A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting

Dung, Van Than; Tjahjowidodo, Tegoeh

doi:10.1371/journal.pone.0173857

Cited by 48 publications

(26 citation statements)

References 28 publications

(40 reference statements)

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“…Adjoining linear segments to model the time-dependence of a variable are known as “splines” and have received considerable attention in scientific literature [6–11]. Several models can be created, each model with a greater number of splines or with a greater degree of freedom, creating a set of nested models of increasing complexity.…”

Section: Methodsmentioning

confidence: 99%

Segmented Linear Regression Modelling of Time-Series of Binary Variables in Healthcare

Valsamis

Husband

Chan

2019

Computational and Mathematical Methods in Medicine

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Introduction In healthcare, change is usually detected by statistical techniques comparing outcomes before and after an intervention. A common problem faced by researchers is distinguishing change due to secular trends from change due to an intervention. Interrupted time-series analysis has been shown to be effective in describing trends in retrospective time-series and in detecting change, but methods are often biased towards the point of the intervention. Binary outcomes are typically modelled by logistic regression where the log-odds of the binary event is expressed as a function of covariates such as time, making model parameters difficult to interpret. The aim of this study was to present a technique that directly models the probability of binary events to describe change patterns using linear sections. Methods We describe a modelling method that fits progressively more complex linear sections to the time-series of binary variables. Model fitting uses maximum likelihood optimisation and models are compared for goodness of fit using Akaike's Information Criterion. The best model describes the most likely change scenario. We applied this modelling technique to evaluate hip fracture patient mortality rate for a total of 2777 patients over a 6-year period, before and after the introduction of a dedicated hip fracture unit (HFU) at a Level 1, Major Trauma Centre. Results The proposed modelling technique revealed time-dependent trends that explained how the implementation of the HFU influenced mortality rate in patients sustaining proximal femoral fragility fractures. The technique allowed modelling of the entire time-series without bias to the point of intervention. Modelling the binary variable of interest directly, as opposed to a transformed variable, improved the interpretability of the results. Conclusion The proposed segmented linear regression modelling technique using maximum likelihood estimation can be employed to effectively detect trends in time-series of binary variables in retrospective studies.

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Section: Methodsmentioning

confidence: 99%

Segmented Linear Regression Modelling of Time-Series of Binary Variables in Healthcare

Valsamis

Husband

Chan

2019

Computational and Mathematical Methods in Medicine

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“…Many algorithms have been proposed for parameter optimization for B-spline curve fitting [26,27]. Parameter optimization gets especially more challenging for the case of discontinuous control points [28] which can occur in the existence of major distortions. Therefore, a linear transformation technique was utilized in this step.…”

Section: Rough Alignment Of Consecutive Tissue Slidesmentioning

confidence: 99%

Regional registration of whole slide image stacks containing major histological artifacts

et al. 2020

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Background High resolution 2D whole slide imaging provides rich information about the tissue structure. This information can be a lot richer if these 2D images can be stacked into a 3D tissue volume. A 3D analysis, however, requires accurate reconstruction of the tissue volume from the 2D image stack. This task is not trivial due to the distortions such as tissue tearing, folding and missing at each slide. Performing registration for the whole tissue slices may be adversely affected by distorted tissue regions. Consequently, regional registration is found to be more effective. In this paper, we propose a new approach to an accurate and robust registration of regions of interest for whole slide images. We introduce the idea of multi-scale attention for registration. Results Using mean similarity index as the metric, the proposed algorithm (mean ± SD $$0.84 \pm 0.11$$ 0.84 ± 0.11 ) followed by a fine registration algorithm ($$0.86 \pm 0.08$$ 0.86 ± 0.08 ) outperformed the state-of-the-art linear whole tissue registration algorithm ($$0.74 \pm 0.19$$ 0.74 ± 0.19 ) and the regional version of this algorithm ($$0.81 \pm 0.15$$ 0.81 ± 0.15 ). The proposed algorithm also outperforms the state-of-the-art nonlinear registration algorithm (original: $$0.82 \pm 0.12$$ 0.82 ± 0.12 , regional: $$0.77 \pm 0.22$$ 0.77 ± 0.22 ) for whole slide images and a recently proposed patch-based registration algorithm (patch size 256: $$0.79 \pm 0.16$$ 0.79 ± 0.16 , patch size 512: $$0.77 \pm 0.16$$ 0.77 ± 0.16 ) for medical images. Conclusion Using multi-scale attention mechanism leads to a more robust and accurate solution to the problem of regional registration of whole slide images corrupted in some parts by major histological artifacts in the imaged tissue.

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“…The {θ, dx, dy} triplet which gives the least sum of squared difference is chosen and its corresponding transformation matrix is applied to the moving image: been proposed for parameter optimization for B-spline curve fitting [26,27]. Parameter optimization gets especially more challenging for the case of discontinuous control points [28] which can occur in the existence of major distortions. Therefore, a linear transformation technique was utilized in this step.…”

Section: Removing Surrounding Artifactsmentioning

confidence: 99%

Regional Registration of Whole Slide Image Stacks Containing Major Histological Artifacts

Paknezhad¹,

Loh²,

Choudhury

et al. 2020

Preprint

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Background: High resolution 2D whole slide imaging provides rich information about the tissue structure. This information can be a lot richer if these 2D images can be stacked into a 3D tissue volume. A 3D analysis, however, requires accurate reconstruction of the tissue volume from the 2D image stack. This task is not trivial due to the distortions such as tissue tearing, folding and missing at each slide. Performing registration for the whole tissue slices may be adversely affected by distorted tissue regions. Consequently, regional registration is found to be more effective. In this paper, we propose a new approach to an accurate and robust registration of regions of interest for whole slide images. We introduce the idea of multi-scale attention for registration. Results: Using mean similarity index as the metric, the proposed algorithm (mean +- std: 0.84 +- 0.11) followed by a fine registration algorithm (0.86 +- 0.08) outperformed the state-of-the-art linear whole tissue registration algorithm (0.74 +- 0.19) and the regional version of this algorithm (0.81 +- 0.15). The proposed algorithm also outperforms the state-of-the-art nonlinear registration algorithm (original: 0.82 +- 0.12, regional: 0.77 +- 0.22) for whole slide images and a recently proposed patch-based registration algorithm (patch size 256: 0.79 +- 0.16 , patch size 512: 0.77 +- 0.16) for medical images. Conclusion: Using multi-scale attention mechanism leads to a more robust and accurate solution to the problem of regional registration of whole slide images corrupted in some parts by major histological artifacts in the imaged tissue.

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A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting

Cited by 48 publications

References 28 publications

Segmented Linear Regression Modelling of Time-Series of Binary Variables in Healthcare

Segmented Linear Regression Modelling of Time-Series of Binary Variables in Healthcare

Regional registration of whole slide image stacks containing major histological artifacts

Regional Registration of Whole Slide Image Stacks Containing Major Histological Artifacts

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