in the presence of sensor biases and missed detections

The paper addresses the problem of robust track-to-track association in the presence of sensor biases and missed detections. Under the condition of large range biases with sensors, it is validated that the structural difference between two sets of local tracks from different sensors can be described by a non-rigid transformation. After that, we turn the robust track-to-track association problem into the non-rigid point matching problem in the framework of TPS-RPM (Thin Plate Spline-Robust Point Matching). Further, to improve the performance of the track-to-track association, the structural feature is introduced for each local track, and the structural similarity is incorporated by regularizing the energy function of the TPS-RPM algorithm. Simulation results demonstrate the effectiveness of the proposed approaches compared with competing algorithms.

SU‐F‐BRF‐09: A Non‐Rigid Point Matching Method for Accurate Bladder Dose Summation in Cervical Cancer HDR Brachytherapy

Purpose:To propose and validate a deformable point matching scheme for surface deformation to facilitate accurate bladder dose summation for fractionated HDR cervical cancer treatment.Method:A deformable point matching scheme based on the thin plate spline robust point matching (TPSRPM) algorithm is proposed for bladder surface registration. The surface of bladders segmented from fractional CT images is extracted and discretized with triangular surface mesh. Deformation between the two bladder surfaces are obtained by matching the two meshes' vertices via the TPS‐RPM algorithm, and the deformation vector fields (DVFs) characteristic of this deformation is estimated by B‐spline approximation. Numerically, the algorithm is quantitatively compared with the Demons algorithm using five clinical cervical cancer cases by several metrics: vertex‐to‐vertex distance (VVD), Hausdorff distance (HD), percent error (PE), and conformity index (CI). Experimentally, the algorithm is validated on a balloon phantom with 12 surface fiducial markers. The balloon is inflated with different amount of water, and the displacement of fiducial markers is benchmarked as ground truth to study TPS‐RPM calculated DVFs' accuracy.Results:In numerical evaluation, the mean VVD is 3.7(±2.0) mm after Demons, and 1.3(±0.9) mm after TPS‐RPM. The mean HD is 14.4 mm after Demons, and 5.3mm after TPS‐RPM. The mean PE is 101.7% after Demons and decreases to 18.7% after TPS‐RPM. The mean CI is 0.63 after Demons, and increases to 0.90 after TPS‐RPM. In the phantom study, the mean Euclidean distance of the fiducials is 7.4±3.0mm and 4.2±1.8mm after Demons and TPS‐RPM, respectively.Conclusions:The bladder wall deformation is more accurate using the feature‐based TPS‐RPM algorithm than the intensity‐based Demons algorithm, indicating that TPS‐RPM has the potential for accurate bladder dose deformation and dose summation for multi‐fractional cervical HDR brachytherapy.This work is supported in part by the National Natural ScienceFoundation of China (no 30970866 and no 81301940).

MO‐C‐17A‐11: A Segmentation and Point Matching Enhanced Deformable Image Registration Method for Dose Accumulation Between HDR CT Images

Purpose:To propose and validate a novel and accurate deformable image registration (DIR) scheme to facilitate dose accumulation among treatment fractions of high‐dose‐rate (HDR) gynecological brachytherapy.Method:We have developed a method to adapt DIR algorithms to gynecologic anatomies with HDR applicators by incorporating a segmentation step and a point‐matching step into an existing DIR framework. In the segmentation step, random walks algorithm is used to accurately segment and remove the applicator region (AR) in the HDR CT image. A semi‐automatic seed point generation approach is developed to obtain the incremented foreground and background point sets to feed the random walks algorithm. In the subsequent point‐matching step, a feature‐based thin‐plate spline‐robust point matching (TPS‐RPM) algorithm is employed for AR surface point matching. With the resulting mapping, a DVF characteristic of the deformation between the two AR surfaces is generated by B‐spline approximation, which serves as the initial DVF for the following Demons DIR between the two AR‐free HDR CT images. Finally, the calculated DVF via Demons combined with the initial one serve as the final DVF to map doses between HDR fractions.Results:The segmentation and registration accuracy are quantitatively assessed by nine clinical HDR cases from three gynecological cancer patients. The quantitative results as well as the visual inspection of the DIR indicate that our proposed method can suppress the interference of the applicator with the DIR algorithm, and accurately register HDR CT images as well as deform and add interfractional HDR doses.Conclusions:We have developed a novel and robust DIR scheme that can perform registration between HDR gynecological CT images and yield accurate registration results. This new DIR scheme has potential for accurate interfractional HDR dose accumulation.This work is supported in part by the National Natural ScienceFoundation of China (no 30970866 and no 81301940).

Accurate CT/MR vessel‐guided nonrigid registration of largely deformed livers

Computer tomography (CT) scans are used for designing radiotherapy treatment plans. However, the tumor is often better visible in magnetic resonance (MR) images. For liver stereotactic body radiation therapy (SBRT), the planning CT scan is acquired while abdominal compression is applied to reduce tumor motion induced by breathing. However, diagnostic MR scans are acquired under voluntary breath-hold without the compression device. The resulting large differences in liver shape hinder the alignment of CT and MR image sets, which severely limits the integration of the information provided by these images. The purpose of the current study is to develop and validate a nonrigid registration method to align breath-hold MR images with abdominal-compressed CT images, using vessels that are automatically segmented within the liver. Contrast-enhanced MR and CT images of seven patients with liver cancer were used for this study. The registration method combines automatic vessel segmentation with an adapted version of thin-plate spline robust point matching. The vessel segmentation uses a multiscale vesselness measure, which allows vessels of various thicknesses to be segmented. The nonrigid registration is point-based, and progressively improves the correspondence and transformation between two point sets. Moreover, the nonrigid registration is capable of identifying and handling outliers (points with no counterpart in the other set). We took advantage of the strengths of both methods and created a multiscale registration algorithm. First, thick vessels are registered, then with each new iteration thinner vessels are included in the registration (strategy A). We compared strategy A to a straightforward approach where vessels of various diameters are segmented and subsequently registered (strategy B). To assess the transformation accuracy, residual distances were calculated for vessel bifurcations. For anatomical validation, residual distances were calculated for additional anatomical landmarks within the liver. To estimate the extent of deformation, the residual distances for the aforementioned anatomical points were calculated after rigid registration. Liver deformations in the range of 2.8-10.7 mm were found after rigid registration of the CT and MR scans. Low residual distances for vessel bifurcations (average 1.6, range 1.3-1.9 mm) and additional anatomical landmarks (1.5, 1.1-2.4 mm) were found after nonrigid registration. A large amount of outliers were identified (25%-55%) caused by vessels present in only one of the image sets and false positives in the vesselness measure. The nonrigid registration was capable of handling these outliers as was demonstrated by the low residual distances. Both strategies yielded very similar results in registration accuracy, but strategy A was faster than strategy B (≥2.0 times). An accurate CT∕MR vessel-guided nonrigid registration for largely deformed livers was developed, tested, and validated. The method, combining vessel segmentation and point matching, was robust against differences in the segmented vessels. The authors conclude that nonrigid registration is required for accurate alignment of abdominal-compressed and uncompressed liver anatomy. Alignment of breath-hold MR and abdominal-compressed CT images can be used to improve tumor localization for liver SBRT.

Analytic differential approach for robust registration of rat brain histological images

Image registration is an important topic in medical image analysis. It is usually used to reconstruct 3D structure of tissues from a series of microscopic images. However, a variety of inherent factors may result in great differences between acquired slices during imaging even if they are adjacent. The common differences include the color difference and geometry discrepancy, which make the registration problem a difficult challenge. In this study, we propose a robust registration method to automatically reconstruct 3D volume data of the rat brain. It mainly consists of three procedures, including multiscale wavelet-based feature extraction, analytic robust point matching (ARPM), and registration refinement with feature-based modified Levenberg-Marquardt algorithm (FMLM). The product of gradient moduli in multi-scales is used to decide if extracted feature points are true according to the characteristic that features could exist in multiscale. The ARPM registration algorithm is proposed to speedily accomplish the registration of two point sets with different size by simultaneously evaluating the spatial correspondence and geometrical transformation. In addition, a FMLM method is also proposed to further refine registration results and achieve subpixel accuracy. The FMLM method converges much faster than most other methods due to its feature-based and nonlinear characteristic. The performance of proposed method is evaluated by comparing it with well-known thin-plate spline robust point matching (TPS-RPM) algorithm. The results indicate that ARPM-FMLM algorithm is a robust and fast method in image registration.

A symmetric nonrigid registration method to handle large organ deformations in cervical cancer patients

Modern radiotherapy requires assessment of patient anatomical changes. By using unidirectional registration methods, the quantified anatomical changes are asymmetric, i.e., depend on the direction of the registration. Moreover, the registration is challenged by the large and complex organ deformations that can occur in, e.g., cervical cancer patients. The aim of this work was to develop, test, and validate a symmetric feature-based nonrigid registration method that can handle organs with large-scale deformations. A symmetric version of the unidirectional thin plate spline robust point matching (TPS-RPM) algorithm was developed, implemented, tested, and validated. Tests were performed by using the delineated cervix and uterus and bladder in CT scans of five cervical cancer patients. For each patient, five CT scans with a large variability in organ shape, volume, and deformations were acquired. Both the symmetric and the unidirectional algorithm were employed to calculate the registration geometric accuracy (surface distance and surface coverage errors), the inverse consistency, the residual distances after transforming anatomical landmarks, and the registration time. Additionally, to facilitate the further use of our symmetric method, a large set of input parameters was tested. The developed symmetric algorithm handled successfully the registration of bladders with extreme volume change for which TPS-RPM failed. Compared to the unidirectional algorithm the symmetric algorithm improved, for the registration of organs with large volume change, the inverse consistency by 78% and the surface coverage by 46%. Similarly, for organs with small volume change, the symmetric algorithm improved the inverse consistency by 69% and the surface coverage by 13%. The method allowed for anatomically coherent registration in only 35 s for cervix-uterus and 151 s for bladder, while keeping the inverse consistency errors around 1 mm and the surface matching errors below 1 mm. Compared to rigid alignment the symmetric method reduced the residual distances between anatomical landmarks from a range of 5.8 +/- 2-70.1 +/- 20.1 mm to a range of 1.9 +/- 0.2-8.5 +/- 5.2 mm. The developed symmetric method could be employed to perform fast, accurate, consistent, and anatomically coherent registration of organs with large and complex deformations. Therefore, the method is a useful tool that could support further developments in high precision image guided radiotherapy.

A novel flexible framework with automatic feature correspondence optimization for nonrigid registration in radiotherapy

Technical improvements in planning and dose delivery and in verification of patient positioning have substantially widened the therapeutic window for radiation treatment of cancer. However, changes in patient anatomy during the treatment limit the exploitation of these new techniques. To further improve radiation treatments, anatomical changes need to be modeled and accounted for Nonrigid registration can be used for this purpose. This article describes the design, the implementation, and the validation of a new framework for nonrigid registration for radiotherapy applications. The core of this framework is an improved version of the thin plate spline robust point matching (TPS-RPM) algorithm. The TPS-RPM algorithm estimates a global correspondence and a transformation between the points that represent organs of interest belonging to two image sets. However, the algorithm does not allow for the inclusion of prior knowledge on the correspondence of subset of points, and therefore, it can lead to inconsistent anatomical solutions. In this article TPS-RPM was improved by employing a novel correspondence filter that supports simultaneous registration of multiple structures. The improved method allows for coherent organ registration and for the inclusion of user-defined landmarks, lines, and surfaces inside and outside of structures of interest. A procedure to generate control points from segmented organs is described. The framework parameters r and lambda, which control the number of points and the nonrigidness of the transformation, respectively, were optimized for three sites with different degrees of deformation (head and neck, prostate, and cervix) using two cases per site. For the head and neck cases, the salivary glands were manually contoured on CT scans, for the prostate cases the prostate and the vesicles, and for the cervix cases the cervix uterus, the bladder, and the rectum. The transformation error obtained using the best set of parameters was below 1 mm for all the studied cases. The lengths of the deformation vectors were on average (+/- 1 standard deviation) 5.8 +/- 2.5 and 2.6 +/- 1.1 mm for the head and neck cases, 7.2 +/- 4.5 and 8.6 +/- 1.9 mm for the prostate cases, and 19.0 +/- 11.6 and 14.5 +/- 9.3 mm for the cervix cases. Distinguishable anatomical features were identified for each case and were used to validate the registration by calculating residual distances after transformation: 1.5 +/- 0.8, 2.3 +/- 1.0, and 6.3 +/- 2.9 mm for the head and neck, prostate, and cervix sites, respectively. Finally, the authors demonstrated how the inclusion of these anatomical features in the registration process reduced the residual distances to 0.8 +/- 0.5, 0.6 +/- 0.5, and 1.3 +/- 0.7 mm for the head and neck, prostate, and cervix sites, respectively. The inclusion of additional anatomical features produced more anatomically coherent transformations without compromising the transformation error. The authors concluded that the presented nonrigid registration framework is a powerful tool to simultaneously register multiple segmented organs with very different complexities.

The Use of Geometric Algebra for 3D Modeling and Registration of Medical Data

We present a new approach to model 2D surfaces and 3D volumetric data, as well as an approach for non-rigid registration; both are developed in the geometric algebra framework. The approach for modeling is based on marching cubes idea using however spheres and their representation in the conformal geometric algebra; it will be called marching spheres. Note that before we can proceed with the modeling, it is needed to segment the object we are interested in; therefore, we include an approach for image segmentation, which is based on texture and border information, developed in a region-growing strategy. We compare the results obtained with our modeling approach against the results obtained with other approach using Delaunay tetrahedrization, and our proposed approach reduces considerably the number of spheres. Afterward, a method for non-rigid registration of models based on spheres is presented. Registration is done in an annealing scheme, as in Thin-Plate Spline Robust Point Matching (TPS-RPM) algorithm. As a final application of geometric algebra, we track in real time objects involved in surgical procedures.