Multiscale Image Registration

Paquin, Dana C.; Levy, Doron; Schreibmann, Eduard; Liu, Xing

doi:10.3934/mbe.2006.3.389

Cited by 29 publications

(3 citation statements)

References 18 publications

(26 reference statements)

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“…The multiple DWI samples acquired at each b -value were averaged together. To correct for patient motion between the two separately-acquired DWI volumes of cohort 1, multiscale image registration by intensity correlation was applied (14). To account for arbitrary signal-intensity scaling between acquisitions, all DWI volumes were normalized by the median signal intensity of urine in the bladder at b =0 s/mm 2 (15).…”

Section: Methodsmentioning

confidence: 99%

Background prostate tissue is quantitatively abnormal on MRI in patients with clinically significant prostate cancer

Conlin

Karunamuni

Hussain

et al. 2022

Preprint

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Background:T2-weighted MRI is well established for detection of clinically significant prostate cancer (csPCa), but prior studies have primarily focused onT2within MRI-visible lesions.Purpose:To determine whether patients with csPCa have systematically abnormalT2-weighted signal in non-lesion, background prostate tissue (BP).Materials and Methods:This retrospective study included two patient cohorts who underwent 3T MRI examination for suspected csPCa between August 2016 and February 2020. Median (urine-normalized)T2-weighted signal was computed for BP. BP signal was compared between patients with and without csPCa, using two-samplet-tests (α=0.05). csPCa discrimination performance ofT2-weighted BP signal was evaluated using area under receiver operating characteristic curves (AUC).T2andS0(a proxy for proton density) were computed and compared between patients with and without csPCa using two-samplet-tests (α=0.05).T2was also recomputed with larger buffers around csPCa lesions. Finally, csPCa discrimination performance was compared between two predictors: maximum Restriction Spectrum Imaging (RSI)C1and maximum RSIC1normalized by global prostate medianT2-weighted signal.Results:Cohort 1: 46 patients (mean age: 64 years ±10 [standard deviation]). Cohort 2: 151 patients (age: 65±8 years). Urine-normalizedT2-weighted signal was systematically lower in BP of subjects with csPCa compared to those without (p≤0.034). BPT2-weighted signal indicated the presence of cancer (cohort 1: AUC=0.80; cohort 2: AUC=0.68). BPT2was significantly lower in csPCa patients compared to those without (p≤0.011), whileS0was not (p≥0.30). BPT2measurements were stable to within 5% using a buffer of 0 to 30 mm around visible csPCa lesions. csPCa discrimination improved with incorporation of global prostate medianT2-weighted signal (cohort 1: AUC=0.72 for maximum RSIC1alone versus 0.81 when normalized by medianT2-weighted signal; cohort 2: AUC=0.63 versus 0.76).Conclusion:LowerT2-weighted signal in BP suggests the presence of csPCa.

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Section: Methodsmentioning

confidence: 99%

Background prostate tissue is quantitatively abnormal on MRI in patients with clinically significant prostate cancer

Conlin

Karunamuni

Hussain

et al. 2022

Preprint

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“…U to survive the L 2;1 -based nonlinearity result argued in the proof of [7, prop. Hierarchical decompositions in this context of images were introduced by us in [35] and were found to be effective tools in image denoising, image deblurring, and image registration, [5,10,21,31,32,36,38], including graph-based signals [19,20]. Thus, the nonlinear aspect of constructing hierarchical solutions for (4.1) becomes essential for highly oscillatory functions such that f 2 L 2 nL 2;1 (and in particular, f … BV.T 2 /).…”

Section: Construction Of Hierarchical Solutions In Critical Regularitmentioning

confidence: 99%

“…Such f 's are encountered in image processing in the form of noise, texture, and blurry images [10,27]. Hierarchical decompositions in this context of images were introduced by us in [35] and were found to be effective tools in image denoising, image deblurring, and image registration, [5,10,21,31,32,36,38], including graph-based signals [19,20]. Here, we are given a noisy and possibly blurry observed image, f D LU C r 2 L 2 .R 2 /, and the purpose is to recover a faithful description of the underlying "clean" image, U "L 1 "f , by denoising r and deblurring L. The inverse "L 1 "f should be properly interpreted, say, in the smaller space BV.R 2 / L 2 .R 2 /, which is known to be well-adapted to represent edges.…”

Section: Construction Of Hierarchical Solutions In Critical Regularitmentioning

confidence: 99%

Hierarchical Construction of Bounded Solutions in Critical Regularity Spaces

Tadmor

2015

Comm Pure Appl Math

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Whenever you can settle a question by explicit construction, be not satisfied with purely existential arguments.Hermann Weyl [43, p. 326] AbstractWe construct uniformly bounded solutions for the equations div U D f and curl U D f in the critical cases f 2 L d # .T d ; R/ and f 2 L 3 # .T 3 ; R 3 /, respectively. Criticality in this context manifests itself by the lack of a linear solution operator mapping L d # 7 ! L 1 .T d /. Thus, the intriguing aspect here is that although the problems are linear, construction of their solutions is not.Our constructions are special cases of a general framework for solving linear equations of the form LU D f , where L is a linear operator densely defined in Banach space B with a closed range in a (proper subspace) of Lebesgue space L # .T d /, which may fail to satisfy the uniform bound sought in the second

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Multiscale Registration

Debroux

Guyader

Vese

2021

Lecture Notes in Computer Science

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In the seminal paper E. Tadmor, S. Nezzar and L. Vese, A multiscale image representation using hierarchical (BV, L 2 ) decompositions, Multiscale Model. Simul., 2(4), 554-579, (2004), the authors introduce a multiscale image decomposition model providing a hierarchical decomposition of a given image into the sum of scale-varying components. In line with this framework, we extend the approach to the case of registration, task which consists of mapping salient features of an image onto the corresponding ones in another, the underlying goal being to obtain such a kind of hierarchical decomposition of the deformation relating the two considered images (-from the coarser one that encodes the main structural/geometrical deformation, to the more refined one -). To achieve this goal, we introduce a functional minimisation problem in a hyperelasticity setting by viewing the shapes to be matched as Ogden materials. This approach is complemented by hard constraints on the L ∞ -norm of both the Jacobian and its inverse, ensuring that the deformation is a bi-Lipschitz homeomorphism. Theoretical results emphasising the mathematical soundness of the model are provided, among which the existence of minimisers, a Γ -convergence result and an analysis of a suitable numerical algorithm, along with numerical simulations demonstrating the ability of the model to produce accurate hierarchical representations of deformations.

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Multiscale Image Registration

Cited by 29 publications

References 18 publications

Background prostate tissue is quantitatively abnormal on MRI in patients with clinically significant prostate cancer

Background prostate tissue is quantitatively abnormal on MRI in patients with clinically significant prostate cancer

Hierarchical Construction of Bounded Solutions in Critical Regularity Spaces

Multiscale Registration

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