New Entropy Estimator with an Application to Test of Normality

Bouzebda, Salim; Elhattab, Issam; Keziou, Amor; Lounis, Tewfik

doi:10.1080/03610926.2011.608473

Cited by 7 publications

(6 citation statements)

References 39 publications

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“…(4) and Eq.(6). Specifically, for the latter criterion, the entropy estimator based on spacings [11] was used in Eq. (4), whereas mutual information (MI) was used in the inter-images comparisons (Eq.(6)).…”

Section: Experimental Validationmentioning

confidence: 99%

Deformable group-wise registration using a physiological model: Application to diffusion-weighted MRI

Kornaropoulos

Zacharaki

Zerbib

et al. 2016

2016 IEEE International Conference on Image Processing (ICIP)

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Intensity variations can often be described by a physiological or temporal model applied on a voxel-wise basis across a group of images. However the voxel correspondence might be unknown, imposing the need for a group-wise deformable registration coupled with the computation of the model parameters. In this paper we propose a group-wise registration method of medical images that incorporates the temporal dimension (reflecting the change of signal amplitude) of the acquisition process. Consistency on the spatiotemporal physiological model, as well as deformation smoothness, is imposed in order to produce anatomically meaningful representations of the 3D images. The performance of the proposed method is compared to two different group-wise registration approaches; one that penalizes the absolute differences in the intensities and one that penalizes the intensity range among the images on corresponding regions. We chose as an application paradigm the registration of diffusion-weighted magnetic resonance (DW-MR) images for the evaluation of patients with lymphomas. A dataset consisting of 25 patients, each scanned with 3 "b values", was used to evaluate the method's accuracy. The proposed registration method outperfomed the other two registration approaches, making it a very promising method for highlighting the importance of DWI as an imaging biomarker.

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Section: Experimental Validationmentioning

confidence: 99%

Deformable group-wise registration using a physiological model: Application to diffusion-weighted MRI

Kornaropoulos

Zacharaki

Zerbib

et al. 2016

2016 IEEE International Conference on Image Processing (ICIP)

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“…An implementation of a state-of-the art group-wise registration approach [24] was examined and the ADC computed based on the derived deformed images was calculated. An entropy estimator based on spacings [6] was used as a global similarity criterion and mutual information (MI) was used in the inter-images comparisons. Finally, we computed an ADC map which values were extracted from the wraped images by our approach.…”

Section: Experimental Validationmentioning

confidence: 99%

Optimal Estimation of Diffusion in DW-MRI by High-Order MRF-Based Joint Deformable Registration and Diffusion Modeling

Kornaropoulos¹,

Zacharaki²,

Zerbib

et al. 2016

2016 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)

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Over the last years, the apparent diffusion coefficient (ADC), computed from diffusion-weighted magnetic resonance (DW-MR) images, has become an important imaging biomarker for evaluating and managing patients with neoplastic or cerebrovascular disease. Standard methods for the calculation of ADC ignore the presence of noise and motion between successive (in time) DW-MR images acquired by changing the b-value. In order to accurately quantify the diffusion process during image acquisition, we introduce a method based on a high-order Markov Random Field (MRF) formulation that jointly registers the DW-MR images and models the spatiotemporal diffusion. Spatial smoothness on the ADC map, as well as spatiotemporal deformation smoothness, is imposed towards producing anatomically meaningful representations. The high-order dependencies in our MRF model are handled through Dual Decomposition. Performance of registration is compared to a state-of-the art registration approach in terms of obtained fitting error of the diffusion model in the core of the tumor. Preliminary results reveal a marginally better performance of our method when compared against the standard ADC map used in clinical practice, which indicates its potential as a means for extracting imaging biomarkers.

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“…Vasicek [23] proposed an entropy estimator based on spacings. Inspired by the work of [23], some authors [22,24,13,7,16] proposed modified entropy estimators, improving in some respects the properties of Vasicek's estimator. The reader will find in [3] detailed accounts of the theory as well as surveys for entropy estimators.…”

Section: Introduction and Estimationmentioning

confidence: 99%

“…Since the entropy is defined as an integral on ]0, 1[ of a functional of q(•), it is not suitable to substitute directly q n (•) in ( 4) to estimate H(X). To circumvent the boundary effects, we will proceed as follows, as in [7]. We set for small ε ∈ ]0, 1/2[:…”

Section: Introduction and Estimationmentioning

confidence: 99%

“…and where 1 A stands for the indicator function of the event A. It is noteworthy here to point out that compared with the estimator given in [7], our estimator, defined in ( 8), reduces the computational requirement that, from a practical standpoint, can be very significant when n is large. The remainder of this Note is organized as follows.…”

Section: Introduction and Estimationmentioning

confidence: 99%

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