Regularization in Deformable Registration of Biomedical Images Based on Divergence and Curl Operators

Riyahi-Alam, S.; Peroni, M.; Baroni, Guido; Riboldi, Marco

doi:10.3414/me12-01-0109

Cited by 10 publications

(8 citation statements)

References 17 publications

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“…An Adaptive Stochastic Gradient Descent optimizer with pixel level step size was used to minimize a cost function (Equation 1) to obtain the transformation ( T ) between baseline ( I b ) and follow-up ( I f ) images:

C false(T, I_{b} ° I_{f} false) = C_{sim} + α C_{Reg}

where C sim was a similarity metric, C reg was a regularization term, and α was a weight that balanced the two terms. We used Sum of Square Difference (SSD) as C sim (Hill et al ) and bending energy of transformation (Equation 2) as C reg (Riyahi-Alam et al , 2014):

C_{Reg} = E_{bending} = true \iint true \int {(\frac{\partial^{2} T}{\partial x^{2}})}^{2} + {(\frac{\partial^{2} T}{\partial y^{2}})}^{2} + {(\frac{\partial^{2} T}{\partial z^{2}})}^{2} + {(\frac{\partial^{2} T}{\partial x \partial y})}^{2} + {(\frac{\partial^{2} T}{\partial x \partial z})}^{2} + {(\frac{\partial^{2} T}{\partial y \partial z})}^{2}

This function penalized discontinuity in DVF such as folding/tearing, but had no impact on sink (converging) and source (diverging) vectors which we intended to preserve. Converging vectors create a sink point that is mapped to many points in its vicinity and represents a morphological shrinkage.…”

Section: Methodsmentioning

confidence: 99%

Quantifying local tumor morphological changes with Jacobian map for prediction of pathologic tumor response to chemo-radiotherapy in locally advanced esophageal cancer

et al. 2018

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We proposed a framework to detect and quantify local tumor morphological changes due to chemo-radiotherapy (CRT) using Jacobian map and to extract quantitative radiomic features from the Jacobian map to predict the pathologic tumor response in locally advanced esophageal cancer patients. In 20 patients who underwent CRT, a multi-resolution BSpline deformable registration was performed to register the follow-up (post-CRT) CT to the baseline CT image. Jacobian map (J) was computed as the determinant of the gradient of the Deformation Vector Field. Jacobian map measured the ratio of local tumor volume change where J < 1 indicated tumor shrinkage and J > 1 denoted expansion. The tumor was manually delineated and corresponding anatomical landmarks were generated on the baseline and follow-up images. Intensity, texture and geometry features were then extracted from the Jacobian map of the tumor to quantify tumor morphological changes. The importance of each Jacobian feature in predicting pathologic tumor response was evaluated by both univariate and multivariate analysis. We constructed a multivariate prediction model by using a support vector machine (SVM) classifier coupled with a least absolute shrinkage and selection operator (LASSO) for feature selection. The SVM-LASSO model was evaluated using ten-times repeated 10-fold cross-validation (10×10-fold CV). After registration, the average Target Registration Error was 4.30±1.09mm (LR:1.63mm AP:1.59mm SI:3.05mm) indicating registration error was within two voxels and close to 4mm slice thickness. Visually, Jacobian map showed smoothly-varying local shrinkage and expansion regions in a tumor. Quantitatively, the average Median Jacobian was 0.80±0.10 and 1.05±0.15 for responder and non-responder tumors, respectively. These indicated that on average responder tumors had 20% median volume shrinkage while non-responder tumors had 5% median volume expansion. In univariate analysis, Minimum Jacobian (p=0.009, AUC=0.98) and Median Jacobian (p=0.004, AUC=0.95) were the most significant predictors. The SVM-LASSO model achieved the highest accuracy when these two features were selected (Sensitivity=94.4%, Specificity=91.8%, AUC=0.94). Novel features extracted from the Jacobian map quantified local tumor morphological changes using only baseline tumor contour without post-treatment tumor segmentation. The SVM-LASSO model using Median Jacobian and Minimum Jacobian achieved high accuracy in predicting pathologic tumor response. Jacobian map showed great potential for longitudinal evaluation of tumor response.

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C false(T, I_{b} ° I_{f} false) = C_{sim} + α C_{Reg}

C_{Reg} = E_{bending} = true \iint true \int {(\frac{\partial^{2} T}{\partial x^{2}})}^{2} + {(\frac{\partial^{2} T}{\partial y^{2}})}^{2} + {(\frac{\partial^{2} T}{\partial z^{2}})}^{2} + {(\frac{\partial^{2} T}{\partial x \partial y})}^{2} + {(\frac{\partial^{2} T}{\partial x \partial z})}^{2} + {(\frac{\partial^{2} T}{\partial y \partial z})}^{2}

Section: Methodsmentioning

confidence: 99%

Quantifying local tumor morphological changes with Jacobian map for prediction of pathologic tumor response to chemo-radiotherapy in locally advanced esophageal cancer

et al. 2018

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“…In order to analyze how physically logic the registration method is, an application to obtain a minimum Jacobian determinant of the transformation (deformation field) for each warped frame of the sequences is implemented [5]. This metric investigates on the singularities of the DF.…”

Section: Dat Registration Evaluation Methodsmentioning

confidence: 99%

“…Depending on the type of a transformation function, it is referred to as a linear or deformable registration [5].…”

Section: Introductionmentioning

confidence: 99%

Comparison of time-series registration methods in breast dynamic infrared imaging

Riyahi-Alam

Agostini

Molinari

et al. 2015

Opto-Electronics Review

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Automated motion reduction in dynamic infrared imaging is on demand in clinical applications, since movement disarranges time−temperature series of each pixel, thus originating thermal artifacts that might bias the clinical decision. All previously proposed registration methods are feature based algorithms requiring manual intervention. The aim of this work is to optimize the registration strategy specifically for Breast Dynamic Infrared Imaging and to make it user−independent. We implemented and evaluated 3 different 3D time−series registration methods: 1. Linear affine, 2. Non−linear Bspline, 3. Demons applied to 12 datasets of healthy breast thermal images. The results are evaluated through normalized mutual information with average values of 0.70 ±0.03, 0.74 ±0.03 and 0.81 ±0.09 (out of 1) for Affine, Bspline and Demons registration, respectively, as well as breast boundary overlap and Jacobian determinant of the deformation field. The statistical analysis of the results showed that symmetric diffeomorphic Demons’ registration method outperforms also with the best breast alignment and non−negative Jacobian values which guarantee image similarity and anatomical consistency of the transformation, due to homologous forces enforcing the pixel geometric disparities to be shortened on all the frames. We propose Demons’ registration as an effective technique for time−series dynamic infrared registration, to stabilize the local temperature oscillation.

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“…Studies have assessed the accuracy of DIR algorithms using digital phantoms, (10) physically deforming phantoms, (11) mathematical descriptors, 12 , 13 and clinical CT scans 14 , 15 , 16 . Digital (10) or physically deforming phantom studies, (11) while useful, may lack clinical complexity.…”

Section: Introductionmentioning

confidence: 99%

“…Digital (10) or physically deforming phantom studies, (11) while useful, may lack clinical complexity. Mathematical descriptors, such as curl and the Jacobian, have been proposed as useful metrics to quantify the deformation vector field 12 , 13 . Though such descriptors could be beneficial in the future, they are untested clinically and lack intuitive clinical meaning.…”

Section: Introductionmentioning

confidence: 99%

Deformable image registration and interobserver variation in contour propagation for radiation therapy planning

Riegel

Antone

Zhang

et al. 2016

J Applied Clin Med Phys

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Deformable image registration (DIR) and interobserver variation inevitably introduce uncertainty into the treatment planning process. The purpose of the current work was to measure deformable image registration (DIR) errors and interobserver variability for regions of interest (ROIs) in the head and neck and pelvic regions. Measured uncertainties were combined to examine planning margin adequacy for contours propagated for adaptive therapy and to assess the trade‐off of DIR and interobserver uncertainty in atlas‐based automatic segmentation. Two experienced dosimetrists retrospectively contoured brainstem, spinal cord, anterior oral cavity, larynx, right and left parotids, optic nerves, and eyes on the planning CT (CT1) and attenuation‐correction CT of diagnostic PET/CT (CT2) for 30 patients who received radiation therapy for head and neck cancer. Two senior radiation oncology residents retrospectively contoured prostate, bladder, and rectum on the postseed‐implant CT (CT1) and planning CT (CT2) for 20 patients who received radiation therapy for prostate cancer. Interobserver variation was measured by calculating mean Hausdorff distances between the two observers' contours. CT2 was deformably registered to CT1 via commercially available multipass B‐spline DIR. CT2 contours were propagated and compared with CT1 contours via mean Hausdorff distances. These values were summed in quadrature with interobserver variation for margin analysis and compared with interobserver variation for statistical significance using two‐tailed t‐tests for independent samples (α=0.05). Combined uncertainty ranged from 1.5‐5.8 mm for head and neck structures and 3.1‐3.7 mm for pelvic structures. Conventional 5 mm margins may not be adequate to cover this additional uncertainty. DIR uncertainty was significantly less than interobserver variation for four head and neck and one pelvic ROI. DIR uncertainty was not significantly different than interobserver variation for four head and neck and one pelvic ROI. DIR uncertainty was significantly greater than interobserver variation for two head and neck and one pelvic ROI. The introduction of DIR errors may offset any reduction in interobserver variation by using atlas‐based automatic segmentation.PACS number(s): 87.57.nj, 87.55.D‐

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Regularization in Deformable Registration of Biomedical Images Based on Divergence and Curl Operators

Abstract: The implemented divergence/curl regularization was successfully tested, leading to promising results in comparison with competitive regularization methods. Future work is required to establish parameter tuning and reduce the computational cost.

Cited by 10 publications

References 17 publications

Quantifying local tumor morphological changes with Jacobian map for prediction of pathologic tumor response to chemo-radiotherapy in locally advanced esophageal cancer

Quantifying local tumor morphological changes with Jacobian map for prediction of pathologic tumor response to chemo-radiotherapy in locally advanced esophageal cancer

Comparison of time-series registration methods in breast dynamic infrared imaging

Deformable image registration and interobserver variation in contour propagation for radiation therapy planning

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